[cig-commits] r20558 - in seismo/3D/SPECFEM3D/trunk/doc: . notes_about_CPML
dkomati1 at geodynamics.org
dkomati1 at geodynamics.org
Tue Aug 7 16:03:14 PDT 2012
Author: dkomati1
Date: 2012-08-07 16:03:13 -0700 (Tue, 07 Aug 2012)
New Revision: 20558
Added:
seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/
seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/Biblio1.bib
seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/compile_LaTeX_paper.sh
seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji.bst
seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji_extra.sty
seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji_modified_cours_UPPA.cls
seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/newcommands.tex
seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/notes_about_CPML_for_SPECFEM3D.tex
seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/pml_schematic.png
Log:
added some notes about 3D C-PML
Added: seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/Biblio1.bib
===================================================================
--- seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/Biblio1.bib (rev 0)
+++ seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/Biblio1.bib 2012-08-07 23:03:13 UTC (rev 20558)
@@ -0,0 +1,14037 @@
+% This file was created with JabRef 2.8.1.
+% Encoding: UTF-8
+
+ at STRING{bssa = {Bull. Seismol. Soc. Am.}}
+
+ at STRING{cmame = {Comput. Meth. Appl. Mech. Eng.}}
+
+ at STRING{cmes = {Comput. Model. Eng. Sci.}}
+
+ at STRING{eesd = {Earthquake Eng. Struct. Dynam.}}
+
+ at STRING{eos = {Eos Trans. AGU}}
+
+ at STRING{epsl = {Earth Planet. Sci. Lett.}}
+
+ at STRING{geophysics = {Geophysics}}
+
+ at STRING{gji = {Geophys. J. Int.}}
+
+ at STRING{gjras = {Geophys. J. Roy. Astron. Soc.}}
+
+ at STRING{gp = {Geophys. Prospect.}}
+
+ at STRING{grl = {Geophys. Res. Lett.}}
+
+ at STRING{ijnme = {Int. J. Numer. Meth. Eng.}}
+
+ at STRING{jap = {J. Appl. Phys.}}
+
+ at STRING{jasa = {J. Acoust. Soc. Am.}}
+
+ at STRING{jca = {J. Comput. Acoust.}}
+
+ at STRING{jcp = {J. Comput. Phys.}}
+
+ at STRING{jgr = {J. Geophys. Res.}}
+
+ at STRING{jpdc = {Journal of Parallel and Distributed Computing}}
+
+ at STRING{lncs = {Lecture Notes in Computer Science}}
+
+ at STRING{pageoph = {Pure Appl. Geophys.}}
+
+ at STRING{pepi = {Phys. Earth Planet. In.}}
+
+ at ARTICLE{arnadottiretal2001,
+ author = {T. \'Arnad\'ottir and S. Hreinsd\'ottir and G. Gudmunsson and P.
+ Einarsson and M. Heinert and C. V\"olksen},
+ title = {Crustal deformation measured by {GPS} in the {S}outh {I}celand {S}eismic
+ {Z}one due to two large earthquakes in {J}une 2000},
+ journal = grl,
+ year = {2001},
+ volume = {28},
+ pages = {4031-4033}
+}
+
+ at ARTICLE{EtChViGl10,
+ author = {\'Etienne, V. and Chaljub, E. and Virieux, J. and Glinsky, N.},
+ title = {An hp-adaptive discontinuous {G}alerkin finite-element method for
+ 3-{D} elastic wave modelling},
+ journal = gji,
+ year = {2010},
+ volume = {183},
+ pages = {941-962},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2010.04764.x}
+}
+
+ at ARTICLE{AaHaHe2001,
+ author = {Brad T. Aagaard and John F. Hall and Thomas H. Heaton},
+ title = {Characterization of Near-Source Ground Motions with Earthquake Simulations},
+ journal = {Earthquake Spectra},
+ year = {2001},
+ volume = {17},
+ pages = {177-207},
+ number = {2}
+}
+
+ at ARTICLE{AaHeHa2001,
+ author = {Brad T. Aagaard and Thomas H. Heaton and John F. Hall},
+ title = {Dynamic earthquake ruptures in the presence of lithostatic normal
+ stresses: implications for Friction Models and Heat Production},
+ journal = bssa,
+ year = {2001},
+ volume = {91},
+ pages = {1765-1796},
+ number = {6}
+}
+
+ at ARTICLE{AbGo98,
+ author = {S. Abarbanel and D. Gottlieb},
+ title = {On the construction of absorbing layers in {CEM}},
+ journal = {Applied Numerical Mathematics},
+ year = {1998},
+ volume = {27},
+ pages = {331-340}
+}
+
+ at ARTICLE{AbGoHe02,
+ author = {S. Abarbanel and D. Gottlieb and J. S. Hesthaven},
+ title = {Long time behavior of the perfectly matched layer equations in computational
+ electromagnetics},
+ journal = {Journal of Scientific Computing},
+ year = {2002},
+ volume = {17},
+ pages = {405-422},
+ number = {1-4},
+ doi = {10.1023/A:1015141823608}
+}
+
+ at ARTICLE{AbGoHe99,
+ author = {S. Abarbanel and D. Gottlieb and J. S. Hesthaven},
+ title = {Well-posed Perfectly Matched Layers for Advective Acoustics},
+ journal = jcp,
+ year = {1999},
+ volume = {154},
+ pages = {266-283},
+ number = {2},
+ doi = {10.1006/jcph.1999.6313}
+}
+
+ at MASTERSTHESIS{Abd07,
+ author = {Rached Abdelkhalek},
+ title = {{\'E}valuation des acc\'el\'erateurs de calcul {GPGPU} pour la mod\'elisation
+ sismique},
+ school = {ENSEIRB, Bordeaux, France},
+ year = {2007}
+}
+
+ at CONFERENCE{AbCaCoRoLa09,
+ author = {Abdelkhalek, Rached and Calandra, Henri and Coulaud, Olivier and
+ Roman, Jean and Latu, Guillaume},
+ title = {Fast Seismic Modeling and Reverse Time Migration on a {GPU} Cluster},
+ booktitle = {High Performance Computing \& Simulation 2009},
+ year = {2009},
+ editor = {Waleed W. Smari and John P. McIntire},
+ pages = {36--44},
+ address = {Leipzig, Germany},
+ month = jun,
+ note = {http://hal.inria.fr/docs/00/40/39/33/PDF/hpcs.pdf}
+}
+
+ at ARTICLE{AbMaSoCa08,
+ author = {A. I. Abreu and W. J. Mansur and D. {Soares Jr.} and J. A. M. Carrer},
+ title = {Numerical Computation of Space Derivatives by the Complex-Variable-Differentiation
+ Method in the Convolution Quadrature-Method-Based {BEM} Formulation},
+ journal = cmes,
+ year = {2008},
+ volume = {30},
+ pages = {123-132},
+ number = {3}
+}
+
+ at BOOK{Ach73,
+ title = {Wave Propagation in Elastic Solids},
+ publisher = {North-Holland},
+ year = {1973},
+ author = {J. D. Achenbach},
+ address = {Amsterdam, The Netherlands}
+}
+
+ at ARTICLE{AcKo11,
+ author = {Acosta Minolia, Cesar A. and David A. Kopriva},
+ title = {Discontinuous {G}alerkin spectral element approximations on moving
+ meshes},
+ journal = jcp,
+ year = {2011},
+ volume = {230},
+ pages = {1876-1902},
+ number = {5},
+ doi = {10.1016/j.jcp.2010.11.038}
+}
+
+ at INPROCEEDINGS{AdPaBo07,
+ author = {S. Adams and J. Payne and R. Boppana},
+ title = {Finite Difference Time Domain ({FDTD}) Simulations Using Graphics
+ Processors},
+ booktitle = {Proceedings of the Department of Defense High Performance Computing
+ Modernization Program Users Group Conference},
+ year = {2007},
+ pages = {334-338},
+ address = {Pittsburgh, Pennsylvania, USA},
+ publisher = {IEEE Computer Society, Washington, DC, USA},
+ doi = {10.1109/HPCMP-UGC.2007.34}
+}
+
+ at ARTICLE{AgDeDoHaKuLaLtLuTo09,
+ author = {Emmanuel Agullo and Jim Demmel and Jack Dongarra and Bilel Hadri
+ and Jakub Kurzak and Julien Langou and Hatem Ltaief and Piotr Luszczek
+ and Stanimire Tomov},
+ title = {Numerical linear algebra on emerging architectures: The {PLASMA}
+ and {MAGMA} projects},
+ journal = {Journal of Physics: Conference Series},
+ year = {2009},
+ volume = {180},
+ pages = {012037},
+ doi = {10.1088/1742-6596/180/1/012037}
+}
+
+ at ARTICLE{AiMoMu06,
+ author = {Ainsworth, M. and Monk, P. and Muniz, W.},
+ title = {Dispersive and Dissipative Properties of Discontinuous {G}alerkin
+ Finite Element Methods for the Second-Order Wave Equation},
+ journal = {Journal of Scientific Computing},
+ year = {2006},
+ volume = {27},
+ pages = {5-40},
+ number = {1},
+ doi = {10.1007/s10915-005-9044-x}
+}
+
+ at INPROCEEDINGS{AkBiBiEpFeGhKiLoOhTuUr03,
+ author = {Volkan Ak{\c c}elik and Jacobo Bielak and George Biros and Ioannis
+ Epanomeritakis and Antonio Fernandez and Omar Ghattas and Eui Joong
+ Kim and Julio Lopez and David O'Hallaron and Tiankai Tu and John
+ Urbanic},
+ title = {High-resolution forward and inverse earthquake modeling on terascale
+ computers},
+ booktitle = {SC'03: Proceedings of the 2003 ACM/IEEE conference on Supercomputing},
+ year = {2003},
+ pages = {52-72},
+ address = {Phoenix, Arizona, USA},
+ month = nov,
+ note = {{G}ordon {B}ell {P}rize winner article},
+ doi = {10.1145/1048935.1050202}
+}
+
+ at INCOLLECTION{Aki88,
+ author = {K. Aki},
+ title = {Local site effects on strong ground motion},
+ booktitle = {Earthquake Engineering and Soil Dynamics II- Recent advances in ground
+ motion evaluation},
+ publisher = {American Society of Civil Engineering},
+ year = {1988},
+ editor = {J. L. Von Thun},
+ volume = {20},
+ series = {Geothechnical Special Publication},
+ pages = {103-155},
+ address = {New York, USA}
+}
+
+ at ARTICLE{AkLa70,
+ author = {K. Aki and K. L. Larner},
+ title = {Surface motion of a layered medium having an irregular interface,
+ due to incident plane {{\it SH}} waves},
+ journal = jgr,
+ year = {1970},
+ volume = {75},
+ pages = {933-954}
+}
+
+ at BOOK{AkRi80,
+ title = {Quantitative seismology, theory and methods},
+ publisher = {W. H. Freeman},
+ year = {1980},
+ author = {K. Aki and P. G. Richards},
+ address = {San Francisco, USA}
+}
+
+ at ARTICLE{AlWo08,
+ author = {David Al-Attar and John H. Woodhouse},
+ title = {Calculation of seismic displacement fields in self-gravitating earth
+ models: applications of minors vectors and symplectic structure},
+ journal = gji,
+ year = {2008},
+ volume = {175},
+ pages = {1176-1208},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2008.03961.x}
+}
+
+ at ARTICLE{AlOl98,
+ author = {C. M. Alex and K. B. Olsen},
+ title = {Lens effect in {S}anta {M}onica?},
+ journal = grl,
+ year = {1998},
+ volume = {25},
+ pages = {3441-3444}
+}
+
+ at ARTICLE{AlZeLaBeBeSeKoJu94,
+ author = {F. Alexandre and D. Zerguine and P. Launay and J. L. Benchimol and
+ M. Berz and B. Sermage and D. Komatitsch and M. Juhel},
+ title = {Quasi-planar {G}allium {A}rsenide heterojunction bipolar transistor
+ device entirely grown by {C}hemical {B}eam {E}pitaxy},
+ journal = {J. Crystal Growth},
+ year = {1994},
+ volume = {136},
+ pages = {235-240},
+ number = {1-4},
+ doi = {10.1016/0022-0248(94)90416-2}
+}
+
+ at ARTICLE{AlKeBo74,
+ author = {R. Alford and K. Kelly and D. Boore},
+ title = {Accuracy of finite difference modeling of the acoustic wave equation},
+ journal = geophysics,
+ year = {1974},
+ volume = {39},
+ pages = {834-842}
+}
+
+ at ARTICLE{AlsLot04,
+ author = {V. I. Alshits and J. Lothe},
+ title = {Some basic properties of bulk elastic waves in anisotropic media},
+ journal = {Wave Motion},
+ year = {2004},
+ volume = {40},
+ pages = {297-313}
+}
+
+ at ARTICLE{AlsLot81,
+ author = {V. I. Alshits and J. Lothe},
+ title = {Comments on the relation between surface wave theory and the theory
+ of reflection},
+ journal = {Wave Motion},
+ year = {1981},
+ volume = {3},
+ pages = {297-310}
+}
+
+ at ARTICLE{AlsLot79a,
+ author = {V. I. Alshits and J. Lothe},
+ title = {Elastic waves in triclinic crystals: ({I}) {G}eneral theory and the
+ degeneracy problem},
+ journal = {Soviet Physics Crystallography},
+ year = {1979},
+ volume = {24},
+ pages = {387-392}
+}
+
+ at ARTICLE{AlsLot79b,
+ author = {V. I. Alshits and J. Lothe},
+ title = {Elastic waves in triclinic crystals: ({II}) {T}opology of polarization
+ fields and some general theorems},
+ journal = {Soviet Physics Crystallography},
+ year = {1979},
+ volume = {24},
+ pages = {393-398}
+}
+
+ at ARTICLE{AlsLot79c,
+ author = {V. I. Alshits and J. Lothe},
+ title = {Elastic waves in triclinic crystals: ({III}) {T}he problem of existence
+ and some general properties of exceptional surface waves},
+ journal = {Soviet Physics Crystallography},
+ year = {1979},
+ volume = {24},
+ pages = {644-648}
+}
+
+ at ARTICLE{AlsLot78,
+ author = {V. I. Alshits and J. Lothe},
+ title = {Surface waves in hexagonal crystals},
+ journal = {Soviet Physics Crystallography},
+ year = {1978},
+ volume = {23},
+ pages = {509-515}
+}
+
+ at ARTICLE{AlsLyu83,
+ author = {V. I. Alshits and V. N. Lyubimov},
+ title = {Leaky elastic waves in hexagonal crystals},
+ journal = {Soviet Physics of Crystallograpy},
+ year = {1983},
+ volume = {28},
+ pages = {130-135},
+ number = {2}
+}
+
+ at ARTICLE{AlsLyuNauPerShu85,
+ author = {V. I. Alshits and V. N. Lyubimov and N. F. Naumenko and N. V. Perelomova
+ and A. L. Shuvalov},
+ title = {Exceptional elastic body waves in crystals of various symmetries},
+ journal = {Soviet Physics Crystallography},
+ year = {1985},
+ volume = {30},
+ pages = {123-126}
+}
+
+ at ARTICLE{AlKa68,
+ author = {Z. Alterman and F. C. Karal},
+ title = {Propagation of elastic waves in layered media by finite difference
+ methods},
+ journal = bssa,
+ year = {1968},
+ volume = {58},
+ pages = {367-398}
+}
+
+ at ARTICLE{AmWi94,
+ author = {K. Amaratunga and J. R. Williams},
+ title = {Wavelet-{G}alerkin solutions for one-dimensional partial differential
+ equations},
+ journal = ijnme,
+ year = {1994},
+ volume = {37},
+ pages = {999998-999999}
+}
+
+ at ARTICLE{AmDuKoEx01,
+ author = {P. R. Amestoy and I. S. Duff and J. Koster and J.-Y. L'Excellent},
+ title = {A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic
+ Scheduling},
+ journal = {SIAM Journal on Matrix Analysis and Applications},
+ year = {2001},
+ volume = {23},
+ pages = {15-41},
+ number = {1}
+}
+
+ at ARTICLE{AmmonJiThio2005,
+ author = {C. J. Ammon and C. Ji and H. K. Thio and D. Robinson and S. D. Ni
+ and V. Hjorleifsdottir and H. Kanamori and T. Lay and S. Das and
+ D. Helmberger and G. Ichinose and J. Polet and D. Wald},
+ title = {Rupture process of the 2004 {S}umatra-{A}ndaman earthquake},
+ journal = {Science},
+ year = {2005},
+ volume = {3},
+ pages = {1133-1139},
+ number = {5725}
+}
+
+ at PHDTHESIS{Amp02,
+ author = {Jean-Paul Ampuero},
+ title = {\'Etude physique et num\'erique de la nucl\'eation des s\'eismes
+ ({A} physical and numerical study of earthquake nucleation)},
+ school = {Institut de Physique du Globe},
+ year = {2002},
+ address = {Paris, France}
+}
+
+ at ARTICLE{anderson1987,
+ author = {D. L. Anderson},
+ title = {A seismic equation of state, {P}art~{II}: {S}hear properties and
+ thermodynamics of the lower mantle},
+ journal = pepi,
+ year = {1987},
+ volume = {45},
+ pages = {307-323}
+}
+
+ at ARTICLE{anderson_lorenz_travesset_2008,
+ author = {Joshua A. Anderson and Chris D. Lorenz and Alex Travesset},
+ title = {General purpose molecular dynamics simulations fully implemented
+ on graphics processing units},
+ journal = jcp,
+ year = {2008},
+ volume = {227},
+ pages = {5342--5359},
+ number = {10},
+ month = may,
+ doi = {10.1016/j.jcp.2008.01.047}
+}
+
+ at ARTICLE{AnLeZeDa96,
+ author = {J. G. Anderson and Y. Lee and Y. Zeng and S. M. Day},
+ title = {Control of strong motion by the upper 30~meters},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1749-1759}
+}
+
+ at ARTICLE{AnBa204,
+ author = {X. Antoine and H. Barucq},
+ title = {Approximation by generalized impedance boundary conditions of a transmission
+ problem in acoustic scattering},
+ journal = {Math. Model. Numer. Anal.},
+ year = {2005},
+ volume = {39},
+ pages = {1041-1059},
+ number = {5}
+}
+
+ at INPROCEEDINGS{AnBa104,
+ author = {X. Antoine and H. Barucq},
+ title = {On the construction of approximate boundary conditions for solving
+ the interior problem of the acoustic scattering transmission problem},
+ booktitle = {Methods in Science and Engineering},
+ year = {2004},
+ volume = {40},
+ series = {Lecture Notes in computational science and engineering},
+ pages = {133-140}
+}
+
+ at ARTICLE{AnBa01,
+ author = {X. Antoine and H. Barucq},
+ title = {Microlocal diagonalization of strictly hyperbolic pseudodifferential
+ systems and application to the design of radiation conditions in
+ electromagnetism},
+ journal = {SIAM J. Appl. Math.},
+ year = {2001},
+ volume = {6},
+ pages = {1877-1905}
+}
+
+ at ARTICLE{AnBaBe99,
+ author = {X. Antoine and H. Barucq and A. Bendali},
+ title = {Bayliss-{T}urkel-like radiation conditions on surfaces of arbitrary
+ shape},
+ journal = {J. Math. Anal. Appl.},
+ year = {1999},
+ volume = {229},
+ pages = {184-211}
+}
+
+ at ARTICLE{AnBaVe01,
+ author = {X. Antoine and H. Barucq and L. Vernhet},
+ title = {High-frequency asymptotic analysis of a dissipative transmission
+ problem resulting in generalized impedance boundary conditions},
+ journal = {Asymptotic Analysis},
+ year = {2001},
+ volume = {3},
+ pages = {257-284},
+ number = {4}
+}
+
+ at ARTICLE{AnBeDa04,
+ author = {X. Antoine and A. Bendali and M. Darbas},
+ title = {Analytic Preconditioners for the boundary integral solution of the
+ scattering of acoustic waves by open surfaces},
+ journal = jca,
+ year = {2005},
+ volume = {13},
+ pages = {477-498},
+ number = {3}
+}
+
+ at ARTICLE{AnLaDrRo96,
+ author = {M. Antolik and S. Larsen and D. Dreger and B. Romanowicz},
+ title = {Modeling broadband waveforms in central {C}alifornia using finite
+ differences},
+ journal = {Seis. Res. Lett.},
+ year = {1996},
+ volume = {67},
+ pages = {30}
+}
+
+ at ARTICLE{antonionietal2002,
+ author = {A. Antonioli and M. Cocco and S. Das and C. Henry},
+ title = {Dynamic stress triggering during the great 25~{M}arch 1998 {A}ntarctic
+ {P}late earthquake},
+ journal = bssa,
+ year = {2002},
+ volume = {92},
+ pages = {896-903}
+}
+
+ at ARTICLE{AoDo06,
+ author = {H. Aochi and J. Douglas},
+ title = {Testing the validity of simulated strong ground motion from the dynamic
+ rupture of a finite fault by using empirical equations},
+ journal = {Bull. Earthq. Eng.},
+ year = {2006},
+ volume = {4},
+ pages = {211-229},
+ number = {3},
+ doi = {10.1007/s10518-006-0001-3}
+}
+
+ at ARTICLE{ApKr06,
+ author = {Daniel Appel\"o and Gunilla Kreiss},
+ title = {A new absorbing layer for elastic waves},
+ journal = jcp,
+ year = {2006},
+ volume = {215},
+ pages = {642-660},
+ number = {2},
+ doi = {10.1016/j.jcp.2005.11.006}
+}
+
+ at PHDTHESIS{da,
+ author = {D. Apprato},
+ title = {Approximation de surfaces param\'etr\'ees par \'el\'ements finis},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {1987},
+ address = {Pau, France},
+ note = {Th\`ese d'Etat, 142 p.}
+}
+
+ at ARTICLE{GoKo02,
+ author = {D. Apprato and C. Gout and D. Komatitsch},
+ title = {A new method for {{$C^k$-}}surface approximation from a set of curves,
+ with application to ship track data in the {M}arianas trench},
+ journal = {Math. Geol.},
+ year = {2002},
+ volume = {34},
+ pages = {831-843},
+ number = {7},
+ doi = {10.1023/A:1020976611029}
+}
+
+ at ARTICLE{ApLu83,
+ author = {R. J. Apsel and J. E. Luco},
+ title = {On the {G}reen's functions for a layered half-space},
+ journal = bssa,
+ year = {1983},
+ volume = {73},
+ pages = {931-951}
+}
+
+ at INCOLLECTION{ra1,
+ author = {R. Arcang\'eli},
+ title = {Some Applications of Discrete {$D^m$}-splines},
+ booktitle = {Mathematical Methods in Computer Aided Geometric Design},
+ publisher = {Academic Press, New York, USA},
+ year = {1989},
+ editor = {T. Lyche and L. L. Schumaker},
+ pages = {35-44}
+}
+
+ at TECHREPORT{ra,
+ author = {R. Arcang\'eli},
+ title = {{$D^m$}-splines sur un domaine born\'e de {$R$}},
+ institution = {UA 1204 CNRS, Universit\'e de Pau et des Pays de l'Adour},
+ year = {1986},
+ number = {1986/2},
+ address = {Pau, France},
+ note = {47 p.}
+}
+
+ at ARTICLE{Arn82,
+ author = {Douglas N. Arnold},
+ title = {An Interior Penalty Finite Element Method with Discontinuous Elements},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1982},
+ volume = {19},
+ pages = {742-760},
+ number = {4},
+ doi = {10.1137/0719052}
+}
+
+ at BOOK{AtPr90,
+ title = {\'El\'ements d'analyse num\'erique},
+ publisher = {C\'epadues \'Editions},
+ year = {1990},
+ author = {Marc Atteia and Michel Pradel},
+ address = {Toulouse}
+}
+
+ at INCOLLECTION{AuChMoMo85,
+ author = {D. Aubry and D. Chouvet and H. Modaressi and P. Mouroux},
+ title = {Local amplification of a seismic incident field through an elastoplastic
+ sedimentary valley},
+ booktitle = {Numerical methods in geomechanics},
+ publisher = {Balkema},
+ year = {1985},
+ editor = {T. Kawamoto and Y. Ichikawa},
+ pages = {421-428}
+}
+
+ at ARTICLE{AuHoVaCe11,
+ author = {Aubry, R. and Houzeaux, G. and V\'azquez, M. and Cela, J. M.},
+ title = {Some useful strategies for unstructured edge-based solvers on shared
+ memory machines},
+ journal = ijnme,
+ year = {2011},
+ volume = {85},
+ pages = {537-561},
+ number = {5},
+ doi = {10.1002/nme.2973}
+}
+
+ at INPROCEEDINGS{AuThNaWa09Europar,
+ author = {C{\'e}dric Augonnet and Samuel Thibault and Raymond Namyst and Pierre-Andr{\'e}
+ Wacrenier},
+ title = {{StarPU}: {A} Unified Platform for Task Scheduling on Heterogeneous
+ Multicore Architectures},
+ booktitle = {Proceedings of the 15th EuroPar Conference},
+ year = {2009},
+ volume = {5704},
+ series = {Lecture Notes in Computer Science},
+ pages = {863-874},
+ address = {Delft, The Netherlands},
+ month = aug,
+ publisher = {Springer},
+ bdsk-url-2 = {http://dx.doi.org/10.1007/978-3-642-03869-3%5C_80},
+ doi = {10.1007/978-3-642-03869-3\_80},
+ url = {http://hal.inria.fr/inria-00384363}
+}
+
+ at BOOK{Aul90,
+ title = {Acoustic fields and waves in solids},
+ publisher = {Krieger Publishing},
+ year = {1990},
+ author = {B. A. Auld},
+ volume = {1},
+ edition = {2nd}
+}
+
+ at ARTICLE{Aus93,
+ author = {P. Auscher},
+ title = {Ondelettes \`a support compact et conditions aux limites},
+ journal = {J. Funct. Anal.},
+ year = {1993},
+ volume = {111},
+ pages = {9999998-9999999}
+}
+
+ at ARTICLE{AuzaZiol,
+ author = {F. Auzanneau and R. W. Ziolkowski},
+ title = {{{\'E}}tude th\'eorique de mat\'eriaux bianisotropes synth\'etiques
+ contr\^olables},
+ journal = {J. Phys. III},
+ year = {1997},
+ volume = {7},
+ pages = {2405-2418}
+}
+
+ at TECHREPORT{AzDaMa94,
+ author = {Mejdi Azaiez and Monique Dauge and Yvon Maday},
+ title = {M\'ethodes spectrales et des \'el\'ements spectraux},
+ institution = {Institut de Recherche Math\'ematique de Rennes},
+ year = {1994},
+ address = {Universit\'e de Rennes, France}
+}
+
+ at ARTICLE{BaBiPr98,
+ author = {I. B\'ardi and O. B\'{\i}r\'o and K. Preis},
+ title = {{P}erfectly {M}atched {L}ayers in static fields},
+ journal = {IEEE transactions on Magnetics},
+ year = {1998},
+ volume = {34},
+ pages = {2433-2436},
+ number = {5}
+}
+
+ at ARTICLE{BeFaJo03,
+ author = {E. B\'ecache and S. Fauqueux and P. Joly},
+ title = {Stability of {P}erfectly {M}atched {L}ayers, group velocities and
+ anisotropic waves},
+ journal = jcp,
+ year = {2003},
+ volume = {188},
+ pages = {399-433},
+ number = {2}
+}
+
+ at ARTICLE{BeJo02,
+ author = {E. B\'ecache and P. Joly},
+ title = {On the analysis of {B}\'erenger's perfectly matched layers for {M}axwell's
+ equations},
+ journal = {Mathematical Modelling and Numerical Analysis},
+ year = {2002},
+ volume = {36},
+ pages = {87-120},
+ number = {1}
+}
+
+ at ARTICLE{BeJoTs2001,
+ author = {E. B\'ecache and P. Joly and C. Tsogka},
+ title = {Fictitious Domains, Mixed Finite Elements and {P}erfectly {M}atched
+ {L}ayers for {2-D} Elastic Wave Propagation},
+ journal = jca,
+ year = {2001},
+ volume = {9},
+ pages = {1175-1203},
+ number = {3}
+}
+
+ at ARTICLE{BePeGe04,
+ author = {E. B\'ecache and P. G. Petropoulos and S. G. Gedney},
+ title = {On the Long-Time Behavior of Unsplit Perfectly Matched Layers},
+ journal = {IEEE Transactions on Antennas and Propagation},
+ year = {2004},
+ volume = {52},
+ pages = {1335-1342},
+ number = {5},
+ doi = {10.1109/TAP.2004.827253}
+}
+
+ at ARTICLE{Ber02a,
+ author = {J. P. B\'erenger},
+ title = {Application of the {CFS} {PML} to the absorption of evanescent waves
+ in waveguides},
+ journal = {IEEE Microwave and Wireless Components Letters},
+ year = {2002},
+ volume = {12},
+ pages = {218-220},
+ number = {6},
+ doi = {10.1109/LMWC.2002.1010000}
+}
+
+ at ARTICLE{Ber02b,
+ author = {J. P. B\'erenger},
+ title = {Numerical reflection from {FDTD-PML}s: A comparison of the split
+ {PML} with the unsplit and {CFS PML}s},
+ journal = {IEEE Transactions on Antennas and Propagation},
+ year = {2002},
+ volume = {50},
+ pages = {258-265},
+ number = {3},
+ doi = {10.1109/8.999615}
+}
+
+ at ARTICLE{Ber96,
+ author = {J. P. B\'erenger},
+ title = {Three-dimensional {P}erfectly {M}atched {L}ayer for the absorption
+ of electromagnetic waves},
+ journal = jcp,
+ year = {1996},
+ volume = {127},
+ pages = {363-379}
+}
+
+ at ARTICLE{Ber94,
+ author = {J. P. B\'erenger},
+ title = {A {P}erfectly {M}atched {L}ayer for the absorption of electromagnetic
+ waves},
+ journal = jcp,
+ year = {1994},
+ volume = {114},
+ pages = {185-200}
+}
+
+ at ARTICLE{BaDo81,
+ author = {I. Babu\u{s}ka and M. R. Dorr},
+ title = {Error estimates for the combined $h$ and $p$ version of the finite
+ element method},
+ journal = {Numer. Math.},
+ year = {1981},
+ volume = {37},
+ pages = {257-277}
+}
+
+ at ARTICLE{BaSzKa81,
+ author = {I. Babu\u{s}ka and B. A. Szab\'o and I. N. Katz},
+ title = {The $p$ version of the finite element method},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1981},
+ volume = {18},
+ pages = {512-545}
+}
+
+ at ARTICLE{babuska1995,
+ author = {I. Babuska and F. Ihlenburg and E. T. Paik and S. A. Sauter},
+ title = {A generalized finite element method for solving the {H}elmholtz equation
+ in two dimensions with minimal pollution},
+ journal = cmame,
+ year = {1995},
+ volume = {128},
+ pages = {325-359},
+ number = {3-4}
+}
+
+ at ARTICLE{Bac76,
+ author = {G. A. Backer},
+ title = {Error estimates for the finite element method for second order hyperbolic
+ equations},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1976},
+ volume = {13},
+ pages = {564-575}
+}
+
+ at ARTICLE{Bac62,
+ author = {G. E. Backus},
+ title = {Long-wave elastic anisotropy produced by horizontal layering},
+ journal = jgr,
+ year = {1962},
+ volume = {67},
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+}
+
+ at INPROCEEDINGS{BaRoLiHiSiTaPaGo08,
+ author = {Balevic, A. and Rockstroh, L. and Li, W. and Hillebrand, J. and Simon,
+ S. and Tausendfreund, A. and Patzelt, S. and Goch, G.},
+ title = {Acceleration of a finite-difference method with general purpose {GPU}s:
+ {L}esson learned},
+ booktitle = {Proceedings of the 8th IEEE International Conference on Computer
+ and Information Technology},
+ year = {2008},
+ pages = {291-294},
+ address = {Sydney, Australia},
+ publisher = {IEEE Computer Society, Washington, DC, USA},
+ doi = {10.1109/CIT.2008.4594689}
+}
+
+ at INPROCEEDINGS{BaRoTaPaGoSi08,
+ author = {A. Balevic and L. Rockstroh and A. Tausendfreund and S. Patzelt and
+ G. Goch and S. Simon},
+ title = {Accelerating Simulations of Light Scattering Based on a Finite-Difference
+ Time-Domain Method with General Purpose {GPU}s},
+ booktitle = {Proceedings of the 11th IEEE International Conference on Computational
+ Science and Engineering},
+ year = {2008},
+ pages = {327-334},
+ address = {Sao Paulo, Brazil},
+ publisher = {IEEE Computer Society, Washington, DC, USA}
+}
+
+ at ARTICLE{BaEnHaJo88,
+ author = {A. Bamberger and B. Engquist and L. Halpern and P. Joly},
+ title = {Higher order paraxial wave equation approximations in heterogeneous
+ media},
+ journal = {SIAM J. Appl. Math.},
+ year = {1988},
+ volume = {48},
+ pages = {129-154}
+}
+
+ at ARTICLE{BaJoRo90,
+ author = {A. Bamberger and P. Joly and J. E. Roberts},
+ title = {Second order absorbing boundary conditions for the wave equation:
+ a solution for the corner problem},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1990},
+ volume = {27},
+ pages = {323-352}
+}
+
+ at ARTICLE{BaBiGhKaOhShXu98,
+ author = {H. Bao and J. Bielak and O. Ghattas and L. F. Kallivokas and D. R.
+ O'Hallaron and J. R. Shewchuk and J. Xu},
+ title = {Large-scale simulation of elastic wave propagation in heterogeneous
+ media on parallel computers},
+ journal = cmame,
+ year = {1998},
+ volume = {152},
+ pages = {85-102}
+}
+
+ at ARTICLE{Bar82,
+ author = {P. Y. Bard},
+ title = {Diffracted waves and displacement field over two dimensional topographies},
+ journal = gjras,
+ year = {1982},
+ volume = {71},
+ pages = {731-760}
+}
+
+ at ARTICLE{BaBo85,
+ author = {Pierre-Yves Bard and Michel Bouchon},
+ title = {The two-dimensional resonance of sediment-filled valleys},
+ journal = bssa,
+ year = {1985},
+ volume = {75},
+ pages = {519-541}
+}
+
+ at ARTICLE{BaBo80a,
+ author = {Pierre-Yves Bard and Michel Bouchon},
+ title = {The seismic response of sediment-filled valleys, {P}art 1: The case
+ of incident {SH} waves},
+ journal = bssa,
+ year = {1980},
+ volume = {70},
+ pages = {1263-1286}
+}
+
+ at ARTICLE{BaBo80b,
+ author = {Pierre-Yves Bard and Michel Bouchon},
+ title = {The seismic response of sediment-filled valleys, {P}art 2: The case
+ of incident {P} and {SV} waves},
+ journal = bssa,
+ year = {1980},
+ volume = {70},
+ pages = {1921-1941}
+}
+
+ at ARTICLE{bardos,
+ author = {C. Bardos and G. Lebeau and J. Rauch},
+ title = {Gevrey regularity and distribution of the scattering frequencies},
+ journal = {Invent. Math.},
+ year = {1987},
+ volume = {90},
+ pages = {77-114}
+}
+
+ at ARTICLE{Bar00,
+ author = {D. M. Barnett},
+ title = {Bulk, surface, and interfacial waves in anisotropic linear elastic
+ solids},
+ journal = {International Journal of Solids and Structures},
+ year = {2000},
+ volume = {37},
+ pages = {45-54}
+}
+
+ at ARTICLE{Bar92,
+ author = {D. M. Barnett},
+ title = {On the non-existence of subsonic boundary-polarized two-component
+ free surface waves},
+ journal = {Physica Scripta},
+ year = {1992},
+ volume = {T44},
+ pages = {98-103}
+}
+
+ at INCOLLECTION{BarCha91,
+ author = {D. M. Barnett and P. Chadwick},
+ title = {The existence of one-component surface waves and exceptional transonic
+ states of types 2, 4 and {E}1 in anisotropic elastic media},
+ booktitle = {Modern Theory of Anisotropic Elasticity and Applications},
+ publisher = {SIAM},
+ year = {1991},
+ editor = {J. J. Wu and T. C. T. Ting and D. M. Barnett},
+ pages = {199-214},
+ address = {Philadelphia, USA}
+}
+
+ at ARTICLE{BarChaLot91,
+ author = {D. M. Barnett and P. Chadwick and J. Lothe},
+ title = {The behaviour of elastic surface waves polarized in a plane of material
+ symmetry. {I}. {A}ddendum},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1991},
+ volume = {A433},
+ pages = {699-710}
+}
+
+ at ARTICLE{BarGavLot88,
+ author = {D. M. Barnett and S. D. Gavazza and J. Lothe},
+ title = {Slip waves along the interface between two anisotropic elastic half-spaces
+ in sliding contact},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1988},
+ volume = {A415},
+ pages = {389-419}
+}
+
+ at ARTICLE{BarLot85,
+ author = {D. M. Barnett and J. Lothe},
+ title = {Free surface ({R}ayleigh) waves in anisotropic elastic halfspaces:
+ the surface impedance method},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1985},
+ volume = {A402},
+ pages = {135-152}
+}
+
+ at ARTICLE{BarLot74,
+ author = {D. M. Barnett and J. Lothe},
+ title = {Consideration of the existence of surface wave ({R}ayleigh wave)
+ solutions in anisotropic elastic crystals},
+ journal = {Journal of Physics F: Metal Physics},
+ year = {1974},
+ volume = {4},
+ pages = {671-686}
+}
+
+ at ARTICLE{BarLot73,
+ author = {D. M. Barnett and J. Lothe},
+ title = {Synthesis of the {S}extic and the {I}ntegral {F}ormalism for dislocations,
+ {G}reens functions, and surface waves in anisotropic elastic solids},
+ journal = {Physica Norvegica},
+ year = {1973},
+ volume = {7},
+ pages = {13-22}
+}
+
+ at ARTICLE{BarLotNisAsa73,
+ author = {D. M. Barnett and J. Lothe and K. Nishioka and R. J. Asaro},
+ title = {Elastic surface waves in anisotropic crystals: a simplified method
+ for calculating {R}ayleigh velocities using dislocation theory},
+ journal = {Journal of Physics F: Metal Physics},
+ year = {1973},
+ volume = {3},
+ pages = {1083-1096}
+}
+
+ at INPROCEEDINGS{BaSaFiRo05,
+ author = {Baron, G. S. and Sarris, C. D. and Fiume, E. and Rogers Sr., Edward
+ S.},
+ title = {Fast and accurate time-domain simulations with commodity graphics
+ hardware},
+ booktitle = {Proceedings of the 2005 IEEE Antennas and Propagation Society International
+ Symposium},
+ year = {2005},
+ volume = {4A},
+ pages = {193-196},
+ address = {Seoul, Korea},
+ publisher = {IEEE Computer Society, Washington, DC, USA},
+ doi = {10.1109/APS.2005.1552619}
+}
+
+ at INPROCEEDINGS{Ba03,
+ author = {H. Barucq},
+ title = {A family of first-order conditions for the long-time stability of
+ the {M}axwell system},
+ booktitle = {Mathematical and Numerical Aspects of Wave Propagation: Waves 2003},
+ year = {2003},
+ editor = {Gary Cohen and Erkki Heikkola and Patrick Joly and Pekka Neittaanm\"aki},
+ series = {Proceedings of the Sixth International Conference on Mathematical
+ and Numerical Aspects of Wave Propagation},
+ address = {Jyv\"askyl\"a, Finland},
+ publisher = {Springer-Verlag}
+}
+
+ at ARTICLE{Bar02,
+ author = {H. Barucq},
+ title = {A new family of first-order boundary conditions for the {M}axwell
+ system: derivation, well-posedness and long-time behavior},
+ journal = {J. Math. Pures Appl.},
+ year = {2002},
+ volume = {82},
+ pages = {67-88}
+}
+
+ at ARTICLE{BaBeDj04,
+ author = {H. Barucq and C. Bekkey and R. Djellouli},
+ title = {Construction of local boundary conditions for an eigenvalue problem
+ using micro-local analysis. Application to optical waveguide problem},
+ journal = {J. Comp. Phys.},
+ year = {2004},
+ volume = {193},
+ pages = {666-696},
+ number = {2},
+ note = {to appear}
+}
+
+ at ARTICLE{BaDeHa98,
+ author = {H. Barucq and F. Delaurens and B. Hanouzet},
+ title = {Method of Absorbing Boundary conditions: Phenomena of error stabilization},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1998},
+ volume = {35},
+ pages = {1113-1129}
+}
+
+ at ARTICLE{BaHa97,
+ author = {H. Barucq and B. Hanouzet},
+ title = {Asymptotic Behavior of solutions to {M}axwell's system with absorbing
+ {S}ilver-{M}uller condition on the exterior boundary},
+ journal = {Asympt. Anal.},
+ year = {1997},
+ volume = {15},
+ pages = {465-473}
+}
+
+ at ARTICLE{BaMaSm204,
+ author = {H. Barucq and M. Madaune-Tort and P. Saint-Macary},
+ title = {Asymptotic models in porous media arising from a {B}iot system},
+ journal = {Advances in Differential Equations},
+ year = {2006},
+ volume = {11},
+ pages = {61-90},
+ number = {1}
+}
+
+ at ARTICLE{BarucqMadauneSaintMacary12005,
+ author = {H. Barucq and M. Madaune-Tort and P. Saint-Macary},
+ title = {Some existence-uniqueness results for a class of one-dimensional
+ nonlinear {B}iot models},
+ journal = {Nonlinear Analysis: Theory, Methods and Applications},
+ year = {2005},
+ volume = {61},
+ pages = {591-612},
+ number = {4}
+}
+
+ at ARTICLE{BarucqMadauneSaintMacary22005,
+ author = {H. Barucq and M. Madaune-Tort and P. Saint-Macary},
+ title = {On nonlinear {B}iot consolidation models},
+ journal = {Nonlinear Analysis: Theory, Methods and Applications},
+ year = {2005},
+ volume = {63},
+ pages = {e985-e995},
+ number = {5-7}
+}
+
+ at ARTICLE{BaLaMa00,
+ author = {C. Bassin and G. Laske and G. Masters},
+ title = {The Current Limits of Resolution for Surface Wave Tomography in {N}orth
+ {A}merica},
+ journal = {EOS},
+ year = {2000},
+ volume = {81},
+ pages = {F897}
+}
+
+ at ARTICLE{Bas09,
+ author = {Ushnish Basu},
+ title = {Explicit finite-element perfectly matched layer for transient three-dimensional
+ elastic waves},
+ journal = ijnme,
+ year = {2009},
+ volume = {77},
+ pages = {151-176},
+ doi = {10.1002/nme.2397}
+}
+
+ at ARTICLE{BaCh04,
+ author = {U. Basu and A. K. Chopra},
+ title = {Perfectly matched layers for transient elastodynamics of unbounded
+ domains},
+ journal = ijnme,
+ year = {2004},
+ volume = {59},
+ pages = {1039-1074}
+}
+
+ at ARTICLE{BaCh03,
+ author = {U. Basu and A. K. Chopra},
+ title = {Perfectly matched layers for time-harmonic elastodynamics of unbounded
+ domains: theory and finite-element implementation},
+ journal = cmame,
+ year = {2003},
+ volume = {192},
+ pages = {1337-1375}
+}
+
+ at ARTICLE{Bat87,
+ author = {G. Battle},
+ title = {A block spin construction of wavelets, Part 1: {L}emari\'e functions},
+ journal = {Communications in Mathematical Physics},
+ year = {1987},
+ volume = {110},
+ pages = {9999998-9999999}
+}
+
+ at INPROCEEDINGS{BaKoMaTsCaMaNa11,
+ author = {Leonardo Arturo Bautista-Gomez and Dimitri Komatitsch and Naoya Maruyama
+ and Seiji Tsuboi and Franck Cappello and Satoshi Matsuoka and Takeshi
+ Nakamura},
+ title = {{FTI}: high performance {F}ault {T}olerance {I}nterface for hybrid
+ systems},
+ booktitle = {SC'11: Proceedings of the 2011 ACM/IEEE conference on Supercomputing},
+ year = {2011},
+ pages = {32:1-32:12},
+ address = {Seattle, Washington, USA},
+ month = nov,
+ note = {Article \#32},
+ articleno = {32},
+ doi = {10.1145/2063384.2063427}
+}
+
+ at ARTICLE{BaJoLeTu86,
+ author = {A. Bayliss and K. E. Jordan and B. J. Lemesurier and E. Turkel},
+ title = {A fourth-order accurate finite-difference scheme for the computation
+ of elastic waves},
+ journal = bssa,
+ year = {1986},
+ volume = {76},
+ pages = {1115-1132}
+}
+
+ at ARTICLE{BaTu80,
+ author = {A. Bayliss and E. Turkel},
+ title = {Radiation boundary conditions for wave-like equations},
+ journal = {Comm. Pure Appl. Math.},
+ year = {1980},
+ volume = {33},
+ pages = {707-725}
+}
+
+ at ARTICLE{baysal83,
+ author = {E. Baysal and D. D. Kosloff and J. W. C. Sherwood},
+ title = {Reverse-time migration},
+ journal = {Geophysics},
+ year = {1983},
+ volume = {48},
+ pages = {1514-1524}
+}
+
+ at ARTICLE{beckerboschi2002,
+ author = {T. W. Becker and L. Boschi},
+ title = {A comparison of tomographic and geodynamic mantle models},
+ journal = {Geochem. Geophys. Geosyst.},
+ year = {2002},
+ volume = {3},
+ pages = {1003},
+ number = {1},
+ doi = {10.1029/2001GC000168}
+}
+
+ at INPROCEEDINGS{Bell:2009:ISM,
+ author = {Nathan Bell and Michael Garland},
+ title = {Implementing sparse matrix-vector multiplication on throughput-oriented
+ processors},
+ booktitle = {SC'09: Proceedings of the 2009 ACM/IEEE conference on Supercomputing},
+ year = {2009},
+ pages = {1--11},
+ address = {New York, USA},
+ month = nov,
+ publisher = {ACM},
+ doi = {10.1145/1654059.1654078},
+ location = {Portland, Oregon, USA}
+}
+
+ at INCOLLECTION{BeMu78,
+ author = {Ted Belytschko and R. Mullen},
+ title = {On dispersive properties of finite element solutions},
+ booktitle = {Modern problems in elastic wave propagation},
+ publisher = {John Wiley and Sons},
+ year = {1978},
+ editor = {J. Miklowitz and J. D. Achenbach},
+ volume = {67},
+ address = {New York}
+}
+
+ at ARTICLE{BePlKeGr90,
+ author = {Ted Belytschko and E. J. Plaskacz and J. M. Kennedy and D. L. Greenwell},
+ title = {Finite element analysis on the {C}onnection {M}achine},
+ journal = cmame,
+ year = {1990},
+ volume = {81},
+ pages = {229-254}
+}
+
+ at ARTICLE{BeOl05,
+ author = {Rafael Benites and Kim B. Olsen},
+ title = {Modeling Strong Ground Motion in the {W}ellington Metropolitan Area,
+ {N}ew {Z}ealand},
+ journal = bssa,
+ year = {2005},
+ volume = {95},
+ pages = {2180-2196},
+ number = {6},
+ doi = {10.1785/0120040223}
+}
+
+ at ARTICLE{BeGlCrVi09,
+ author = {M. Benjemaa and Glinsky-Olivier, N. and Cruz-Atienza, V. M. and Virieux,
+ J.},
+ title = {3{D} dynamic rupture simulation by a finite volume method},
+ journal = gji,
+ year = {2009},
+ volume = {178},
+ pages = {541-560},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2009.04088.x}
+}
+
+ at ARTICLE{BeGlCrViPi07,
+ author = {Benjemaa, M. and Glinsky-Olivier, N. and Cruz-Atienza, V. M. and
+ Virieux, J. and Piperno, S.},
+ title = {{D}ynamic non-planar crack rupture by a finite volume method},
+ journal = gji,
+ year = {2007},
+ volume = {171},
+ pages = {271-285},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2006.03500.x}
+}
+
+ at BOOK{Ben81,
+ title = {Seismic waves and sources},
+ publisher = {Springer-Verlag},
+ year = {1981},
+ author = {Ari Ben-Menahem and Sarva Jit. Singh},
+ address = {New York}
+}
+
+ at INCOLLECTION{BeIfNiSk94,
+ author = {P. Berg and F. If and P. Nielsen and O. Skovegaard},
+ title = {Analytic reference solutions},
+ booktitle = {Modeling the Earth for oil exploration, Final report of the CEC's
+ GEOSCIENCE~I Program 1990-1993},
+ publisher = {Pergamon Press, Oxford, United Kingdom},
+ year = {1994},
+ editor = {K. Helbig},
+ pages = {421-427}
+}
+
+ at INCOLLECTION{BeBrSy82,
+ author = {Ph. Berger and P. Brouaye and J. C. Syre},
+ title = {A mesh coloring method for efficient {MIMD} processing in finite
+ element problems},
+ booktitle = {Proceedings of the International Conference on Parallel Processing,
+ ICPP'82, August 24-27, 1982, Bellaire, Michigan, USA},
+ publisher = {IEEE Computer Society},
+ year = {1982},
+ pages = {41-46}
+}
+
+ at INPROCEEDINGS{BeHePrRo06b,
+ author = {Alfredo Berm\'udez and Luis Hervella-Nieto and Andr\'es Prieto and
+ Rodolfo Rodr\'{\i}guez},
+ title = {An optimal finite-element/{PML} method for the simulation of acoustic
+ wave propagation phenomena},
+ booktitle = {Variational Formulations in Mechanics: Theory and Applications},
+ year = {2006},
+ editor = {E. Taroco and E. A. de Souza Neto and A. A. Novotny},
+ address = {Barcelona, Spain},
+ publisher = {CIMNE}
+}
+
+ at ARTICLE{BeHePrRo06,
+ author = {Alfredo Berm\'udez and Luis Hervella-Nieto and Andr\'es Prieto and
+ Rodolfo Rodr\'{\i}guez},
+ title = {An optimal perfectly matched layer with unbounded absorbing function
+ for time-harmonic acoustic scattering problems},
+ journal = jcp,
+ year = {2007},
+ volume = {223},
+ pages = {469-488},
+ number = {2},
+ doi = {10.1016/j.jcp.2006.09.018}
+}
+
+ at ARTICLE{BeHeRo99,
+ author = {A. Berm\'udez and L. Hervella-Nieto and R. Rodriguez},
+ title = {Finite-element computation of three-dimensional elastoacoustic vibrations},
+ journal = {J. Sound Vibr.},
+ year = {1999},
+ volume = {219},
+ pages = {279-306}
+}
+
+ at ARTICLE{BeRo94,
+ author = {A. Berm\'udez and R. {Rodr\'\i guez}},
+ title = {Finite-element computation of the vibration modes of a fluid-solid
+ system},
+ journal = cmame,
+ year = {1994},
+ volume = {119},
+ pages = {355-370}
+}
+
+ at ARTICLE{BeLaPi06,
+ author = {Marc Bernacki and St\'ephane Lanteri and Serge Piperno},
+ title = {Time-Domain Parallel Simulation Of Heterogeneous Wave Propagation
+ On Unstructured Grids Using Explicit, Nondiffusive, Discontinuous
+ {G}alerkin Methods},
+ journal = jca,
+ year = {2006},
+ volume = {14},
+ pages = {57-81},
+ number = {1}
+}
+
+ at ARTICLE{BeDeMa90,
+ author = {C. Bernardi and N. Debit and Y. Maday},
+ title = {Coupling finite element and spectral methods: first results},
+ journal = {Mathematics of Computation},
+ year = {1990},
+ volume = {54},
+ pages = {21-39}
+}
+
+ at BOOK{BeMa92,
+ title = {Approximations spectrales de probl\`emes aux limites elliptiques},
+ publisher = {Springer-Verlag},
+ year = {1992},
+ author = {C. Bernardi and Y. Maday},
+ address = {Paris}
+}
+
+ at INPROCEEDINGS{BeMaPa94,
+ author = {C. Bernardi and Y. Maday and A. T. Patera},
+ title = {A new nonconforming approach to domain decomposition: the {M}ortar
+ element method},
+ booktitle = {Nonlinear partial differential equations and their applications},
+ year = {1994},
+ editor = {H. Brezis and J. L. Lions},
+ series = {S\'eminaires du Coll\`ege de France},
+ pages = {13-51},
+ address = {Paris},
+ publisher = {Pitman}
+}
+
+ at ARTICLE{BesDes98a,
+ author = {C. Bescond and M. Deschamps},
+ title = {Dynamical surface response of a semi-infinite anisotropic elastic
+ medium to an impulsive force},
+ journal = jasa,
+ year = {1998},
+ volume = {103},
+ pages = {114-124},
+ number = {1}
+}
+
+ at ARTICLE{BesDes98b,
+ author = {C. Bescond and M. Deschamps},
+ title = {Erratum to `{D}ynamical surface response of a semi-infinite anisotropic
+ elastic medium to an impulsive force'},
+ journal = jasa,
+ year = {1998},
+ volume = {104},
+ pages = {599},
+ number = {1}
+}
+
+ at ARTICLE{BiCh84,
+ author = {J. Bielak and P. Christiano},
+ title = {On the effective seismic input for non-linear soil-structure interaction
+ systems},
+ journal = {Earthquake Eng. Struct. Dyn.},
+ year = {1984},
+ volume = {12},
+ pages = {107-119}
+}
+
+ at ARTICLE{BiGhKi05,
+ author = {J. Bielak and O. Ghattas and E. J. Kim},
+ title = {Parallel Octree-Based Finite Element Method for Large-Scale Earthquake
+ Ground Motion Simulation},
+ journal = cmes,
+ year = {2005},
+ volume = {10},
+ pages = {99-112},
+ number = {2}
+}
+
+ at ARTICLE{BiXuGh99,
+ author = {J. Bielak and J. Xu and O. Ghattas},
+ title = {Earthquake ground motion and structural response in alluvial valleys},
+ journal = {J. Geotech. Geoenv. Eng.},
+ year = {1999},
+ volume = {125},
+ pages = {413-423}
+}
+
+ at ARTICLE{Biot56a,
+ author = {M. A. Biot},
+ title = {Theory of propagation of elastic waves in a fluid-saturated porous
+ solid. {I: L}ow-frequency range},
+ journal = jasa,
+ year = {1956},
+ volume = {28},
+ pages = {168-178}
+}
+
+ at ARTICLE{Biot56b,
+ author = {M. A. Biot},
+ title = {Theory of propagation of elastic waves in a fluid-saturated porous
+ solid. {II: H}igher-frequency range},
+ journal = jasa,
+ year = {1956},
+ volume = {28},
+ pages = {179-191}
+}
+
+ at ARTICLE{Bio52,
+ author = {M. A. Biot},
+ title = {The interaction of {R}ayleigh and {S}toneley waves in the ocean bottom},
+ journal = bssa,
+ year = {1952},
+ volume = {42},
+ pages = {81-93}
+}
+
+ at BOOK{BirGulKryPle95,
+ title = {Surface acoustic waves in inhomogeneous media},
+ publisher = {Springer-Verlag},
+ year = {1995},
+ author = {S. V. Biryukov and Y. V. Gulyaev and V. V. Krylov and V. P. Plessky},
+ volume = {20},
+ series = {Springer Series on Wave Phenomena},
+ address = {Berlin, Germany}
+}
+
+ at ARTICLE{Bit05,
+ author = {M. L. Bittencourt},
+ title = {Fully tensorial nodal and modal shape functions for triangles and
+ tetrahedra},
+ journal = ijnme,
+ year = {2005},
+ volume = {63},
+ pages = {1530-1558},
+ number = {11},
+ doi = {10.1002/nme.1325}
+}
+
+ at MANUAL{Bl94,
+ title = {{CUBIT} Mesh Generation Environment Users Manual Vol. 1},
+ author = {T.D. Blacker and P. Knupp and R. r. Lober and D. Melander and G.
+ D. Sjaardema and W. A. Sample and M. K. Smith and T. J. Tautges and
+ D. R. White and S. Benzley and R. Kerr and S. R. Jankovich and D.
+ B. McRae and M. Panthaki},
+ organization = {Sandia National Laboratories},
+ address = {Albuquerque, NM},
+ year = {1994}
+}
+
+ at ARTICLE{BlLoKoBa09,
+ author = {C\'eline Blitz and Philippe Lognonn\'e and Dimitri Komatitsch and
+ David Baratoux},
+ title = {Effects of ejecta accumulation on the crater population of asteroid
+ 433 {E}ros},
+ journal = jgr,
+ year = {2009},
+ volume = {114},
+ pages = {E06006},
+ doi = {10.1029/2008JE003229}
+}
+
+ at ARTICLE{BoSaenger06,
+ author = {Thomas Bohlen and Erik H. Saenger},
+ title = {Accuracy of heterogeneous staggered-grid finite-difference modeling
+ of {R}ayleigh waves},
+ journal = geophysics,
+ year = {2006},
+ volume = {71},
+ pages = {T109-T115},
+ number = {4},
+ doi = {10.1190/1.2213051}
+}
+
+ at ARTICLE{BoHa77,
+ author = {B. A. Bolt and R. A. Hansen},
+ title = {The upthrow of objects in earthquakes},
+ journal = bssa,
+ year = {1977},
+ volume = {67},
+ pages = {1415-1427}
+}
+
+ at ARTICLE{Bolz:2003:SMS,
+ author = {Jeff Bolz and Ian Farmer and Eitan Grinspun and Peter Schr{\"o}der},
+ title = {Sparse matrix solvers on the {GPU}: {C}onjugate Gradients and Multigrid},
+ journal = {ACM Transactions on Graphics},
+ year = {2003},
+ volume = {22},
+ pages = {917--924},
+ number = {3},
+ month = jul,
+ doi = {10.1145/882262.882364}
+}
+
+ at ARTICLE{BoVi91,
+ author = {O. Bonamassa and J. E. Vidale},
+ title = {Directional site resonances observed from aftershocks of the 18 october
+ 1989 {L}oma {P}rieta earthquake},
+ journal = bssa,
+ year = {1991},
+ volume = {81},
+ pages = {1945-1957}
+}
+
+ at BOOK{Bon95,
+ title = {\'Equations int\'egrales et \'el\'ements de fronti\`ere},
+ publisher = {CNRS \'Editions, Eyrolles},
+ year = {1995},
+ author = {M. Bonnet},
+ address = {Paris}
+}
+
+ at INCOLLECTION{Boo72a,
+ author = {D. M. Boore},
+ title = {Finite difference methods for seismic wave propagation in heterogeneous
+ materials},
+ booktitle = {Methods in Computational Physics},
+ publisher = {Academic Press},
+ year = {1972},
+ volume = {11},
+ address = {New York}
+}
+
+ at ARTICLE{Boo72b,
+ author = {D. M. Boore},
+ title = {A note on the effect of simple topography on seismic {{\it SH}} waves},
+ journal = bssa,
+ year = {1972},
+ volume = {62},
+ pages = {275-284}
+}
+
+ at ARTICLE{BoHaHa81,
+ author = {D. M. Boore and S. C. Harmsen and S. T. Harding},
+ title = {Wave scattering from a steep change in surface topography},
+ journal = bssa,
+ year = {1981},
+ volume = {71},
+ pages = {117-125}
+}
+
+ at ARTICLE{BoCr83,
+ author = {D. C. Booth and S. Crampin},
+ title = {The anisotropic reflectivity technique: theory},
+ journal = {Geophys. J. R. Astr. Soc.},
+ year = {1983},
+ volume = {72},
+ pages = {755-766}
+}
+
+ at ARTICLE{Bos91,
+ author = {L. Bos},
+ title = {On certain configurations of points in {{\rm I\kern -0.18 em R}$^n$}
+ which are unisolvent for polynomial interpolation},
+ journal = {J. Approx. Theory},
+ year = {1991},
+ volume = {64},
+ pages = {271-280}
+}
+
+ at ARTICLE{BoTaWi01,
+ author = {L. P. Bos and M. A. Taylor and B. A. Wingate},
+ title = {Tensor Product {G}auss-{L}obatto Points are {F}ekete Points for the
+ Cube},
+ journal = {Math. Comp.},
+ year = {2001},
+ volume = {70},
+ pages = {1543-1547}
+}
+
+ at ARTICLE{BoGriMia,
+ author = {A. Bossavit and G. Griso and B. Miara},
+ title = {Modelling of periodic electromagnetic structures bianosotropic materials
+ with memory effects},
+ journal = {Journal de Math\'ematiques Pures et Appliqu\'ees},
+ year = {2005},
+ volume = {84},
+ pages = {819-850},
+ number = {7}
+}
+
+ at ARTICLE{Bos02,
+ author = {M. G. Bostock},
+ title = {Kirchhoff-approximate inversion of teleseismic wavefields},
+ journal = gji,
+ year = {2002},
+ volume = {149},
+ pages = {787-795}
+}
+
+ at ARTICLE{BoRo99,
+ author = {M. G. Bostock and S. Rondenay},
+ title = {Migration of scattered teleseismic body waves},
+ journal = gji,
+ year = {1999},
+ volume = {137},
+ pages = {732-746}
+}
+
+ at ARTICLE{BoRoSh01,
+ author = {M. G. Bostock and S. Rondenay and J. Shragge},
+ title = {Multiparameter two-dimensional inversion of scattered teleseismic
+ body waves - 1. {T}heory for oblique incidence},
+ journal = jgr,
+ year = {2001},
+ volume = {106},
+ pages = {30771-30782}
+}
+
+ at ARTICLE{Bou96,
+ author = {M. Bouchon},
+ title = {The discrete wave number formulation of boundary integral equations
+ and boundary element methods: a review with applications to the simulation
+ of seismic wave propagation in complex geological structures},
+ journal = pageoph,
+ year = {1996},
+ volume = {148},
+ pages = {3-20},
+ number = {1}
+}
+
+ at ARTICLE{Bou85,
+ author = {M. Bouchon},
+ title = {A simple complete numerical solution of the problem of diffraction
+ of {{\it SH}} waves by an irregular surface},
+ journal = jasa,
+ year = {1985},
+ volume = {77},
+ pages = {1-5}
+}
+
+ at ARTICLE{Bou81,
+ author = {M. Bouchon},
+ title = {A simple method to calculate {G}reen's functions for elastic layered
+ media},
+ journal = bssa,
+ year = {1981},
+ volume = {71},
+ pages = {959-971}
+}
+
+ at ARTICLE{Bou79,
+ author = {M. Bouchon},
+ title = {Discrete wavenumber representation of elastic wave fields in three
+ space dimensions},
+ journal = jgr,
+ year = {1979},
+ volume = {84},
+ pages = {3609-3614}
+}
+
+ at ARTICLE{Bou78,
+ author = {M. Bouchon},
+ title = {The importance of the surface interface {{\it P}} wave in near-earthquake
+ studies},
+ journal = bssa,
+ year = {1978},
+ volume = {68},
+ pages = {1293-1311}
+}
+
+ at ARTICLE{Bou73,
+ author = {M. Bouchon},
+ title = {Effect of topography on surface motion},
+ journal = bssa,
+ year = {1973},
+ volume = {63},
+ pages = {615-632}
+}
+
+ at ARTICLE{BoAk77,
+ author = {M. Bouchon and K. Aki},
+ title = {Discrete wavenumber representation of seismic-source wave fields},
+ journal = bssa,
+ year = {1977},
+ volume = {67},
+ pages = {259-277}
+}
+
+ at ARTICLE{BoBa96,
+ author = {M. Bouchon and J. S. Barker},
+ title = {Seismic response of a hill: the example of {T}arzana, {C}alifornia},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {66-72},
+ number = {1A}
+}
+
+ at ARTICLE{BoCaGa89,
+ author = {M. Bouchon and M. Campillo and S. Gaffet},
+ title = {A boundary integral equation-discrete wavenumber representation method
+ to study wave propagation in multilayered media having irregular
+ interfaces},
+ journal = geophysics,
+ year = {1989},
+ volume = {54},
+ pages = {1134-1140}
+}
+
+ at INCOLLECTION{BoSanchez06,
+ author = {M. Bouchon and F. J. S\'anchez-Sesma},
+ title = {Boundary-integral equations and boundary-element methods in elastodynamics},
+ booktitle = {Advances in wave propagation in heterogeneous media},
+ publisher = {Elsevier},
+ year = {2006},
+ editor = {Ru-Shan Wu and Val\'erie Maupin},
+ series = {Advances in Geophysics}
+}
+
+ at ARTICLE{BoScTo96,
+ author = {M. Bouchon and C. A. Schultz and M. Nafi T\"oksoz},
+ title = {Effect of three-dimensional topography on seismic motion},
+ journal = jgr,
+ year = {1996},
+ volume = {101},
+ pages = {5835-5846}
+}
+
+ at ARTICLE{BoScTo95,
+ author = {M. Bouchon and C. A. Schultz and M. Nafi T\"oksoz},
+ title = {A fast implementation of boundary integral equation methods to calculate
+ the propagation of seismic waves in laterally varying layered media},
+ journal = bssa,
+ year = {1995},
+ volume = {85},
+ pages = {1679-1687}
+}
+
+ at PHDTHESIS{ab,
+ author = {A. Bouhamidi},
+ title = {Interpolation et approximation par des fonctions splines radiales
+ \`a plusieurs variables},
+ school = {Universit\'e de Nantes},
+ year = {1992},
+ address = {Nantes, France},
+ note = {190 p.}
+}
+
+ at BOOK{BouHay93,
+ title = {Bivectors and waves in {M}echanics and {O}ptics},
+ publisher = {Chapman and Hall},
+ year = {1993},
+ author = {Ph. Boulanger and M. Hayes},
+ address = {London, United Kingdom}
+}
+
+ at ARTICLE{brandvik_pullan_euler_2d,
+ author = {Tobias Brandvik and Graham Pullan},
+ title = {Acceleration of a two-dimensional {E}uler flow solver using commodity
+ Graphics Hardware},
+ journal = {Proceedings of the Institution of Mechanical Engineers, Part C: Journal
+ of Mechanical Engineering Science},
+ year = {2007},
+ volume = {221},
+ pages = {1745--1748},
+ number = {12},
+ doi = {10.1243/09544062JMES813FT}
+}
+
+ at BOOK{BreGod90,
+ title = {Acoustics of layered media {I}},
+ publisher = {Springer-Verlag},
+ year = {1990},
+ author = {L. M. Brekhovskikh and O. A. Godin},
+ volume = {5},
+ series = {Springer Series on Wave phenomena},
+ address = {Berlin, Germany}
+}
+
+ at ARTICLE{Bremmer,
+ author = {H. Bremmer},
+ title = {The {WKB} approximation as the first term of a geometric-optical
+ series},
+ journal = {Comm. Pure Appl. Math.},
+ year = {1951},
+ volume = {9999999},
+ pages = {105-115}
+}
+
+ at INCOLLECTION{brezzifortin,
+ author = {F. Brezzi and M. Fortin},
+ title = {Mixed and Hybrid Finite Element Methods},
+ booktitle = {Springer Series in Computational Mathematics},
+ publisher = {Springer},
+ year = {1991},
+ volume = {15},
+ address = {New York, USA}
+}
+
+ at BOOK{Bri64,
+ title = {Tensors in Mechanics and Elasticity},
+ publisher = {Academic Press},
+ year = {1964},
+ author = {L. Brillouin},
+ address = {New York, USA},
+ edition = {3rd}
+}
+
+ at ARTICLE{Buc61,
+ author = {V. T. Buchwald},
+ title = {Rayleigh waves in anisotropic media},
+ journal = {Quarterly Journal of Mechanics and Applied Mathematics},
+ year = {1961},
+ volume = {14},
+ pages = {461-468},
+ number = {4}
+}
+
+ at ARTICLE{Buc59,
+ author = {V. T. Buchwald},
+ title = {Elastic waves in anisotropic media},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1959},
+ volume = {A253},
+ pages = {563-580}
+}
+
+ at ARTICLE{BucDav63,
+ author = {V. T. Buchwald and A. Davis},
+ title = {Surface waves in elastic media with cubic symmetry},
+ journal = {Quarterly Journal of Mechanics and Applied Mathematics},
+ year = {1963},
+ volume = {16},
+ pages = {283-293}
+}
+
+ at INPROCEEDINGS{Buc06,
+ author = {Ian Buck},
+ title = {Ge{F}orce 8800 and {NVIDIA CUDA}: A New Architecture for Computing
+ on the {GPU}},
+ booktitle = {Proceedings of the Supercomputing'06 Workshop on "General-Purpose
+ GPU Computing: Practice And Experience"},
+ year = {2006},
+ pages = {1-29},
+ url = {www.gpgpu.org/sc2006/workshop/presentations/Buck\_NVIDIA\_Cuda.pdf}
+}
+
+ at ARTICLE{Buck:2004:BFG,
+ author = {Ian Buck and Tim Foley and Daniel R. Horn and Jeremy Sugerman and
+ Kayvon Fatahalian and Mike Houston and Pat Hanrahan},
+ title = {Brook for {GPUs}: {S}tream computing on graphics hardware},
+ journal = {ACM Transactions on Graphics},
+ year = {2004},
+ volume = {23},
+ pages = {777--786},
+ number = {3},
+ month = aug,
+ doi = {10.1145/1015706.1015800}
+}
+
+ at ARTICLE{Bur71,
+ author = {R. Burridge},
+ title = {Lamb's problem for an anisotropic half-space},
+ journal = {Quarterly Journal of Mechanics and Applied Mathematics},
+ year = {1971},
+ volume = {24},
+ pages = {81-98},
+ number = {1}
+}
+
+ at ARTICLE{Bur70,
+ author = {R. Burridge},
+ title = {The directions in which {R}ayleigh waves may be propagated on crystals},
+ journal = {Quarterly Journal of Mechanics and Applied Mathematics},
+ year = {1970},
+ volume = {23},
+ pages = {217-224},
+ number = {2}
+}
+
+ at ARTICLE{But30,
+ author = {S. Butterworth},
+ title = {On the Theory of Filter Amplifiers},
+ journal = {Experimental Wireless and the Wireless Engineer},
+ year = {1930},
+ volume = {7},
+ pages = {536-541}
+}
+
+ at BOOK{Cag39,
+ title = {R\'eflexion et R\'efraction des Ondes Sismiques Progressives},
+ publisher = {Gauthiers-Villars},
+ year = {1939},
+ author = {L. Cagniard},
+ address = {Paris}
+}
+
+ at PHDTHESIS{Calvet_thesis,
+ author = {M. Calvet},
+ title = {Apport des noyaux de sensibilit\'e des ondes {PKP} et {P} diffract\'ees
+ pour l'\'etude de la graine anisotrope et de la couche {D}''},
+ school = {Universit\'e Paul Sabatier, Toulouse, France},
+ year = {2006}
+}
+
+ at ARTICLE{Calvet05,
+ author = {M. Calvet and S. Chevrot},
+ title = {Traveltime sensitivity kernels for {PKP} phases in the mantle},
+ journal = pepi,
+ year = {2005},
+ volume = {153},
+ pages = {21-31}
+}
+
+ at ARTICLE{Calvet06a,
+ author = {M. Calvet and S. Chevrot and A. Souriau},
+ title = {P wave propagation in transversely isotropic media: {I}. {F}inite-frequency
+ theory},
+ journal = pepi,
+ year = {2006},
+ volume = {156},
+ pages = {12-20}
+}
+
+ at ARTICLE{Calvet06b,
+ author = {M. Calvet and S. Chevrot and A. Souriau},
+ title = {P wave propagation in transversely isotropic media: {II}. {A}pplication
+ to inner core anisotropy: {E}ffects of data averaging, parameterization
+ and a priori information},
+ journal = pepi,
+ year = {2006},
+ volume = {156},
+ pages = {21-40}
+}
+
+ at ARTICLE{CamMar83,
+ author = {R. E. Camley and A. A. Maradudin},
+ title = {Phonon focusing at surfaces},
+ journal = {Physical Review B},
+ year = {1983},
+ volume = {27},
+ pages = {1959-1964},
+ number = {4}
+}
+
+ at ARTICLE{Cam87,
+ author = {M. Campillo},
+ title = {{$L_g$} wave propagation in a laterally varying crust and the distribution
+ of the apparent quality factor in {C}entre {F}rance},
+ journal = jgr,
+ year = {1987},
+ volume = {92},
+ pages = {12604-12614}
+}
+
+ at ARTICLE{CaBo85,
+ author = {M. Campillo and M. Bouchon},
+ title = {Synthetic {{\it SH}} seismograms in laterally varying medium by discrete
+ wavenumber method},
+ journal = gjras,
+ year = {1985},
+ volume = {83},
+ pages = {307-317}
+}
+
+ at INCOLLECTION{CaDo99,
+ author = {E. J. Cand\`es and D. L. Donoho},
+ title = {Curvelets: A Surprisingly Effective Nonadaptive Representation for
+ Objects with Edges, Curves and Surfaces},
+ booktitle = {Curve and Surface Fitting},
+ publisher = {Vanderbilt University Press},
+ year = {1999},
+ editor = {A. Cohen and C. Rabut and L. L. Schumaker},
+ address = {Nashville, Tennessee, USA}
+}
+
+ at ARTICLE{CaFu88,
+ author = {C. Canuto and D. Funaro},
+ title = {The {S}chwarz algorithm for spectral methods},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1988},
+ volume = {25},
+ pages = {24-40}
+}
+
+ at BOOK{CaHuQuZa88,
+ title = {Spectral methods in fluid dynamics},
+ publisher = {Springer-Verlag},
+ year = {1988},
+ author = {C. Canuto and M. Y. Hussaini and A. Quarteroni and T. A. Zang},
+ address = {New York, USA}
+}
+
+ at ARTICLE{CaQu82,
+ author = {C. Canuto and A. Quarteroni},
+ title = {Approximation results for orthogonal polynomials in {S}obolev spaces},
+ journal = {Math. Comp.},
+ year = {1982},
+ volume = {38},
+ pages = {67-86}
+}
+
+ at PHDTHESIS{Ca00,
+ author = {Y. Capdeville},
+ title = {M\'ethode coupl\'ee \'el\'ements spectraux - solution modale pour
+ la propagation d'ondes dans la {T}erre \`a l'\'echelle globale ({A}
+ coupled method using spectral elements and normal modes for global
+ wave propagation in the {E}arth)},
+ school = {Universit\'e Paris {\sc VII} Denis Diderot},
+ year = {2000},
+ address = {Paris, France}
+}
+
+ at ARTICLE{CaChViMo03,
+ author = {Y. Capdeville and E. Chaljub and J. P. Vilotte and J. P. Montagner},
+ title = {Coupling the spectral element method with a modal solution for elastic
+ wave propagation in global {E}arth models},
+ journal = gji,
+ year = {2003},
+ volume = {152},
+ pages = {34-67}
+}
+
+ at ARTICLE{CaGuRo05,
+ author = {Y. Capdeville and Y. Gung and B. Romanowicz},
+ title = {Towards global {E}arth tomography using the spectral element method:
+ a technique based on source stacking},
+ journal = gji,
+ year = {2005},
+ volume = {162},
+ pages = {541-554}
+}
+
+ at ARTICLE{Caetal00,
+ author = {Y. Capdeville and E. Stutzmann and J.P. Montagner},
+ title = {Effect of a plume on long-period surface waves computed with normal-mode
+ coupling},
+ journal = pepi,
+ year = {2000},
+ volume = {119},
+ pages = {54-71}
+}
+
+ at ARTICLE{CaToRo03,
+ author = {Yann Capdeville and A. To and Barbara Romanowicz},
+ title = {Coupling spectral elements and modes in a spherical {E}arth: an extension
+ to the `sandwich' case},
+ journal = gji,
+ year = {2003},
+ volume = {154},
+ pages = {44-57}
+}
+
+ at BOOK{Car07,
+ title = {Wave fields in real media: {T}heory and numerical simulation of wave
+ propagation in anisotropic, anelastic, porous and electromagnetic
+ media},
+ publisher = {Elsevier Science},
+ year = {2007},
+ author = {Jos\'e M. Carcione},
+ address = {Amsterdam, The Netherlands},
+ edition = {Second}
+}
+
+ at ARTICLE{Car99,
+ author = {J. M. Carcione},
+ title = {Staggered mesh for the anisotropic and viscoelastic wave equation},
+ journal = geophysics,
+ year = {1999},
+ volume = {64},
+ pages = {1863-1866}
+}
+
+ at ARTICLE{Car96,
+ author = {J. M. Carcione},
+ title = {A 2{D} {C}hebyshev differential operator for the elastic wave equation},
+ journal = cmame,
+ year = {1996},
+ volume = {130},
+ pages = {33-45}
+}
+
+ at ARTICLE{Carcio96,
+ author = {J. M. Carcione},
+ title = {Elastodynamic of a non-ideal interface: application to crack and
+ fracture scattering},
+ journal = jgr,
+ year = {1996},
+ volume = {101},
+ pages = {28177-28188},
+ number = {B12}
+}
+
+ at ARTICLE{Car94,
+ author = {J. M. Carcione},
+ title = {The wave equation in generalized coordinates},
+ journal = geophysics,
+ year = {1994},
+ volume = {59},
+ pages = {1911-1919}
+}
+
+ at ARTICLE{Car93,
+ author = {Jos\'e M. Carcione},
+ title = {Seismic modeling in viscoelastic media},
+ journal = geophysics,
+ year = {1993},
+ volume = {58},
+ pages = {110-120},
+ number = {1},
+ doi = {10.1190/1.1443340}
+}
+
+ at ARTICLE{Car92,
+ author = {J. M. Carcione},
+ title = {Modeling anelastic singular surface waves in the {E}arth},
+ journal = {Geophysics},
+ year = {1992},
+ volume = {57},
+ pages = {781-792},
+ number = {6}
+}
+
+ at ARTICLE{Car91,
+ author = {J. M. Carcione},
+ title = {Domain decomposition for wave propagation problems},
+ journal = {J. Sci. Comp.},
+ year = {1991},
+ volume = {6},
+ pages = {453-472},
+ number = {4}
+}
+
+ at ARTICLE{Car90,
+ author = {J. M. Carcione},
+ title = {Wave propagation in anisotropic linear viscoelastic media: theory
+ and simulated wavefields},
+ journal = gji,
+ year = {1990},
+ volume = {101},
+ pages = {739-750}
+}
+
+ at ARTICLE{CarHel04,
+ author = {J. M. Carcione and H. B. Helle},
+ title = {On the physics and simulation of wave propagation at the ocean bottom},
+ journal = {Geophysics},
+ year = {2004},
+ volume = {69},
+ pages = {825-839}
+}
+
+ at ARTICLE{CaHeKr02,
+ author = {J. M. Carcione and G. Herman and F. P. E. {ten Kroode}},
+ title = {Seismic modeling},
+ journal = geophysics,
+ year = {2002},
+ volume = {67},
+ pages = {1304-1325}
+}
+
+ at ARTICLE{CaKoBeSe92,
+ author = {J. M. Carcione and D. Kosloff and A. Behle and G. Seriani},
+ title = {A spectral scheme for wave propagation simulation in 3-{D} elastic-anisotropic
+ media},
+ journal = geophysics,
+ year = {1992},
+ volume = {57},
+ pages = {1593-1607},
+ number = {12}
+}
+
+ at ARTICLE{CaKoKo88,
+ author = {J. M. Carcione and D. Kosloff and R. Kosloff},
+ title = {Wave propagation simulation in an elastic anisotropic (transversely
+ isotropic) solid},
+ journal = {Q. J. Mech. Appl. Math.},
+ year = {1988},
+ volume = {41},
+ pages = {319-345},
+ number = {3}
+}
+
+ at ARTICLE{CaKoKo88b,
+ author = {J. M. Carcione and D. Kosloff and R. Kosloff},
+ title = {Wave propagation simulation in a linear viscoelastic medium},
+ journal = gji,
+ year = {1988},
+ volume = {95},
+ pages = {597-611}
+}
+
+ at ARTICLE{CaPoGe04,
+ author = {J. M. Carcione and F. Poletto and D. Gei},
+ title = {3-{D} wave simulation in anelastic media using the {K}elvin-{V}oigt
+ constitutive equation},
+ journal = jcp,
+ year = {2004},
+ volume = {196},
+ pages = {282-297}
+}
+
+ at ARTICLE{CaWa93,
+ author = {J. M. Carcione and P. J. Wang},
+ title = {A {C}hebyshev Collocation Method for the Wave Equation in Generalized
+ Coordinates},
+ journal = {Comp. Fluid Dyn. J.},
+ year = {1993},
+ volume = {2},
+ pages = {269-290}
+}
+
+ at INPROCEEDINGS{CaKoLaTiMiLeSnTr08,
+ author = {Laura Carrington and Dimitri Komatitsch and Michael Laurenzano and
+ Mustafa Tikir and David Mich\'ea and Nicolas {Le Goff} and Allan
+ Snavely and Jeroen Tromp},
+ title = {High-frequency simulations of global seismic wave propagation using
+ {SPECFEM3D\_GLOBE} on 62 thousand processor cores},
+ booktitle = {SC'08: Proceedings of the 2008 ACM/IEEE conference on Supercomputing},
+ year = {2008},
+ pages = {1-11},
+ address = {Austin, Texas, USA},
+ month = nov,
+ note = {Article \#60, {G}ordon {B}ell {P}rize finalist article},
+ doi = {10.1145/1413370.1413432}
+}
+
+ at ARTICLE{CaKiCrWoSpMu90,
+ author = {D. L. Carver and K. W. King and E. Cranswick and D. W. Worley and
+ P. Spudich and C. Mueller},
+ title = {Digital recordings of aftershocks of the {O}ctober 17, 1989, {L}oma
+ {P}rieta, {C}alifornia, earthquake: {S}anta {C}ruz, {L}os {G}atos,
+ and surrounding areas},
+ journal = {U.S. Geol. Surv. Open File Rep.},
+ year = {1990},
+ volume = {90},
+ pages = {90-683}
+}
+
+ at TECHREPORT{CaGa97,
+ author = {F. Casadei and E. Gabellini},
+ title = {Implementation of a 3{D} coupled {S}pectral {E}lement solver for
+ wave propagation and soil-structure interaction simulations},
+ institution = {European Commission Joint Research Center Report EUR17730EN},
+ year = {1997},
+ address = {Ispra, Italy}
+}
+
+ at ARTICLE{CaHa09,
+ author = {Folco Casadei and Jean-Pierre Halleux},
+ title = {Binary spatial partitioning of the central-difference time integration
+ scheme for explicit fast transient dynamics},
+ journal = ijnme,
+ year = {2009},
+ volume = {78},
+ pages = {1436-1473},
+ number = {12},
+ doi = {10.1002/nme.2533}
+}
+
+ at INPROCEEDINGS{CaStLeKoPiTr08,
+ author = {E. Casarotti and M. Stupazzini and S. Lee and D. Komatitsch and A.
+ Piersanti and J. Tromp},
+ title = {CUBIT and Seismic Wave Propagation Based Upon the Spectral-Element
+ Method: An Advanced Unstructured Mesher for Complex 3D Geological
+ Media},
+ booktitle = {Proceedings of the 16th International Meshing Roundtable},
+ year = {2008},
+ volume = {5B.4},
+ pages = {579-597}
+}
+
+ at ARTICLE{CaKiSa97,
+ author = {V. Caselles and R. Kimmel and G. Sapiro},
+ title = {Geodesic {A}ctive {C}ontours},
+ journal = {Int. J. Comput. Vis.},
+ year = {1997},
+ volume = {22},
+ pages = {61-79},
+ number = {1}
+}
+
+ at ARTICLE{CasBer92,
+ author = {B. Castagn\`ede and Y. Berthelot},
+ title = {Photoacoustic interactions by modulation and laser impact: applications
+ in mechanics and physics of anisotropic solids},
+ journal = {Journal d'Acoustique},
+ year = {1992},
+ volume = {5},
+ pages = {417-453}
+}
+
+ at ARTICLE{CaKaBr10,
+ author = {C. E. Castro and M. K\"aser and G. B. Brietzke},
+ title = {Seismic waves in heterogeneous material: subcell resolution of the
+ discontinuous Galerkin method},
+ journal = gji,
+ year = {2010},
+ volume = {182},
+ pages = {250-264},
+ number = {1}
+}
+
+ at ARTICLE{CaLe96,
+ author = {R. D. Catchings and W. H. K. Lee},
+ title = {Shallow velocity structure and {P}oisson's ratio at the {T}arzana,
+ {C}alifornia, strong-motion accelerometer site},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1704-1713}
+}
+
+ at ARTICLE{CeMcMcOwQuWr09,
+ author = {Elena Celledoni and Robert I. McLachlan and David I. McLaren and
+ Brynjulf Owren and G. Reinout W. Quispel and William M. Wright},
+ title = {Energy-preserving {R}unge-{K}utta methods},
+ journal = {M2AN},
+ year = {2009},
+ volume = {43},
+ pages = {645-649},
+ doi = {10.1051/m2an/2009020}
+}
+
+ at ARTICLE{CeKoKoRe85,
+ author = {C. Cerjan and D. Kosloff and R. Kosloff and M. Reshef},
+ title = {A nonreflecting boundary condition for discrete acoustic and elastic
+ wave equation},
+ journal = geophysics,
+ year = {1985},
+ volume = {50},
+ pages = {705-708}
+}
+
+ at BOOK{cerveny01,
+ title = {Seismic Ray Theory},
+ publisher = {Cambridge University Press},
+ year = {2001},
+ author = {V. Cerven\'{y}},
+ address = {Cambridge, UK}
+}
+
+ at ARTICLE{CeNuMa10,
+ author = {Ali Cevahir and Akira Nukada and Satoshi Matsuoka},
+ title = {High performance conjugate gradient solver on multi-{GPU} clusters
+ using hypergraph partitioning},
+ journal = {Computer Science Research and Development},
+ year = {2010},
+ volume = {25},
+ pages = {83-91},
+ number = {1-2},
+ doi = {10.1007/s00450-010-0112-6}
+}
+
+ at ARTICLE{ChSaHa96,
+ author = {F. J. Ch\'avez-Garc\'{\i}a and L. S\'anchez and D. Hatzfeld},
+ title = {Topographic site effects and HVSR. A comparison between observation
+ and theory},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1559-1573}
+}
+
+ at ARTICLE{Cha92,
+ author = {P. Chadwick},
+ title = {Some remarks on the existence of one-component surface waves in elastic
+ materials with symmetry},
+ journal = {Physica Scripta},
+ year = {1992},
+ volume = {T44},
+ pages = {94-97}
+}
+
+ at ARTICLE{Cha90,
+ author = {P. Chadwick},
+ title = {The behaviour of elastic surface waves polarized in a plane of material
+ symmetry. {I}. {G}eneral analysis},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1990},
+ volume = {A430},
+ pages = {213-240}
+}
+
+ at ARTICLE{Cha89,
+ author = {P. Chadwick},
+ title = {Wave propagation in transversely isotropic elastic media. {II}. {S}urface
+ waves},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1989},
+ volume = {A422},
+ pages = {67-101}
+}
+
+ at INCOLLECTION{ChaSmi82,
+ author = {P. Chadwick and G. D. Smith},
+ title = {Surface waves in cubic elastic materials},
+ booktitle = {Mechanics of solids},
+ publisher = {Pergamon Press},
+ year = {1982},
+ editor = {H. G. Hopkins and M. J. Sewell},
+ pages = {47-100},
+ address = {Oxford, United Kingdom}
+}
+
+ at INCOLLECTION{ChaSmi77,
+ author = {P. Chadwick and G. D. Smith},
+ title = {Foundations of the theory of surface waves in anisotropic elastic
+ materials},
+ booktitle = {Advances in Applied Mechanics},
+ publisher = {Academic Press, New York, USA},
+ year = {1977},
+ editor = {C. S. Yih},
+ volume = {17},
+ pages = {303-376}
+}
+
+ at ARTICLE{ChaWil92a,
+ author = {P. Chadwick and N. J. Wilson},
+ title = {The behaviour of elastic surface waves polarized in a plane of material
+ symmetry. {II}. {M}onoclinic media},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1992},
+ volume = {A438},
+ pages = {207-223}
+}
+
+ at ARTICLE{ChaWil92b,
+ author = {P. Chadwick and N. J. Wilson},
+ title = {The behaviour of elastic surface waves polarized in a plane of material
+ symmetry. {III}. {O}rthorhombic and cubic media},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1992},
+ volume = {A438},
+ pages = {225-247}
+}
+
+ at ARTICLE{ChaWu94,
+ author = {J. F. Chai and T. T. Wu},
+ title = {Determination of anisotropic elastic constants using laser-generated
+ surface waves},
+ journal = jasa,
+ year = {1994},
+ volume = {95},
+ pages = {3232-3241}
+}
+
+ at ARTICLE{ChBoSe08,
+ author = {St\'{e}phanie Chaillat and Marc Bonnet and Jean-Fran\c{c}ois Semblat},
+ title = {A multi-level fast multipole {BEM} for {3-D} elastodynamics in the
+ frequency domain},
+ journal = cmame,
+ year = {2008},
+ volume = {197},
+ pages = {4233-4249},
+ number = {49-50},
+ doi = {10.1016/j.cma.2008.04.024}
+}
+
+ at PHDTHESIS{Ch00,
+ author = {E. Chaljub},
+ title = {Mod\'elisation num\'erique de la propagation d'ondes sismiques en
+ g\'eom\'etrie sph\'erique : application \`a la sismologie globale
+ ({N}umerical modeling of the propagation of seismic waves in spherical
+ geometry: {a}pplication to global seismology)},
+ school = {Universit\'e Paris {\sc VII} Denis Diderot},
+ year = {2000},
+ address = {Paris, France}
+}
+
+ at ARTICLE{ChCaVi03,
+ author = {E. Chaljub and Y. Capdeville and J. P. Vilotte},
+ title = {Solving Elastodynamics in a Fluid-Solid Heterogeneous Sphere: a Parallel
+ Spectral-Element Approximation on Non-Conforming Grids},
+ journal = jcp,
+ year = {2003},
+ volume = {187},
+ pages = {457-491},
+ number = {2}
+}
+
+ at INPROCEEDINGS{CCGCK05,
+ author = {Emmanuel Chaljub and C\'ecile Cornou and Philippe Gu\'eguen and Mathieu
+ Causse and Dimitri Komatitsch},
+ title = {Spectral-element modeling of 3{D} wave propagation in the alpine
+ valley of {G}renoble, {F}rance},
+ booktitle = {Geophysical Research Abstracts},
+ year = {2005},
+ volume = {7, 05225},
+ publisher = {EGU 2nd general assembly, Wien, Austria}
+}
+
+ at INCOLLECTION{ChKoViCaVaFe07,
+ author = {Emmanuel Chaljub and Dimitri Komatitsch and Jean Pierre Vilotte and
+ Yann Capdeville and Bernard Valette and Gaetano Festa},
+ title = {Spectral Element Analysis in Seismology},
+ booktitle = {Advances in wave propagation in heterogeneous media},
+ publisher = {Elsevier - Academic Press, London, UK},
+ year = {2007},
+ editor = {Ru-Shan Wu and Val\'erie Maupin},
+ volume = {48},
+ series = {Advances in Geophysics},
+ pages = {365-419}
+}
+
+ at ARTICLE{ChMoTsBaKrKaStKr10,
+ author = {E. Chaljub and P. Moczo and S. Tsuno and P.-Y. Bard and J. Kristek
+ and M. K\"aser and M. Stupazzini and M. Kristekova},
+ title = {Quantitative Comparison of Four Numerical Predictions of 3D Ground
+ Motion in the Grenoble Valley, France},
+ journal = {Bull. Seismol. Soc. Am.},
+ year = {2010},
+ volume = {100},
+ pages = {1427-1455},
+ number = {4}
+}
+
+ at ARTICLE{ChTa97,
+ author = {E. Chaljub and A. Tarantola},
+ title = {Sensitivity of {SS} precursors to topography on the upper-mantle
+ 660-km discontinuity},
+ journal = grl,
+ year = {1997},
+ volume = {24},
+ pages = {2613-2616},
+ number = {21}
+}
+
+ at ARTICLE{ChVa04,
+ author = {E. Chaljub and B. Valette},
+ title = {Spectral element modelling of three-dimensional wave propagation
+ in a self-gravitating {E}arth with an arbitrarily stratified outer
+ core},
+ journal = gji,
+ year = {2004},
+ volume = {158},
+ pages = {131-141}
+}
+
+ at BOOK{openmp,
+ title = {Parallel Programming in {O}pen{MP}},
+ publisher = {Morgan Kaufmann, Elsevier},
+ year = {2000},
+ author = {Rohit Chandra and Ramesh Menon and Leo Dagum and David Kohr and Dror
+ Maydan and Jeff McDonald},
+ address = {San Francisco, USA}
+}
+
+ at ARTICLE{ChPr92,
+ author = {C. Chapman and R. G. Pratt},
+ title = {Traveltime tomography in anisotropic media -{I}: Theory},
+ journal = gji,
+ year = {1992},
+ volume = {109},
+ pages = {1-19}
+}
+
+ at ARTICLE{ChPh72,
+ author = {C. H. Chapman and R. A. Phinney},
+ title = {Diffracted seismic signals and their numerical solution},
+ journal = {Methods Comput. Phys.},
+ year = {1972},
+ volume = {12},
+ pages = {165-230}
+}
+
+ at ARTICLE{Che:2008:APS,
+ author = {Shuai Che and Michael Boyer and Jiayuan Meng and David Tarjan and
+ Jeremy W. Sheaffer and Kevin Skadron},
+ title = {A performance study of general-purpose applications on graphics processors
+ using {CUDA}},
+ journal = {Journal of Parallel and Distributed Computing},
+ year = {2008},
+ volume = {68},
+ pages = {1370--1380},
+ number = {10},
+ month = jun,
+ doi = {10.1016/j.jpdc.2008.05.014}
+}
+
+ at ARTICLE{ChTr07,
+ author = {Min Chen and Jeroen Tromp},
+ title = {Theoretical and numerical investigations of global and regional seismic
+ wave propagation in weakly anisotropic earth models},
+ journal = gji,
+ year = {2007},
+ volume = {168},
+ pages = {1130-1152},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2006.03218.x}
+}
+
+ at ARTICLE{ChTrHeKa07,
+ author = {M. Chen and J. Tromp and D. Helmberger and H. Kanamori},
+ title = {Waveform modeling of the slab beneath {J}apan},
+ journal = jgr,
+ year = {2007},
+ volume = {112},
+ pages = {B02305},
+ doi = {10.1029/2006JB004394}
+}
+
+ at ARTICLE{ChenBabu96,
+ author = {Q. Chen and I. Babu{\v s}ka},
+ title = {The optimal symmetrical points for polynomial interpolation of real
+ functions in the tetrahedron},
+ journal = cmame,
+ year = {1996},
+ volume = {137},
+ pages = {89-94}
+}
+
+ at ARTICLE{ChenBabu95,
+ author = {Q. Chen and I. Babu{\v s}ka},
+ title = {Approximate optimal points for polynomial interpolation of real functions
+ in an interval and in a triangle},
+ journal = cmame,
+ year = {1995},
+ volume = {128},
+ pages = {405-417}
+}
+
+ at INCOLLECTION{Che06,
+ author = {X. Chen},
+ title = {Generation and propagation of seismic {SH} waves in multilayered
+ media with irregular interfaces},
+ booktitle = {Advances in wave propagation in heterogeneous media},
+ publisher = {Elsevier},
+ year = {2006},
+ editor = {Ru-Shan Wu and Val\'erie Maupin},
+ series = {Advances in Geophysics}
+}
+
+ at ARTICLE{ChPe08,
+ author = {C. Chevalier and F. Pellegrini},
+ title = {{PT-SCOTCH}: a tool for efficient parallel graph ordering},
+ journal = {Parallel Computing},
+ year = {2008},
+ volume = {34},
+ pages = {318-331},
+ number = {6-8}
+}
+
+ at ARTICLE{Che06b,
+ author = {S. Chevrot},
+ title = {Finite-frequency vectorial tomography: a new method for high-resolution
+ imaging of upper mantle anisotropy},
+ journal = gji,
+ year = {2006},
+ volume = {165},
+ pages = {641-657},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2006.02982.x}
+}
+
+ at ARTICLE{ChFaKo04,
+ author = {S. Chevrot and N. Favier and D. Komatitsch},
+ title = {Shear wave splitting in three-dimensional anisotropic media},
+ journal = gji,
+ year = {2004},
+ volume = {159},
+ pages = {711-720},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2004.02432.x}
+}
+
+ at ARTICLE{ChLi96,
+ author = {W. C. Chew and Q. Liu},
+ title = {{P}erfectly {M}atched {L}ayers for elastodynamics: a new absorbing
+ boundary condition},
+ journal = jca,
+ year = {1996},
+ volume = {4},
+ pages = {341-359},
+ number = {4}
+}
+
+ at ARTICLE{ChWe94,
+ author = {W. C. Chew and W. H. Weedon},
+ title = {A {3-D} perfectly matched medium from modified {M}axwell's equations
+ with stretched coordinates},
+ journal = {Microwave Opt. Technol. Lett.},
+ year = {1994},
+ volume = {7},
+ pages = {599-604},
+ number = {13}
+}
+
+ at ARTICLE{Cho68,
+ author = {Alexandre Joel Chorin},
+ title = {Numerical solution of the {N}avier-{S}tokes equations},
+ journal = {Math. Comput.},
+ year = {1968},
+ volume = {22},
+ pages = {745-762}
+}
+
+ at BOOK{Cia89,
+ title = {Introduction to Numerical Linear Algebra and Optimisation},
+ publisher = {Cambridge University Press},
+ year = {1989},
+ author = {P. G. Ciarlet},
+ series = {Cambridge Texts in Applied Mathematics},
+ address = {Cambridge}
+}
+
+ at BOOK{pgc,
+ title = {The Finite Element Method for Elliptic Problems},
+ publisher = {North Holland},
+ year = {1978},
+ author = {P. G. Ciarlet},
+ address = {Amsterdam},
+ note = {530 p.}
+}
+
+ at ARTICLE{ClMeRoLo00,
+ author = {Eric Cl\'ev\'ed\'e and Charles M\'egnin and Barabara Romanowicz and
+ Philippe Lognonn\'e},
+ title = {Seismic waveform modeling and surface wave tomography in a three-dimensional
+ {E}arth: asymptotic and non-asymptotic approaches},
+ journal = pepi,
+ year = {2000},
+ volume = {119(1)},
+ pages = {37-56}
+}
+
+ at ARTICLE{Cla72,
+ author = {M. N. Clark},
+ title = {Intensity of shaking estimated from displaced stones},
+ journal = {U.S. Geol. Surv. Prof. Pap.},
+ year = {1972},
+ volume = {787},
+ pages = {175-182}
+}
+
+ at ARTICLE{ClSiYeJaWaBe95,
+ author = {T. J. Clarke and P. G. Silver and Y. L. Yeh and D. E. James and T.
+ C. Wallace and S. L. Beck},
+ title = {Close in {ScS} and {sScS} reverberations from the 9 {J}une 1994 {B}olivian
+ earthquake},
+ journal = grl,
+ year = {1995},
+ volume = {22},
+ pages = {2313-2316},
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+}
+
+ at ARTICLE{ClEn77,
+ author = {R. Clayton and B. Engquist},
+ title = {Absorbing boundary conditions for acoustic and elastic wave equations},
+ journal = bssa,
+ year = {1977},
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+}
+
+ at ARTICLE{ClLa95,
+ author = {R. H. Clouser and C. A. Langston},
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+ features near the {NORESS} array},
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+}
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+ at ARTICLE{CoSc95,
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+}
+
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+ of earthquake interaction},
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+}
+
+ at BOOK{CoKaSh00,
+ title = {Discontinuous {G}alerkin Methods: Theory, Computation and Applications},
+ publisher = {Springer},
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+}
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+ title = {Ondelettes et traitement num\'erique du signal},
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+ at BOOK{Coh02,
+ title = {Higher-order numerical methods for transient wave equations},
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+}
+
+ at INPROCEEDINGS{Coh88,
+ author = {G. Cohen},
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+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
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+}
+
+ at ARTICLE{CoFa05,
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+ title = {Mixed Spectral Finite Elements for the Linear Elasticity System in
+ Unbounded Domains},
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+ volume = {26},
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+ number = {3},
+ doi = {10.1137/S1064827502407457}
+}
+
+ at ARTICLE{CoFa00,
+ author = {G. Cohen and S. Fauqueux},
+ title = {Mixed finite elements with mass lumping for the transient wave equation},
+ journal = jca,
+ year = {2000},
+ volume = {8},
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+ number = {1},
+ doi = {10.1142/S0218396X0000011X}
+}
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+ author = {G. Cohen and P. Joly},
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+
+ at ARTICLE{CoJoRoTo01,
+ author = {G. Cohen and P. Joly and J. E. Roberts and N. Tordjman},
+ title = {Higher-Order Triangular Finite Elements with Mass Lumping for the
+ Wave Equation},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {2001},
+ volume = {38},
+ pages = {2047-2078},
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+ doi = {10.1137/S0036142997329554}
+}
+
+ at INPROCEEDINGS{CoJoTo93,
+ author = {G. Cohen and P. Joly and N. Tordjman},
+ title = {Construction and analysis of higher-order finite elements with mass
+ lumping for the wave equation},
+ booktitle = {Proceedings of the second international conference on mathematical
+ and numerical aspects of wave propagation},
+ year = {1993},
+ editor = {R. Kleinman},
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+ publisher = {SIAM, Philadelphia, Pennsylvania, USA}
+}
+
+ at ARTICLE{Col97,
+ author = {F. Collino},
+ title = {{P}erfectly matched absorbing layers for the paraxial equations},
+ journal = jcp,
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+}
+
+ at ARTICLE{CoFoJo03a,
+ author = {Collino, F. and Fouquet, T. and Joly, P.},
+ title = {A conservative space-time mesh refinement method for the 1-{D} wave
+ equation. {I}. {C}onstruction},
+ journal = {Numerische Mathematik},
+ year = {2003},
+ volume = {95},
+ pages = {197-221},
+ number = {2}
+}
+
+ at ARTICLE{CoFoJo03b,
+ author = {Collino, F. and Fouquet, T. and Joly, P.},
+ title = {A conservative space-time mesh refinement method for the 1-{D} wave
+ equation. {II}. {A}nalysis},
+ journal = {Numerische Mathematik},
+ year = {2003},
+ volume = {95},
+ pages = {223-251},
+ number = {2}
+}
+
+ at TECHREPORT{CoFoJo98,
+ author = {F. Collino and T. Fouquet and P. Joly},
+ title = {Analyse num\'erique d'une m\'ethode de raffinement de maillage espace-temps
+ pour l'\'equation des ondes},
+ institution = {INRIA},
+ year = {1998},
+ note = {Research report RR-3474}
+}
+
+ at ARTICLE{CoMo98a,
+ author = {F. Collino and P. Monk},
+ title = {Optimizing the {P}erfectly {M}atched {L}ayer},
+ journal = cmame,
+ year = {1998},
+ volume = {164},
+ pages = {157-171}
+}
+
+ at ARTICLE{CoMo98b,
+ author = {F. Collino and P. Monk},
+ title = {The {P}erfectly {M}atched {L}ayer in curvilinear coordinates},
+ journal = {SIAM J. Sci. Comput.},
+ year = {1998},
+ volume = {19},
+ pages = {2061-2090},
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+}
+
+ at ARTICLE{CoTs01,
+ author = {F. Collino and C. Tsogka},
+ title = {Application of the {PML} absorbing layer model to the linear elastodynamic
+ problem in anisotropic heterogeneous media},
+ journal = geophysics,
+ year = {2001},
+ volume = {66},
+ pages = {294-307},
+ number = {1}
+}
+
+ at ARTICLE{cormier1999,
+ author = {V. F. Cormier},
+ title = {Anisotropy of heterogeneity scale lengths in the lower mantle from
+ PKIKP precursors},
+ journal = gji,
+ year = {1999},
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+}
+
+ at ARTICLE{Cor86,
+ author = {V. F. Cormier},
+ title = {Synthesis of body waves in transversely isotropic {E}arth models},
+ journal = bssa,
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+}
+
+ at ARTICLE{cornou03b,
+ author = {C\'ecile Cornou and Pierre-Yves Bard and Michel Dietrich},
+ title = {Contribution of Dense Array Analysis to the identification and quantification
+ of basin-edge-induced waves, {P}art {II}: {A}pplication to the {G}renoble
+ basin ({F}rench {A}lps)},
+ journal = bssa,
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+ volume = {93},
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+ at ARTICLE{Corones,
+ author = {J. Corones},
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+
+ at INPROCEEDINGS{Corrigan:2009:RUG,
+ author = {Andrew Corrigan and Fernando Camelli and Rainald L{\"o}hner and John
+ Wallin},
+ title = {Running unstructured grid based {CFD} solvers on modern graphics
+ hardware},
+ booktitle = {19th AIAA Computational Fluid Dynamics Conference},
+ year = {2009},
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+}
+
+ at ARTICLE{CoFrLe28,
+ author = {R. Courant and K. O. Friedrichs and H. Lewy},
+ title = {\"{U}ber die partiellen {D}ifferenzengleichungen der mathematischen
+ {P}hysik},
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+}
+
+ at ARTICLE{CoIsRe52,
+ author = {R. Courant and E. Isaacson and M. Rees},
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+ finite differences},
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+ at ARTICLE{Cow41,
+ author = {T. G. Cowling},
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+
+ at ARTICLE{Cra84,
+ author = {S. Crampin},
+ title = {An introduction to wave propagation in anisotropic media},
+ journal = gjras,
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+}
+
+ at ARTICLE{CrChHi84,
+ author = {S. Crampin and E. M. Chesnokov and R. G. Hipkin},
+ title = {Seismic anisotropy - the state of the art {II}},
+ journal = gjras,
+ year = {1984},
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+}
+
+ at ARTICLE{CraTay77,
+ author = {S. Crampin and D. B. Taylor},
+ title = {The propagation of surface waves in anisotropic media},
+ journal = gji,
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+}
+
+ at ARTICLE{CrPiNoMcTa90,
+ author = {E. Crase and A. Pica and M. Noble and J. McDonald and A. Tarantola},
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+
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+ phase {PKP} and {PKIKP}},
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+}
+
+ at INCOLLECTION{CrJeMoPiSe99,
+ author = {P. Cristini and F. Jensen and D. Morisset and J. Piraux and J. P.
+ Sessarego},
+ title = {Experimental benchmarks for numerical propagation models: comparison
+ between numerical results and tank experiments for deep and shallow
+ water environments},
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+}
+
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+}
+
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+}
+
+ at INPROCEEDINGS{CuMc69,
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+}
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+}
+
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+}
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+ {F}ortran90 and {MPI}},
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+}
+
+ at ARTICLE{Dar98a,
+ author = {A. N. Darinskii},
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+ journal = {Wave Motion},
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+}
+
+ at ARTICLE{Dar98b,
+ author = {A. N. Darinskii},
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+ solid layer interface. {II} {L}eaky waves given rise to by exceptional
+ bulk waves},
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+ year = {1998},
+ volume = {103},
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+}
+
+ at ARTICLE{Dar97,
+ author = {A. N. Darinskii},
+ title = {On the theory of leaky waves in crystals},
+ journal = {Wave Motion},
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+}
+
+ at ARTICLE{DarAlsLot99,
+ author = {A. N. Darinskii and V. I. Alshits and J. Lothe},
+ title = {Simple reflection and leaky waves in the vicinity of a line of exceptional
+ bulk waves},
+ journal = {Wave Motion},
+ year = {1999},
+ volume = {30},
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+}
+
+ at ARTICLE{DarAlsLotLyuShu98,
+ author = {A. N. Darinskii and V. I. Alshits and J. Lothe and V. N. Lyubimov
+ and A. L. Shuvalov},
+ title = {An existence criterion for the branch of two-component surface waves
+ in anisotropic elastic media},
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+ year = {1998},
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+}
+
+ at ARTICLE{DarWei05,
+ author = {A. N. Darinskii and M. Weihnacht},
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+ and computations},
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+ year = {2005},
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+}
+
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+ author = {E. Darrigrand},
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+ for the 3{D} {H}elmholtz {E}quation},
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+ year = {2003},
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+}
+
+ at ARTICLE{Dau88,
+ author = {I. Daubechies},
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+}
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+ at ARTICLE{DaWe73,
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+
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+ author = {P. M. Davis and J. L. Rubinstein and K. H. Liu and S. S. Gao and
+ L. Knopoff},
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+ waves},
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+}
+
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+ author = {T. L. Davis and J. Namson and R. F. Yerkes},
+ title = {A cross-section of the {L}os {A}ngeles area: seismically active fold-and-thrust
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+}
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+}
+
+ at ARTICLE{DeSeWh08,
+ author = {De Basabe, J. D. and Sen, M. K. and Wheeler, M. F.},
+ title = {The interior penalty discontinuous {G}alerkin method for elastic
+ wave propagation: grid dispersion},
+ journal = gji,
+ year = {2008},
+ volume = {175},
+ pages = {83-93},
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+}
+
+ at ARTICLE{DeSe10,
+ author = {Jon{\'a}s D. {De Basabe} and Mrinal K. Sen},
+ title = {Stability of the high-order finite elements for acoustic or elastic
+ wave propagation with high-order time stepping},
+ journal = gji,
+ year = {2010},
+ volume = {181},
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+ number = {1},
+ doi = {10.1111/j.1365-246X.2010.04536.x}
+}
+
+ at ARTICLE{DeSe07,
+ author = {Jon{\'a}s D. {De Basabe} and Mrinal K. Sen},
+ title = {Grid dispersion and stability criteria of some common finite-element
+ methods for acoustic and elastic wave equations},
+ journal = geophysics,
+ year = {2007},
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+}
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+ title = {A practical guide to splines},
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+ author = {J. C. {De Bremaecker}},
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+}
+
+ at INPROCEEDINGS{DeCuFeVi06,
+ author = {E. Delavaud and P. Cupillard and G. Festa and J.-P. Vilotte},
+ title = {3{D} Spectral Element Method simulations of the seismic response
+ in the Caracas basin},
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+ Geology on Seismic Motion},
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+}
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+ title = {Analyse num\'erique et \'equations diff\'erentielles},
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+}
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+}
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+}
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+}
+
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+ author = {J. X. Dessa and G. Pascal},
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+}
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+ title = {High-Order Methods for Incompressible Fluid Flow},
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+ author = {C. DeWitt-Morette},
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+ author = {Julien Diaz and Abdela\^aziz Ezziani},
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+ media. {Part I: the 2D} case},
+ journal = {Communications in Computational Physics},
+ year = {2010},
+ volume = {7},
+ pages = {171-194},
+ number = {1},
+ note = {In preparation.}
+}
+
+ at ARTICLE{DiGr09,
+ author = {Julien Diaz and Marcus J. Grote},
+ title = {Energy Conserving Explicit Local Time Stepping for Second-Order Wave
+ Equations},
+ journal = {SIAM J. Sci. Comput.},
+ year = {2009},
+ volume = {31},
+ pages = {1985-2014},
+ number = {3}
+}
+
+ at ARTICLE{DiJo06,
+ author = {J. Diaz and P. Joly},
+ title = {A time-domain analysis of {PML} models in acoustics},
+ journal = cmame,
+ year = {2006},
+ volume = {195},
+ pages = {3820-3853},
+ number = {29-32},
+ doi = {10.1016/j.cma.2005.02.031}
+}
+
+ at ARTICLE{DiJo05,
+ author = {J. Diaz and P. Joly},
+ title = {A robust high-order non-conforming finite-element formulation for
+ time domain fluid-structure interaction},
+ journal = jca,
+ year = {2005},
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+}
+
+ at MISC{dobbswebsite,
+ author = {Dr. Dobb's},
+ month = {March},
+ year = {2008},
+ note = {{D}r. Dobb's Portal web site},
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+}
+
+ at INPROCEEDINGS{DoBiBo07,
+ author = {R. Dolbeau and S. Bihan and F. Bodin},
+ title = {{HMPP: A} Hybrid Multi-core Parallel Programming Environment},
+ booktitle = {Proceedings of the Workshop on General Purpose Processing on Graphics
+ Processing Units (GPGPU'2007)},
+ year = {2007},
+ pages = {1-5},
+ address = {Boston, Massachusetts, USA},
+ month = {October},
+ url = {www.irisa.fr/caps/projects/Astex}
+}
+
+ at ARTICLE{DoShGuMa05,
+ author = {Liangguo Dong and Deping She and Luping Guan and Zaitian Ma},
+ title = {An eigenvalue decomposition method to construct absorbing boundary
+ conditions for acoustic and elastic wave equations},
+ journal = {J. Geophys. Eng.},
+ year = {2005},
+ volume = {2},
+ pages = {192-198},
+ doi = {10.1088/1742-2132/2/3/003}
+}
+
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+ journal = {Geophys. J. R. astr. Soc.},
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+
+ at ARTICLE{Doornbos79,
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+}
+
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+ author = {Christophe Doursat},
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+ et elliptiques},
+ school = {Universit\'e Paris {\sc VI} Jussieu},
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+}
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+
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+ title = {A nonsplit complex frequency-shifted {PML} based on recursive integration
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+ journal = geophysics,
+ year = {2007},
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+}
+
+ at ARTICLE{DrGi07b,
+ author = {F. H. Drossaert and A. Giannopoulos},
+ title = {Complex frequency shifted convolution {PML} for {FDTD} modelling
+ of elastic waves},
+ journal = {Wave Motion},
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+}
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+ and Freysteinn Sigmundsson},
+ title = {Three-dimensional mechanical models for the {J}une 2000 earthquake
+ sequence in the south {I}celand seismic zone},
+ journal = {Tectonophysics},
+ year = {2008},
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+ pages = {12-29},
+ doi = {10.1016/j.tecto.2008.05.020}
+}
+
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+ author = {N. Dubos and A. Souriau and C. Ponsolles and J. F. Fels and G. S\'en\'echal},
+ title = {{\'E}tude des effets de sites dans la ville de {L}ourdes ({P}yr\'en\'ees,
+ {F}rance) par la m\'ethode des rapports spectraux},
+ journal = {Bull. Soc. G\'eol. Fr.},
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+}
+
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+ author = {Th. S. Duffy},
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+ deep mantle},
+ journal = {Phil. Trans. R. Soc. A},
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+}
+
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+ author = {M. Dumbser and M. K\"aser},
+ title = {An arbitrary high-order discontinuous {G}alerkin method for elastic
+ waves on unstructured meshes-{II}. {T}he three-dimensional isotropic
+ case},
+ journal = gji,
+ year = {2006},
+ volume = {167},
+ pages = {319-336},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2006.03120.x}
+}
+
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+ title = {An arbitrary high-order discontinuous {G}alerkin method for elastic
+ waves on unstructured meshes, {P}art {V}: Local time stepping and
+ $p$-adaptivity},
+ journal = gji,
+ year = {2007},
+ volume = {171},
+ pages = {695-717},
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+}
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+ author = {Fabrice Dupros and de Martin, Florent and Evelyne Foerster and Dimitri
+ Komatitsch and Jean Roman},
+ title = {High-performance finite-element simulations of seismic wave propagation
+ in three-dimensional non linear inelastic geological media},
+ journal = {Parallel Computing},
+ year = {2010},
+ volume = {36},
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+ doi = {10.1016/j.parco.2009.12.011}
+}
+
+ at ARTICLE{DuJoGuKeKo10,
+ author = {Guilhem Dupuy and Bruno Jobard and Sebastien Guillon and Noomane
+ Keskes and Dimitri Komatitsch},
+ title = {Parallel extraction and simplification of large isosurfaces using
+ an extended tandem algorithm},
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+ year = {2010},
+ volume = {42},
+ pages = {129-138},
+ number = {2},
+ doi = {10.1016/j.cad.2009.04.016}
+}
+
+ at INPROCEEDINGS{DuLaPr,
+ author = {B. Duquet and B. Lavaud and F. Prat},
+ title = {Improving {GSP} Extrapolators},
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+}
+
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+ title = {M\'ecanique des milieux continus},
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+}
+
+ at INCOLLECTION{dziewonski:2000,
+ author = {A. M. Dziewo\'nski},
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+ G. Anderson and G. A. Carver and A. J. Crone and T. E. Dawson and
+ H. Fletcher and R. Hansen and E. L. Harp and R. A. Harris and D.
+ P. Hill and S. Hreinsdottir and R. W. Jibson and L. M. Jones and
+ R. Kayen and D. K. Keefer and C. F. Larsen and S. C. Moran and S.
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+}
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+
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+}
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+}
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+ title = {Surface dynamic response functions of anisotropic solids},
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+}
+
+ at ARTICLE{EveKimMaz97,
+ author = {A. G. Every and K. Y. Kim and A. A. Maznev},
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+}
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+ {B}iot},
+ journal = {Revue Africaine de la Recherche en Informatique et Math\'ematiques
+ Appliqu\'ees ARIMA},
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+}
+
+ at PHDTHESIS{Ez2005,
+ author = {A. Ezziani},
+ title = {Mod\'elisation math\'ematique et num\'erique de la propagation d'ondes
+ dans des milieux visco\'elastiques et poro\'elastiques},
+ school = {Universit\'e Paris IX, France},
+ year = {2005},
+ address = {Paris, France}
+}
+
+ at ARTICLE{FaMaPaQu97,
+ author = {E. Faccioli and F. Maggio and R. Paolucci and A. Quarteroni},
+ title = {2{D} and 3{D} elastic wave propagation by a pseudo-spectral domain
+ decomposition method},
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+ year = {1997},
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+}
+
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+ author = {E. Faccioli and F. Maggio and A. Quarteroni and A. Tagliani},
+ title = {Spectral-domain decomposition methods for the solution of acoustic
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+ year = {1996},
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+}
+
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+ author = {Falk, Richard S. and Richter, Gerard R.},
+ title = {Explicit Finite Element Methods for Symmetric Hyperbolic Equations},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1999},
+ volume = {36},
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+}
+
+ at ARTICLE{FaLiHe02,
+ author = {G. X. Fan and Q. H. Liu and J. S. Hesthaven},
+ title = {Multidomain pseudospectral time-domain simulations of scattering
+ by objects buried in lossy media},
+ journal = {IEEE Trans. Geosci. Remote Sens.},
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+ volume = {GE-40},
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+}
+
+ at INPROCEEDINGS{FaQiKa08,
+ author = {Zhe Fan and Feng Qiu and Arie E. Kaufman},
+ title = {Zippy: A Framework for Computation and Visualization on a {GPU} Cluster},
+ booktitle = {Proceedings of the Eurographics'2008 Symposium on Parallel Graphics
+ and Visualization (EGPGV'08)},
+ year = {2008},
+ editor = {G. Drettakis and R. Scopigno},
+ volume = {27(2)},
+ pages = {341-350},
+ address = {Hersonissos, Crete, Greece},
+ month = {April}
+}
+
+ at INPROCEEDINGS{Fan:2004:GCF,
+ author = {Zhe Fan and Feng Qiu and Arie E. Kaufman and Suzanne Yoakum-Stover},
+ title = {{GPU} Cluster for High Performance Computing},
+ booktitle = {{SC '04}: Proceedings of the 2004 {ACM/IEEE} conference on Supercomputing},
+ year = {2004},
+ pages = {47},
+ month = nov,
+ doi = {10.1109/SC.2004.26}
+}
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+}
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+ title = {The discontinuous enrichment method},
+ journal = cmame,
+ year = {2001},
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+}
+
+ at ARTICLE{farhathararihetmaniuk20031,
+ author = {C. Farhat and I. Harari and U. Hetmaniuk},
+ title = {A discontinuous {G}alerkin method with {L}agrange multipliers for
+ the solution of {H}elmholtz problems in the mid-frequency regime},
+ journal = cmame,
+ year = {2003},
+ volume = {192},
+ pages = {1389-1419}
+}
+
+ at ARTICLE{farhathararihetmaniuk20032,
+ author = {C. Farhat and I. Harari and U. Hetmaniuk},
+ title = {The discontinuous enrichment method for multiscale analysis},
+ journal = cmame,
+ year = {2003},
+ volume = {192},
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+}
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+ at TECHREPORT{Far87,
+ author = {C. H. Farhat},
+ title = {A simple and efficient automatic {FEM} domain decomposer},
+ institution = {University of Colorado},
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+ address = {Boulder, Colorado}
+}
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+ author = {G. W. Farnell},
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+ (ISSWAS86)" International Symposium},
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+}
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+ author = {V. Farra},
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+}
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+ author = {Kayvon Fatahalian and Mike Houston},
+ title = {A Closer Look at {GPUs}},
+ journal = {Communications of the ACM},
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+ volume = {51},
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+ doi = {10.1145/1400181.1400197}
+}
+
+ at INPROCEEDINGS{Fatica:2009:ALW,
+ author = {Massimiliano Fatica},
+ title = {Accelerating {L}inpack with {CUDA} on heterogenous clusters},
+ booktitle = {GPGPU-2: Proceedings of 2nd Workshop on General Purpose Processing
+ on Graphics Processing Units},
+ year = {2009},
+ editor = {David Kaeli and Miriam Leeser},
+ number = {383},
+ series = {ACM International Conference Proceeding Series},
+ pages = {46--51},
+ month = mar,
+ doi = {10.1145/1513895.1513901}
+}
+
+ at PHDTHESIS{Fau03,
+ author = {Sandrine Fauqueux},
+ title = {El\'ements finis mixtes spectraux et couches absorbantes parfaitement
+ adapt\'ees pour la propagation d'ondes \'elastiques en r\'egime transitoire},
+ school = {Universit\'e Paris-Dauphine},
+ year = {2003},
+ address = {Paris, France},
+ month = {February}
+}
+
+ at ARTICLE{FaCh03,
+ author = {N. Favier and S. Chevrot},
+ title = {Sensitivity kernels for shear wave splitting in transverse isotropic
+ media},
+ journal = gji,
+ year = {2003},
+ volume = {153},
+ pages = {213-228},
+ number = {1}
+}
+
+ at ARTICLE{FaChKo04,
+ author = {N. Favier and S. Chevrot and D. Komatitsch},
+ title = {Near-field influences on shear wave splitting and traveltime sensitivity
+ kernels},
+ journal = gji,
+ year = {2004},
+ volume = {156},
+ pages = {467-482},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2004.02178.x}
+}
+
+ at ARTICLE{gp03,
+ author = {N. Favretto-Cristini and E. de Bazelaire},
+ title = {P{P} amplitude bias caused by interface scattering: are diffracted
+ waves guilty?},
+ journal = {Geophysical Prospecting},
+ year = {2003},
+ volume = {51},
+ pages = {99-115}
+}
+
+ at ARTICLE{FaKoCaCa11,
+ author = {Nathalie Favretto-Cristini and Dimitri Komatitsch and Jos\'e Carcione
+ and Fabio Cavallini},
+ title = {Elastic surface waves in crystals: {P}art {I} : Review of the physics},
+ journal = {Ultrasonics},
+ year = {2011},
+ volume = {51},
+ pages = {653-660},
+ number = {6},
+ doi = {10.1016/j.ultras.2011.02.007}
+}
+
+ at ARTICLE{Fejer32,
+ author = {L. Fej\'er},
+ title = {Bestimmung derjenigen {A}bszissen eines {I}ntervalles f\"ur welche
+ die {Q}uadratsumme der {G}rundfunktionen der {L}agrangeschen {I}nterpolation
+ im {I}ntervalle $[-1,1]$ ein m\"oglichst kleines {M}aximum besitzt},
+ journal = {Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mt. Ser. II},
+ year = {1932},
+ volume = {1},
+ pages = {263-276}
+}
+
+ at ARTICLE{FeDe84,
+ author = {C. A. Felippa and J. A. Deruntz},
+ title = {Finite-element analysis of shock-induced hull cavitation},
+ journal = cmame,
+ year = {1984},
+ volume = {44},
+ pages = {297-337}
+}
+
+ at ARTICLE{Felsen,
+ author = {L. B. Felsen},
+ title = {Geometrical Theory of Diffraction, Evanescent Waves, Complex Rays
+ and {G}aussian Beams},
+ journal = gjras,
+ year = {1984},
+ volume = {79},
+ pages = {77-88}
+}
+
+ at ARTICLE{FeBo06,
+ author = {Clark H. Fenton and Julian J. Bommer},
+ title = {The {M}w7 {M}achaze, {M}ozambique, Earthquake of 23 {F}ebruary 2006},
+ journal = {Seismological Research Letters},
+ year = {2006},
+ volume = {77},
+ pages = {426-439},
+ number = {4}
+}
+
+ at ARTICLE{FeDeVi05,
+ author = {G. Festa and E. Delavaud and J. P. Vilotte},
+ title = {Interaction between surface waves and absorbing boundaries for wave
+ propagation in geological basins: {2D} numerical simulations},
+ journal = grl,
+ year = {2005},
+ volume = {32},
+ pages = {L20306},
+ number = {20},
+ doi = {10.1029/2005GL024091}
+}
+
+ at ARTICLE{FeNi03,
+ author = {Gaetano Festa and Stefan Nielsen},
+ title = {{PML} absorbing boundaries},
+ journal = bssa,
+ year = {2003},
+ volume = {93},
+ pages = {891-903}
+}
+
+ at ARTICLE{FeVi05,
+ author = {G. Festa and J. P. Vilotte},
+ title = {The {N}ewmark scheme as velocity-stress time-staggering: an efficient
+ {PML} implementation for spectral-element simulations of elastodynamics},
+ journal = gji,
+ year = {2005},
+ volume = {161},
+ pages = {789-812},
+ doi = {10.1111/j.1365-246X.2005.02601.x}
+}
+
+ at BOOK{Fic10,
+ title = {{Full Seismic Waveform Modelling and Inversion}},
+ publisher = {Springer Verlag},
+ year = {2010},
+ author = {Andreas Fichtner}
+}
+
+ at ARTICLE{FiIgBuKe09,
+ author = {Andreas Fichtner and Heiner Igel and Hans-Peter Bunge and Brian L.
+ N. Kennett},
+ title = {Simulation and inversion of seismic wave propagation on continental
+ scales based on a spectral-element method},
+ journal = {Journal of Numerical Analysis, Industrial and Applied Mathematics},
+ year = {2009},
+ volume = {4},
+ pages = {11-22},
+ number = {1-2}
+}
+
+ at ARTICLE{fink99,
+ author = {Mathias Fink and Didier Cassereau and Arnaud Derode and Claire Prada
+ and Philippe Roux and Mickael Tanter and Jean-Louis Thomas and F.
+ Wu},
+ title = {Time-reversed acoutics},
+ journal = {Reports on Progress in Physics},
+ year = {2000},
+ volume = {63},
+ pages = {1933},
+ number = {12},
+ doi = {10.1088/0034-4885/63/12/202}
+}
+
+ at ARTICLE{Fis90,
+ author = {P. F. Fischer},
+ title = {Analysis and application of a parallel spectral element method for
+ the solution of the {N}avier-{S}tokes equations},
+ journal = cmame,
+ year = {1990},
+ volume = {80},
+ pages = {483-491}
+}
+
+ at PHDTHESIS{Fis89,
+ author = {P. F. Fischer},
+ title = {Spectral element solution of the {N}avier-{S}tokes equations on high
+ performance distributed-memory parallel processors},
+ school = {Massachusetts Institute of Technology},
+ year = {1989},
+ address = {Cambridge, Massachusetts}
+}
+
+ at ARTICLE{FiHoKaRoPa88,
+ author = {P. F. Fischer and L. W. Ho and G. E. Karniadakis and E. M. R{\o}nquist
+ and A. T. Patera},
+ title = {Recent advances in parallel spectral element simulation of unsteady
+ incompressible flows},
+ journal = {Computers and Structures},
+ year = {1988},
+ volume = {30},
+ pages = {217-231}
+}
+
+ at ARTICLE{FiRo94,
+ author = {P. F. Fischer and E. M. R{\o}nquist},
+ title = {{S}pectral-element Methods for Large Scale Parallel {N}avier-{S}tokes
+ Calculations},
+ journal = cmame,
+ year = {1994},
+ volume = {116},
+ pages = {69-76}
+}
+
+ at ARTICLE{Fish3,
+ author = {L. Fishman},
+ title = {Applications of {D}irectional {W}avefield {D}ecomposition, {P}hase
+ {S}pace and {P}ath {I}ntegral {M}ethods to {S}eismic {W}ave {P}ropagation
+ and {I}nversion},
+ journal = {Pure and Applied Geophysics},
+ year = {2002},
+ volume = {159},
+ pages = {1637-1679}
+}
+
+ at ARTICLE{Fish1,
+ author = {L. Fishman},
+ title = {Exact and {O}perator {R}ational {A}pproximate {S}olutions of the
+ {H}elmholtz, {W}eyl {C}omposition {E}quation in {U}nderwater {A}coustics
+ - the {Q}uadratic {P}rofile},
+ journal = {J. Math. Phys.},
+ year = {1992},
+ volume = {33},
+ pages = {1887-1914}
+}
+
+ at ARTICLE{Fish2,
+ author = {L. Fishman and J. J. McCoy and S. C. Wales},
+ title = {Factorization and Path Integration of the {H}elmholtz Equation :
+ {N}umerical Algorithms},
+ journal = {J. Acoust. Soc. Am.},
+ year = {1987},
+ volume = {81},
+ pages = {1355-1376}
+}
+
+ at BOOK{Fle91,
+ title = {Computational Fluid Dynamics},
+ publisher = {Springer-Verlag},
+ year = {1991},
+ author = {C. A. J. Fletcher},
+ address = {New York}
+}
+
+ at ARTICLE{taf,
+ author = {T. A. Foley},
+ title = {Weighted bicubic spline interpolation to rapidly varying data},
+ journal = {ACM Trans. Graphics},
+ year = {1987},
+ volume = {6},
+ pages = {1-18}
+}
+
+ at PHDTHESIS{Fon06,
+ author = {Mathieu Fontes},
+ title = {Propri\'et\'es math\'ematiques de mod\`eles g\'eophysiques pour l'absorption
+ des ondes. {A}pplication aux conditions de bords absorbants. ({M}athematical
+ properties of geophysical models for the absorption of waves. {A}pplication
+ to absorbing boundary conditions)},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {2006},
+ address = {Pau, France},
+ month = {July}
+}
+
+ at ARTICLE{For88,
+ author = {B. Fornberg},
+ title = {The pseudospectral method: accurate representation of interfaces
+ in elastic wave calculations},
+ journal = geophysics,
+ year = {1988},
+ volume = {53},
+ pages = {625-637}
+}
+
+ at ARTICLE{For75,
+ author = {D. W. Forsyth},
+ title = {The early structural evolution and anisotropy of the oceanic upper
+ mantle},
+ journal = gjras,
+ year = {1975},
+ volume = {43},
+ pages = {103-162}
+}
+
+ at ARTICLE{FoFiWy01,
+ author = {M. J. Fouch and K. M. Fischer and M. E. Wysession},
+ title = {Lowermost mantle anisotropy beneath the {P}acific: {I}maging the
+ source of the {H}awaiian plume},
+ journal = epsl,
+ year = {2001},
+ volume = {190},
+ pages = {167-180}
+}
+
+ at ARTICLE{rf,
+ author = {R. Franke},
+ title = {Thin plate spline with tension},
+ journal = {Computer Aided Geometric Design},
+ year = {1985},
+ volume = {2},
+ pages = {87-95}
+}
+
+ at ARTICLE{Fra93,
+ author = {A. Frankel},
+ title = {Three-dimensional simulations of ground motions in the {S}an {B}ernardino
+ valley, {C}alifornia, for hypothetical earthquakes on the {S}an {A}ndreas
+ fault},
+ journal = bssa,
+ year = {1993},
+ volume = {83},
+ pages = {1020-1041}
+}
+
+ at ARTICLE{FrLe92,
+ author = {A. Frankel and W. Leith},
+ title = {Evaluation of topographic effects on {{\it P}} and {{\it S}} waves
+ of explosions at the northern {N}ovaya {Z}emlya test site using 3-{D}
+ numerical simulations},
+ journal = grl,
+ year = {1992},
+ volume = {19},
+ pages = {1887-1890}
+}
+
+ at ARTICLE{FrVi92,
+ author = {A. Frankel and J. Vidale},
+ title = {A three-dimensional simulation of seismic waves in the {S}anta {C}lara
+ valley, {C}alifornia, from the {L}oma {P}rieta aftershock},
+ journal = bssa,
+ year = {1992},
+ volume = {82},
+ pages = {2045-2074}
+}
+
+ at ARTICLE{FrDa95,
+ author = {Wolfgang Friederich and J\"org Dalkolmo},
+ title = {Complete synthetic seismograms for a spherically-symmetric {E}arth
+ by a numerical computation of the {G}reen's function in the frequency
+ domain},
+ journal = gji,
+ year = {1995},
+ volume = {122},
+ pages = {537-550},
+ number = {2},
+ doi = {10.1111/j.1365-246X.1995.tb07012.x}
+}
+
+ at ARTICLE{fuchsmuller1971,
+ author = {K. Fuchs and G. Muller},
+ title = {Computation of synthetic seismograms with the reflectivity method
+ and comparison of observations},
+ journal = gjras,
+ year = {1971},
+ volume = {23},
+ pages = {417-433}
+}
+
+ at ARTICLE{Fuisetal2003,
+ author = {G. S. Fuis and R. W. Clayton and P. M. Davis and T. Ryberg and W.
+ J. Lutter and D. A. Okaya and E. Hauksson and C. Prodehl and J. M.
+ Murphy and M. L. Benthien and S. A. Baher and M. D. Kohler and K.
+ Thygesen and G. Simila and G. R. Keller},
+ title = {Fault systems of the 1971 {S}an {F}ernando and 1994 {N}orthridge
+ earthquakes, {S}outhern {C}alifornia: relocated aftershocks and seismic
+ images from {LARSE~II}},
+ journal = {Geology},
+ year = {2003},
+ volume = {31},
+ pages = {171-174}
+}
+
+ at BOOK{Fun92,
+ title = {Polynomial approximation of differential equations},
+ publisher = {Springer Verlag},
+ year = {1992},
+ author = {D. Funaro},
+ volume = {8},
+ series = {Lecture Notes in Physics},
+ address = {Heidelberg, Germany}
+}
+
+ at ARTICLE{FuKeFu99,
+ author = {M. Furumura and B. L. N. Kennett and T. Furumura},
+ title = {Seismic wavefield calculation for laterally heterogeneous {E}arth
+ models-{II}. The influence of upper mantle heterogeneity},
+ journal = gji,
+ year = {1999},
+ volume = {139},
+ pages = {623-644},
+ number = {3},
+ doi = {10.1046/j.1365-246x.1999.00962.x}
+}
+
+ at ARTICLE{FuKeFu98,
+ author = {T. Furumura and B. L. N. Kennett and M. Furumura},
+ title = {Seismic wavefield calculation for laterally heterogeneous whole {E}arth
+ models using the pseudospectral method},
+ journal = gji,
+ year = {1998},
+ volume = {135},
+ pages = {845-860},
+ number = {3},
+ doi = {10.1046/j.1365-246X.1998.00682.x}
+}
+
+ at PHDTHESIS{Goeddeke:2010:FAA,
+ author = {Dominik G{\"o}ddeke},
+ title = {Fast and Accurate Finite-Element Multigrid Solvers for {PDE} Simulations
+ on {GPU} Clusters},
+ school = {{T}echnische {U}niversit{\"a}t Dortmund, {F}akult{\"a}t f{\"u}r {M}athematik},
+ year = {2010},
+ month = may,
+ note = {\url{http://hdl.handle.net/2003/27243}}
+}
+
+ at INPROCEEDINGS{Goeddeke:2009:GAO,
+ author = {Dominik G{\"o}ddeke and Sven H.M. Buijssen and Hilmar Wobker and
+ Stefan Turek},
+ title = {{GPU} Acceleration of an Unmodified Parallel Finite Element {N}avier-{S}tokes
+ Solver},
+ booktitle = {High Performance Computing \& Simulation 2009},
+ year = {2009},
+ editor = {Waleed W. Smari and John P. McIntire},
+ pages = {12-21},
+ address = {Leipzig, Germany},
+ month = jun
+}
+
+ at ARTICLE{Goeddeke:2009:CPA,
+ author = {Dominik G{\"o}ddeke and Hilmar Wobker and Robert Strzodka and Jamaludin
+ Mohd-Yusof and Patrick S. McCormick and Stefan Turek},
+ title = {Co-Processor Acceleration of an Unmodified Parallel Solid Mechanics
+ Code with {FEASTGPU}},
+ journal = {International Journal of Computational Science and Engineering},
+ year = {2009},
+ volume = {4},
+ pages = {254--269},
+ number = {4},
+ month = oct,
+ editor = {Hans Petter Langtangen and Michael Thun{\'e}}
+}
+
+ at ARTICLE{GeBaJu88,
+ author = {L. G\'eli and P. Y. Bard and B. Julien},
+ title = {The effect of topography on earthquake ground motion: a review and
+ new results},
+ journal = bssa,
+ year = {1988},
+ volume = {78},
+ pages = {42-63}
+}
+
+ at ARTICLE{GoStMoMcBuGrTu07,
+ author = {Dominik G\"oddeke and Robert Strzodka and Jamaludin Mohd-Yusof and
+ Patrick McCormick and Sven H. M. Buijssen and Matthias Grajewski
+ and Stefan Turek},
+ title = {Exploring weak scalability for {FEM} calculations on a {GPU}-enhanced
+ cluster},
+ journal = {Parallel Computing},
+ year = {2007},
+ volume = {33},
+ pages = {685-699},
+ number = {10-11}
+}
+
+ at ARTICLE{GoStTu07,
+ author = {Dominik G\"oddeke and Robert Strzodka and Stefan Turek},
+ title = {Performance and accuracy of hardware-oriented native-, emulated-
+ and mixed-precision solvers in {FEM} simulations},
+ journal = {International Journal of Parallel, Emergent and Distributed Systems},
+ year = {2007},
+ volume = {22},
+ pages = {221-256},
+ number = {4}
+}
+
+ at ARTICLE{GaBo89,
+ author = {S. Gaffet and M. Bouchon},
+ title = {Effects of two-dimensional topographies using the discrete wavenumber-boundary
+ integral equation method in {{\it P-SV}} cases},
+ journal = jasa,
+ year = {1989},
+ volume = {85},
+ pages = {2277-2283}
+}
+
+ at TECHREPORT{GaMaNaHelene,
+ author = {M. J. Gander and F. Magoul\`es and F. Nataf},
+ title = {Optimized {S}chwarz method without overlap for the {H}elmholtz equation},
+ institution = {CMAP, UMR CNRS 67641},
+ year = {2001}
+}
+
+ at ARTICLE{sympl2,
+ author = {L. Gao and Y. M. Li and X. R. Chen and K. Q. Yang},
+ title = {An attempt to seismic ray tracing with symplectic algorithm},
+ journal = {Chinese J. Geophys.},
+ year = {2000},
+ volume = {43},
+ pages = {433-440},
+ number = {3}
+}
+
+ at ARTICLE{GaLiDaKn96,
+ author = {S. Gao and H. Liu and P. M. Davis and L. Knopoff},
+ title = {Localized amplification of seismic waves and correlation with damage
+ due to the {N}orthridge earthquake: evidence for focusing in {S}anta
+ {M}onica},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {S209-S230},
+ number = {1B}
+}
+
+ at ARTICLE{geofem01,
+ author = {Kazuteru Garatani and Hisashi Nakamura and Hiroshi Okuda and Genki
+ Yagawa},
+ title = {Geo{FEM}: a High Performance Parallel finite element method for the
+ Solid {E}arth},
+ journal = {J. Future Generation Computer Systems},
+ year = {2001},
+ volume = {18},
+ pages = {107-114}
+}
+
+ at ARTICLE{geofem00,
+ author = {Kazuteru Garatani and Hisashi Nakamura and Hiroshi Okuda and Genki
+ Yagawa},
+ title = {Large-Scale Parallel Wave Propagation Analysis by {G}eo{FEM}},
+ journal = {Lecture Notes in Computer Science},
+ year = {2000},
+ volume = {1823},
+ pages = {445-453}
+}
+
+ at ARTICLE{Gar02,
+ author = {R. Garcia},
+ title = {Constraints on upper inner core structure by waveform inversion of
+ core phases},
+ journal = gji,
+ year = {2002},
+ volume = {150},
+ pages = {651-664}
+}
+
+ at ARTICLE{GaChWe04,
+ author = {R. Garcia and S. Chevrot and M. Weber},
+ title = {Non-linear waveform and delay time analysis of triplicated core phases},
+ journal = jgr,
+ year = {2004},
+ volume = {109},
+ pages = {B01306},
+ doi = {10.1029/2003JB002429}
+}
+
+ at ARTICLE{GaSo00,
+ author = {R. Garcia and A. Souriau},
+ title = {Inner core anisotropy and heterogeneity level},
+ journal = grl,
+ year = {2000},
+ volume = {27},
+ pages = {3121-3125}
+}
+
+ at ARTICLE{Garcia06,
+ author = {R. Garcia and H. Tkalcic and S. Chevrot},
+ title = {A new global {PKP} dataset to study {E}arth's core and deep mantle},
+ journal = pepi,
+ year = {2006},
+ volume = {159},
+ pages = {15-31}
+}
+
+ at ARTICLE{Garland:2008:PCE,
+ author = {Michael Garland and Scott Le Grand and John Nickolls and Joshua A.
+ Anderson and Jim Hardwick and Scott Morton and Everett H. Phillips
+ and Yao Zhang and Vasily Volkov},
+ title = {Parallel Computing Experiences with {CUDA}},
+ journal = {IEEE Micro},
+ year = {2008},
+ volume = {28},
+ pages = {13--27},
+ number = {4},
+ month = jul,
+ doi = {10.1109/MM.2008.57}
+}
+
+ at ARTICLE{GaLa97,
+ author = {E. Garnero and T. Lay},
+ title = {Lateral variations in lowermost mantle shear wave anisotropy beneath
+ the north {P}acific and {A}laska},
+ journal = {J. Geophys. Res.},
+ year = {1997},
+ volume = {102},
+ pages = {8121-8135}
+}
+
+ at ARTICLE{garnero2000,
+ author = {E. J. Garnero},
+ title = {Heterogeneity of the lowermost mantle},
+ journal = {Annual Review of Earth and Planetary Sciences},
+ year = {2000},
+ volume = {33},
+ pages = {1-66}
+}
+
+ at ARTICLE{Gar56,
+ author = {W. W. Garvin},
+ title = {Exact transient solution of the buried line source problem},
+ journal = {Proc. R. Soc. London Ser. A},
+ year = {1956},
+ volume = {234},
+ pages = {528-541}
+}
+
+ at ARTICLE{GoViTa86,
+ author = {O. Gauthier and J. Virieux and A. Tarantola},
+ title = {Two-dimensional non-linear inversion of seismic waveforms: numerical
+ results},
+ journal = geophysics,
+ year = {1986},
+ volume = {51},
+ pages = {1387-1403}
+}
+
+ at ARTICLE{Gaz81,
+ author = {J. Gazdag},
+ title = {Modeling of the acoustic wave equation with transform methods},
+ journal = geophysics,
+ year = {1981},
+ volume = {46},
+ pages = {854-859}
+}
+
+ at ARTICLE{GazHerWal60a,
+ author = {D. C. Gazis and R. Herman and R. F. Wallis},
+ title = {Surface elastic waves in cubic crystals},
+ journal = {Physical Review},
+ year = {1960},
+ volume = {119},
+ pages = {533-544},
+ number = {2}
+}
+
+ at ARTICLE{GazHerWal60b,
+ author = {D. C. Gazis and R. Herman and R. F. Wallis},
+ title = {Surface elastic waves in semiconductors},
+ journal = {Journal of Physics and Chemistry of Solids},
+ year = {1960},
+ volume = {14},
+ pages = {268-270}
+}
+
+ at ARTICLE{GazWal66,
+ author = {D. C. Gazis and R. F. Wallis},
+ title = {Surface elastic waves in body-centered cubic lattices},
+ journal = {Surface Science},
+ year = {1966},
+ volume = {5},
+ pages = {482-492}
+}
+
+ at INCOLLECTION{Ged98,
+ author = {S. D. Gedney},
+ title = {The {P}erfectly {M}atched {L}ayer absorbing medium},
+ booktitle = {Advances in Computational Electrodynamics: the Finite-Difference
+ Time-Domain method},
+ publisher = {Artech House},
+ year = {1998},
+ editor = {Allen Taflove},
+ chapter = {5},
+ pages = {263-343},
+ address = {Boston, USA}
+}
+
+ at ARTICLE{Ged96,
+ author = {S. D. Gedney},
+ title = {An anisotropic perfectly matched layer-absorbing medium for the truncation
+ of {FDTD} lattices},
+ journal = {IEEE Transactions on Antennas and Propagation},
+ year = {1996},
+ volume = {44},
+ pages = {1630-1639},
+ number = {12},
+ doi = {10.1109/8.546249}
+}
+
+ at ARTICLE{GeZh10,
+ author = {S. D. Gedney and B. Zhao},
+ title = {An Auxiliary Differential Equation Formulation for the Complex-Frequency
+ Shifted {PML}},
+ journal = {IEEE Transactions on Antennas and Propagation},
+ year = {2010},
+ volume = {58},
+ pages = {838-847},
+ number = {3},
+ doi = {10.1109/TAP.2009.2037765}
+}
+
+ at ARTICLE{GeOh94,
+ author = {R. J. Geller and T. Ohminato},
+ title = {Computation of synthetic seismograms and their partial derivatives
+ for heterogeneous media with arbitrary natural boundary conditions
+ using the {D}irect {S}olution {M}ethod},
+ journal = gji,
+ year = {1994},
+ volume = {116},
+ pages = {421-446}
+}
+
+ at ARTICLE{GeOsDeMeNeGo09,
+ author = {Luigi Genovese and Matthieu Ospici and Thierry Deutsch and Jean-Fran\c{c}ois
+ M\'{e}haut and Alexey Neelov and Stefan Goedecker},
+ title = {Density functional theory calculation on many-cores hybrid central
+ processing unit-graphic processing unit architectures},
+ journal = {Journal of Chemical Physics},
+ year = {2009},
+ volume = {131},
+ pages = {034103},
+ number = {3},
+ doi = {10.1063/1.3166140}
+}
+
+ at BOOK{GeMu94,
+ title = {Introduction \`a la m\'ecanique des milieux continus},
+ publisher = {Masson},
+ year = {1994},
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+}
+
+ at ARTICLE{GeRe09,
+ author = {C. Geuzaine and J. F. Remacle},
+ title = {Gmsh: a three-dimensional finite element mesh generator with built-in
+ pre- and post-processing facilities},
+ journal = ijnme,
+ year = {2009},
+ volume = {79},
+ pages = {1309-1331},
+ number = {11},
+ owner = {komatits},
+ timestamp = {2011.01.23}
+}
+
+ at ARTICLE{gilbert1970,
+ author = {F. Gilbert},
+ title = {Excitation of the normal modes of the {E}arth by earthquake sources},
+ journal = gjras,
+ year = {1970},
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+}
+
+ at ARTICLE{gilbertdziewonski1975,
+ author = {F. Gilbert and A. M. Dziewo\'nski},
+ title = {An Application of Normal Mode Theory to the Retrieval of Structural
+ Parameters and Source Mechanisms from Seismic Spectra},
+ journal = {Philos. Trans. R. Soc. London A},
+ year = {1975},
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+}
+
+ at ARTICLE{gilberthelmberger1972,
+ author = {F. Gilbert and D. V. Helmberger},
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+ journal = gjras,
+ year = {1972},
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+}
+
+ at ARTICLE{GiKn61,
+ author = {F. Gilbert and L. Knopoff},
+ title = {The directivity problem of a burried line source},
+ journal = geophysics,
+ year = {1961},
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+ pages = {626-634}
+}
+
+ at ARTICLE{GiKn60,
+ author = {F. Gilbert and L. Knopoff},
+ title = {Seismic scattering from topographic irregularities},
+ journal = jgr,
+ year = {1960},
+ volume = {65},
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+}
+
+ at ARTICLE{GiLa62,
+ author = {F. Gilbert and S. J. Laster},
+ title = {Excitation and propagation of pulses on an interface},
+ journal = bssa,
+ year = {1962},
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+}
+
+ at ARTICLE{GiHeWa02,
+ author = {F. X. Giraldo and J. S. Hesthaven and T. Warburton},
+ title = {Nodal High-Order Discontinuous {G}alerkin Methods for the Spherical
+ Shallow Water Equations},
+ journal = jcp,
+ year = {2002},
+ volume = {181},
+ pages = {499-525},
+ number = {2},
+ doi = {10.1006/jcph.2002.7139}
+}
+
+ at ARTICLE{GiWa05,
+ author = {F. X. Giraldo and T. Warburton},
+ title = {A nodal triangle-based spectral element method for the shallow water
+ equations on the sphere},
+ journal = jcp,
+ year = {2005},
+ volume = {207},
+ pages = {129-150},
+ number = {1},
+ doi = {10.1016/j.jcp.2005.01.004}
+}
+
+ at ARTICLE{GiLaSy06,
+ author = {L. Giraud and J. Langou and G. Sylvand},
+ title = {On The Parallel Solution Of Large Industrial Wave Propagation Problems},
+ journal = jca,
+ year = {2006},
+ volume = {14},
+ pages = {83-111},
+ number = {1}
+}
+
+ at INCOLLECTION{Giv08,
+ author = {D. Givoli},
+ title = {Computational Absorbing Boundaries},
+ booktitle = {Computational acoustics noise propagation in fluids},
+ publisher = {Springer-Verlag},
+ year = {2008},
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+}
+
+ at ARTICLE{Giv04,
+ author = {D. Givoli},
+ title = {High-Order Local Non-Reflecting Boundary Conditions: A Review},
+ journal = {Wave Motion},
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+}
+
+ at BOOK{Giv92,
+ title = {Numerical Methods for Problems in Infinite Domains},
+ publisher = {Elsevier Science Publishers},
+ year = {1992},
+ author = {Dan Givoli},
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+}
+
+ at ARTICLE{Giv91,
+ author = {D. Givoli},
+ title = {Non-reflecting boundary conditions: review article},
+ journal = jcp,
+ year = {1991},
+ volume = {94},
+ pages = {1-29}
+}
+
+ at INCOLLECTION{GiKe94,
+ author = {D. Givoli and J. B. Keller},
+ title = {Non-reflecting finite elements},
+ booktitle = {The mathematics of finite elements and applications},
+ publisher = {John Wiley and sons},
+ year = {1994},
+ address = {New York}
+}
+
+ at ARTICLE{GiKe90,
+ author = {D. Givoli and J. B. Keller},
+ title = {Non-reflecting boundary conditions for elastic waves},
+ journal = {Wave motion},
+ year = {1990},
+ volume = {12},
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+}
+
+ at ARTICLE{GNHelene,
+ author = {D. Givoli and B. Neta},
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+}
+
+ at ARTICLE{GiVi93,
+ author = {D. Givoli and S. Vidgergauz},
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+ journal = cmame,
+ year = {1993},
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+}
+
+ at INPROCEEDINGS{GlLaRaTe90,
+ author = {R. Glowinski and W. Lawton and M. Ravachol and E. Tenebaum},
+ title = {Wavelet solution of linear and nonlinear elliptic, parabolic and
+ hyperbolic problems in one space dimension},
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+}
+
+ at ARTICLE{GoAmTaCaSmSaMaKo09,
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+ C. Smerzini and F. J. S\'anchez-Sesma and R. Madec and Dimitri Komatitsch},
+ title = {Numerical simulation of ground rotations along {2D} topographical
+ profiles under the incidence of elastic plane waves},
+ journal = bssa,
+ year = {2009},
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+ number = {2B},
+ doi = {10.1785/0120080096}
+}
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+}
+
+ at INPROCEEDINGS{Goodnight:2003:AMS,
+ author = {Nolan Goodnight and Cliff Woolley and Gregory Lewin and David P.
+ Luebke and Greg Humphreys},
+ title = {A Multigrid Solver for Boundary Value Problems Using Programmable
+ Graphics Hardware},
+ booktitle = {Graphics Hardware 2003},
+ year = {2003},
+ editor = {Michael Doggett and Wolfgang Heidrich and William R. Mark and Andreas
+ Schilling},
+ pages = {102--111},
+ month = jul
+}
+
+ at INPROCEEDINGS{GoHa72,
+ author = {W. J. Gordon and C. A. Hall},
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+ booktitle = {Mathematical Foundations of the Finite Element Method with Applications
+ to Partial Differential Equations},
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+}
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+}
+
+ at INCOLLECTION{cgnash,
+ author = {C. Gout},
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+ year = {1999},
+ editor = {C. K. Chui and L. L. Schumaker},
+ volume = {1},
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+ address = {Nashville}
+}
+
+ at TECHREPORT{cg1001,
+ author = {C. Gout},
+ title = {Approximation of curves and surfaces from rapidly varying data},
+ institution = {Center for Pure and Applied Mathematics},
+ year = {1998},
+ number = {1001},
+ address = {University of California at Berkeley, USA},
+ note = {36 p.}
+}
+
+ at PHDTHESIS{cgthesis,
+ author = {C. Gout},
+ title = {Etude de changements d'\'echelle en approximation - ajustement spline
+ sur des morceaux de surfaces},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {1997},
+ address = {Pau, France},
+ note = {203 p.}
+}
+
+ at TECHREPORT{GoLeGuVe05,
+ author = {C. Gout and C. Le Guyader and L. Vese},
+ title = {Image segmentation under interpolation conditions},
+ institution = {Univ. of California, Los Angeles},
+ year = {2005},
+ note = {CAM 03-44}
+}
+
+ at ARTICLE{GoKo00,
+ author = {C. Gout and D. Komatitsch},
+ title = {Surface fitting of rapidly varying data using rank coding: application
+ to geophysical surfaces},
+ journal = {Math. Geol.},
+ year = {2000},
+ volume = {32},
+ pages = {873-888},
+ number = {7},
+ doi = {10.1023/A:1007500624487}
+}
+
+ at ARTICLE{GoVi03,
+ author = {C. Gout and S. Vieira-Test\'e},
+ title = {An algorithm for segmentation under interpolation conditions using
+ deformable models},
+ journal = {Int. J. Comput. Math.},
+ year = {2003},
+ volume = {80},
+ pages = {47-54},
+ number = {1}
+}
+
+ at ARTICLE{GoMa07,
+ author = {Naga K. Govindaraju and Dinesh Manocha},
+ title = {Cache-Efficient Numerical Algorithms using Graphics Hardware},
+ journal = {Parallel Computing},
+ year = {2007},
+ volume = {33},
+ pages = {663-684}
+}
+
+ at INCOLLECTION{Gra99,
+ author = {R. W. Graves},
+ title = {Three-dimensional computer simulations of realistic earthquake ground
+ motions in regions of deep sedimentary basin},
+ booktitle = {The Effects of Surface Geology on Seismic Motion},
+ publisher = {Balkema},
+ year = {1999},
+ editor = {K. Irikura and K. Kudo and H. Okada and T. Sasatani},
+ volume = {1},
+ pages = {103-120},
+ address = {Rotterdam, The Netherlands}
+}
+
+ at ARTICLE{Gra96,
+ author = {R. W. Graves},
+ title = {Simulating seismic wave propagation in 3{D} elastic media using staggered-grid
+ finite differences},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1091-1106},
+ number = {4}
+}
+
+ at INPROCEEDINGS{Gra96b,
+ author = {R. W. Graves},
+ title = {Simulating realistic earthquake ground motions in regions of deep
+ sedimentary basins},
+ booktitle = {Proceedings of the 11th World Conference on Earthquake Engineering},
+ year = {1996},
+ address = {Acapulco, Mexico}
+}
+
+ at ARTICLE{GrDa03,
+ author = {R. W. Graves and S. M. Day},
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+ journal = bssa,
+ year = {2003},
+ volume = {93},
+ pages = {283-300}
+}
+
+ at ARTICLE{GrZa10,
+ author = {Michael Griebel and Peter Zaspel},
+ title = {A multi-{GPU} accelerated solver for the three-dimensional two-phase
+ incompressible {N}avier-{S}tokes equations},
+ journal = {Computer Science Research and Development},
+ year = {2010},
+ volume = {25},
+ pages = {65-73},
+ number = {1-2},
+ doi = {10.1007/s00450-010-0111-7}
+}
+
+ at ARTICLE{GrBo79,
+ author = {D. W. Griffiths and G. A. Bollinger},
+ title = {The effect of {A}ppalachian mountain topography on seismic waves},
+ journal = bssa,
+ year = {1979},
+ volume = {69},
+ pages = {1081-1105}
+}
+
+ at ARTICLE{GrLuDoSk96,
+ author = {W. Gropp and E. Lusk and N. Doss and A. Skjellum},
+ title = {A high-performance, portable implementation of the {MPI} message
+ passing interface standard},
+ journal = {Parallel Computing},
+ year = {1996},
+ volume = {22},
+ pages = {789-828},
+ number = {6}
+}
+
+ at BOOK{GrLuSk94,
+ title = {Using {MPI}, portable parallel programming with the {M}essage-{P}assing
+ {I}nterface},
+ publisher = {MIT Press},
+ year = {1994},
+ author = {W. Gropp and E. Lusk and A. Skjellum},
+ address = {Cambridge, USA}
+}
+
+ at ARTICLE{Gro00,
+ author = {M. J. Grote},
+ title = {Nonreflecting boundary conditions for elastodynamics scattering},
+ journal = jcp,
+ year = {2000},
+ volume = {161},
+ pages = {331-353}
+}
+
+ at ARTICLE{GrScSc06,
+ author = {Marcus J. Grote and Anna Schneebeli and Dominik Sch\"{o}tzau},
+ title = {Discontinuous {G}alerkin Finite Element Method for the Wave Equation},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {2006},
+ volume = {44},
+ pages = {2408-2431},
+ number = {6},
+ doi = {10.1137/05063194X}
+}
+
+ at ARTICLE{GuLi06,
+ author = {Murthy N. Guddati and Keng Wit Lim},
+ title = {Continued fraction absorbing boundary conditions for convex polygonal
+ domains},
+ journal = ijnme,
+ year = {2006},
+ volume = {66},
+ pages = {949-977},
+ number = {6},
+ doi = {10.1002/nme.1574}
+}
+
+ at ARTICLE{GuBa86b,
+ author = {W. Gui and I. Babu\u{s}ka},
+ title = {The {\it h}, {\it p} and {\it h-p} versions of the finite element
+ method in one dimension},
+ journal = {Numer. Math.},
+ year = {1986},
+ volume = {49},
+ pages = {577-683}
+}
+
+ at ARTICLE{GuDu08,
+ author = {Nail A. Gumerov and Ramani Duraiswami},
+ title = {Fast multipole methods on graphics processors},
+ journal = jcp,
+ year = {2008},
+ volume = {227},
+ pages = {8290-8313},
+ doi = {10.1016/j.jcp.2008.05.023}
+}
+
+ at ARTICLE{GunWanLot91,
+ author = {S. A. Gundersen and L. Wang and J. Lothe},
+ title = {Secluded supersonic elastic surface waves},
+ journal = {Wave Motion},
+ year = {1991},
+ volume = {14},
+ pages = {129-143}
+}
+
+ at ARTICLE{GuBa86a,
+ author = {B. Guo and I. Babu\u{s}ka},
+ title = {The {\it h-p} version of the finite element method},
+ journal = {Comput. Mech.},
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+}
+
+ at ARTICLE{LeGuApGo05,
+ author = {C. Le Guyader and D. Apprato and C. Gout},
+ title = {Using a level set approach for image segmentation under interpolation
+ conditions},
+ journal = {Numer. Algorithms},
+ year = {2005},
+ volume = {39},
+ pages = {221-235}
+}
+
+ at ARTICLE{HeSa06,
+ author = {Pascal H{\'e}non and Yousef Saad},
+ title = {A Parallel Multistage {ILU} Factorization Based on a Hierarchical
+ Graph Decomposition},
+ journal = {SIAM Journal of Scientific Computing},
+ year = {2006},
+ volume = {28},
+ pages = {2266-2293},
+ number = {6}
+}
+
+ at ARTICLE{Hor2,
+ author = {L. H\o{}rmander},
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+ journal = {Ann. of Math.},
+ year = {1966},
+ volume = {83},
+ pages = {129-209}
+}
+
+ at ARTICLE{Hor1,
+ author = {L. H\o{}rmander},
+ title = {Pseudo-differential Operators},
+ journal = {Comm. Pure Appl. Math.},
+ year = {1965},
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+}
+
+ at BOOKLET{Haa09,
+ title = {Zur Theorie der orthogonalen Funktionensysteme},
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+}
+
+ at ARTICLE{HaKa77,
+ author = {D. Hadley and H. Kanamori},
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+ journal = {Geol. Soc. Am. Bull.},
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+}
+
+ at ARTICLE{Hager85,
+ author = {Hager, B. H. and R. W. Clayton and M. A. Richards and R. P. Comer
+ and A. M. Dziewo\'nski},
+ title = {Lower mantle heterogeneity, dynamic topography and the geoid},
+ journal = {Nature},
+ year = {1985},
+ volume = {313},
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+}
+
+ at INPROCEEDINGS{Hag03,
+ author = {T. Hagstrom},
+ title = {Perfectly matched layers for hyperbolic systems with applications
+ to the linearized {E}uler equations},
+ booktitle = {Mathematical and Numerical Aspects of Wave Propagation: Waves 2003},
+ year = {2003},
+ editor = {Gary Cohen and Erkki Heikkola and Patrick Joly and Pekka Neittaanm\"aki},
+ series = {Proceedings of the Sixth International Conference on Mathematical
+ and Numerical Aspects of Wave Propagation},
+ pages = {125-129},
+ address = {Jyv\"askyl\"a, Finland},
+ publisher = {Springer-Verlag}
+}
+
+ at ARTICLE{Ha99,
+ author = {T. Hagstrom},
+ title = {Radiation boundary conditions for the numerical simulation of waves},
+ journal = {Acta Numerica},
+ year = {1999},
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+ pages = {47-106}
+}
+
+ at ARTICLE{HaHa98,
+ author = {T. Hagstrom and S. I. Hariharan},
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+ operators},
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+}
+
+ at BOOK{HaLuWa06,
+ title = {Geometric numerical integration},
+ publisher = {Springer-Verlag},
+ year = {2006},
+ author = {Hairer, Ernst and Lubich, Christian and Wanner, Gerhard},
+ volume = {31},
+ series = {Springer Series in Computational Mathematics},
+ address = {Berlin, Germany},
+ edition = {Second}
+}
+
+ at ARTICLE{HalHelene,
+ author = {L. Halpern},
+ title = {Artificial boundary conditions for incompletely parabolic perturbations
+ of hyperbolic systems},
+ journal = {SIAM Journal on Numerical Analysis},
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+ volume = {22},
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+ number = {5}
+}
+
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+ author = {M. A. Hamdi and Y. Ousset and G. Verchery},
+ title = {A displacement method for the analysis of vibrations of coupled fluid-structure
+ systems},
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+}
+
+ at ARTICLE{HaKoGi10,
+ author = {Shravan M. Hanasoge and Dimitri Komatitsch and Laurent Gizon},
+ title = {An absorbing boundary formulation for the stratified, linearized,
+ ideal {MHD} equations based on an unsplit, convolutional perfectly
+ matched layer},
+ journal = {Astronomy and Astrophysics},
+ year = {2010},
+ volume = {522},
+ pages = {1-8},
+ number = {A87},
+ doi = {10.1051/0004-6361/201014345}
+}
+
+ at ARTICLE{HaSe93,
+ author = {B. Hanouzet and M. Sesques},
+ title = {Absorbing boundary conditions for {M}axwell's equations},
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+}
+
+ at ARTICLE{Haetal91,
+ author = {T. Hara and S. Tsuboi and R.J. Geller},
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+ heterogeneous starting model: preliminary results},
+ journal = gji,
+ year = {1991},
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+}
+
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+ author = {I. Harari},
+ title = {A survey of finite element methods for time-harmonic acoustics},
+ journal = cmame,
+ year = {2006},
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+ pages = {1594-1607}
+}
+
+ at ARTICLE{HaSlTu00,
+ author = {I. Harari and M. Slavutin and E. Turkel},
+ title = {Analytical and numerical studies of a finite element {PML} for the
+ {H}elmholtz equation},
+ journal = jca,
+ year = {2000},
+ volume = {8},
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+}
+
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+ title = {Elastic waves in solids, with application to non destructive testing
+ of pipelines},
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+}
+
+ at PHDTHESIS{Harris:2003:RTC,
+ author = {Mark J. Harris},
+ title = {Real-Time Cloud Simulation and Rendering},
+ school = {University of North Carolina at Chapel Hill, USA},
+ year = {2003},
+ month = sep
+}
+
+ at ARTICLE{HaDa99,
+ author = {R. A. Harris and S. M. Day},
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+ journal = grl,
+ year = {1999},
+ volume = {26},
+ pages = {2089-2092}
+}
+
+ at ARTICLE{HaHaFrCaCrMeMi98,
+ author = {S. Hartzell and S. Harmsen and A. Frankel and D. Carver and E. Cranswick
+ and M. Meremonte and J. Michael},
+ title = {First-generation site-response maps for the {L}os {A}ngeles region
+ based on earthquake ground motions},
+ journal = bssa,
+ year = {1998},
+ volume = {88},
+ pages = {463-472}
+}
+
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+ author = {S. H. Hartzell and D. L. Carver and K. W. King},
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+ year = {1994},
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+}
+
+ at ARTICLE{HaLeFrMi96,
+ author = {S. H. Hartzell and A. Leeds and A. Frankel and J. Michael},
+ title = {Site response for urban {L}os {A}ngeles using aftershocks of the
+ {N}orthridge earthquake},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {S168-S192},
+ number = {1B}
+}
+
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+ author = {F. D. Hastings and J. B. Schneider and S. L. Broschat},
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+ journal = jasa,
+ year = {1996},
+ volume = {100},
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+}
+
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+ author = {E. Hauksson},
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+ journal = jgr,
+ year = {2000},
+ volume = {105},
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+}
+
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+ author = {E. Hauksson},
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+ journal = jgr,
+ year = {1990},
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+}
+
+ at ARTICLE{HaHa97,
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+ title = {Three-dimensional {$V_p$} and {$V_p/V_s$} velocity models of the
+ {L}os {A}ngeles basin and central {T}ransverse {R}anges, {C}alifornia},
+ journal = jgr,
+ year = {1997},
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+}
+
+ at ARTICLE{HaTeHe87,
+ author = {E. Hauksson and T. L. Teng and T. L. Henyey},
+ title = {Results from a 1500~m deep, three-level downhole seismometer array:
+ site response, low {$Q$} values, and $f_{max}$},
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+ year = {1987},
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+}
+
+ at TECHREPORT{HaKeLe02,
+ author = {P. Hav\'e and M. Kern and Ch. Lemuet},
+ title = {R\'esolution num\'erique de l'\'equation des ondes par une m\'ethode
+ d'\'el\'ements finis d'ordre \'elev\'e sur calculateur parall\`ele},
+ institution = {INRIA},
+ year = {2002},
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+ address = {France},
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+}
+
+ at BOOK{Hea00,
+ title = {Beowulf, a new verse translation, bilingual edition},
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+}
+
+ at INCOLLECTION{Hel94,
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+}
+
+ at ARTICLE{helmbergerburdick1979,
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+}
+
+ at ARTICLE{helmbergeretal1996,
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+}
+
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+
+ at INCOLLECTION{HeKa93,
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+ booktitle = {Finite elements in fluids},
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+}
+
+ at ARTICLE{Hest98,
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+ in a simplex},
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+}
+
+ at ARTICLE{Hest98b,
+ author = {J. S. Hesthaven},
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+ the linearized {E}uler equations},
+ journal = jcp,
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+
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+}
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+ author = {S. Hestholm and B. Ruud},
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+ journal = gp,
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+
+ at ARTICLE{Hickey97,
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+}
+
+ at ARTICLE{Hig91,
+ author = {R. L. Higdon},
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+ journal = geophysics,
+ year = {1991},
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+}
+
+ at ARTICLE{Hig90,
+ author = {R. L. Higdon},
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+ journal = {SIAM Journal on Numerical Analysis},
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+
+ at BOOK{Hij87,
+ title = {Propagation of transient elastic waves in stratified anisotropic
+ media},
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+}
+
+ at ARTICLE{hilletal1993,
+ author = {D. P. Hill and {et al.}},
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+ earthquake},
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+}
+
+ at ARTICLE{HoRo94,
+ author = {L. W. Ho and E. M. R{\o}nquist},
+ title = {Spectral-Element Solution of Steady Incompressible Viscous Free-Surface
+ Flows},
+ journal = {Finite Elements in Analysis and Design},
+ year = {1994},
+ volume = {16},
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+}
+
+ at ARTICLE{Hol87,
+ author = {O. Holberg},
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+ for numerical differentiation in large-scale simulation of wave phenomena},
+ journal = gp,
+ year = {1987},
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+}
+
+ at ARTICLE{Hoo60,
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+
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+}
+
+ at ARTICLE{dehoop3,
+ author = {M. V. De Hoop and J. H. Le Rousseau},
+ title = {Scalar Generalized-Screen Algorithms in Transversely Isotropic Media
+ with a Vertical Symmetry Axis},
+ journal = {Geophysics},
+ year = {2001},
+ volume = {66},
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+ number = {5}
+}
+
+ at ARTICLE{dehoop2000,
+ author = {M. V. De Hoop and J. H. Le Rousseau and R. S. Wu},
+ title = {Generalization of the phase-screen approximation for the scattering
+ of acoustic waves},
+ journal = {Wave Motion},
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+}
+
+ at ARTICLE{dehoop2,
+ author = {M. V. De Hoop and C. Spencer and R. Burridge},
+ title = {The Resolving Power of Seismic Amplitude Data: An Isotropic Inversion/Migration
+ Approach},
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+ year = {1999},
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+}
+
+ at ARTICLE{HoUeTa90,
+ author = {M. Horike and H. Uebayashi and T. Takeuchi},
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+ {{\it S}} wave incidence},
+ journal = {J. Phys. Earth},
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+
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+ title = {Matrix analysis},
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+}
+
+ at ARTICLE{hch,
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+ year = {1994},
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+}
+
+ at ARTICLE{Hu01,
+ author = {Fang Q. Hu},
+ title = {A Stable Perfectly Matched Layer for Linearized {E}uler Equations
+ in Unsplit Physical Variables},
+ journal = jcp,
+ year = {2001},
+ volume = {173},
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+}
+
+ at ARTICLE{HuHuRa99,
+ author = {Hu, Fang Q. and Hussaini, M. Y. and Rasetarinera, Patrick},
+ title = {An analysis of the discontinuous {G}alerkin method for wave propagation
+ problems},
+ journal = jcp,
+ year = {1999},
+ volume = {151},
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+ number = {2},
+ doi = {10.1006/jcph.1999.6227}
+}
+
+ at ARTICLE{Huang95,
+ author = {J. Y. Huang},
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+ journal = {Eng. Frac. Mech.},
+ year = {1995},
+ volume = {51},
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+}
+
+ at ARTICLE{Hud67,
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+
+ at ARTICLE{Hubo80,
+ author = {J. A. Hudson and D. M. Boore},
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+ journal = gjras,
+ year = {1980},
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+}
+
+ at ARTICLE{HuKn64a,
+ author = {J. A. Hudson and L. Knopoff},
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+ {L}ove waves},
+ journal = jgr,
+ year = {1964},
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+}
+
+ at ARTICLE{HuKn64b,
+ author = {J. A. Hudson and L. Knopoff},
+ title = {Transmission and reflection of surface waves at a corner, part 2:
+ {R}ayleigh waves (theoretical)},
+ journal = jgr,
+ year = {1964},
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+}
+
+ at ARTICLE{Hud96,
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+ and pores},
+ journal = gji,
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+}
+
+ at ARTICLE{HuYe95,
+ author = {G. J. Huftile and R. S. Yeats},
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+ {T}ransverse {R}anges, {V}entura Basin, {C}alifornia},
+ journal = jgr,
+ year = {1995},
+ volume = {100},
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+ number = {2}
+}
+
+ at BOOK{Hug87,
+ title = {The finite element method, linear static and dynamic finite element
+ analysis},
+ publisher = {Prentice-Hall International},
+ year = {1987},
+ author = {Thomas J. R. Hughes},
+ address = {Englewood Cliffs, New Jersey, USA}
+}
+
+ at ARTICLE{HuFeHa87,
+ author = {T. J. R. Hughes and R. M. Ferencz and J. O. Hallquist},
+ title = {Large-scale vectorized implicit calculations in solid mechanics on
+ a {Cray X-MP/48} utilizing {EBE} preconditioned conjugate gradients},
+ journal = cmame,
+ year = {1987},
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+}
+
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+ title = {Space-time finite element methods for elastodynamics, formulation
+ and error estimates},
+ journal = cmame,
+ year = {1988},
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+}
+
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+}
+
+ at PHDTHESIS{Hul89,
+ author = {G. M. Hulbert},
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+ school = {Stanford University},
+ year = {1989},
+ address = {Stanford}
+}
+
+ at ARTICLE{HuCh92,
+ author = {G. M. Hulbert and J. Chung},
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+ explicit generalized $\alpha$-method},
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+}
+
+ at ARTICLE{HuHu90,
+ author = {G. M. Hulbert and T. J. R. Hughes},
+ title = {Space-time finite element methods for second-order hyperbolic equations},
+ journal = cmame,
+ year = {1990},
+ volume = {84},
+ pages = {327-348}
+}
+
+ at INCOLLECTION{HuPrDuKeMa06,
+ author = {John R. Humphrey and Daniel K. Price and James P. Durbano and Eric
+ J. Kelmelis and Richard D. Martin},
+ title = {High performance {2D} and {3D FDTD} solvers on {GPU}s},
+ booktitle = {Proceedings of the 10th WSEAS International Conference on Applied
+ Mathematics},
+ publisher = {World Scientific and Engineering Academy and Society (WSEAS)},
+ year = {2006},
+ pages = {547-550},
+ address = {Dallas, Texas, USA}
+}
+
+ at ARTICLE{HuFo98,
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+ using the parallel multidomain pseudo-spectral method},
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+ year = {1998},
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+ number = {3}
+}
+
+ at ARTICLE{HurTewRic01,
+ author = {D. C. Hurley and V. K. Tewary and A. J. Richards},
+ title = {Surface acoustic wave methods to determine the anisotropic elastic
+ properties of thin films},
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+}
+
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+}
+
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+ non-reflecting boundary conditions},
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+}
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+ spectral method},
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+ year = {1999},
+ volume = {136},
+ pages = {559-566}
+}
+
+ at PHDTHESIS{Ige93,
+ author = {Heiner Igel},
+ title = {Seismic modeling and inversion},
+ school = {Universit\'e Paris {\sc VII} Jussieu},
+ year = {1993},
+ address = {Paris}
+}
+
+ at ARTICLE{IgGe00,
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+}
+
+ at ARTICLE{IgMoRi95,
+ author = {H. Igel and P. Mora and B. Riollet},
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+ journal = geophysics,
+ year = {1995},
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+ number = {4}
+}
+
+ at ARTICLE{IgWe96,
+ author = {H. Igel and M. Weber},
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+ differences: application to lowermost mantle structure},
+ journal = grl,
+ year = {1996},
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+}
+
+ at ARTICLE{IgWe95,
+ author = {H. Igel and M. Weber},
+ title = {{SH}-wave propagation in the whole mantle using high-order finite
+ differences},
+ journal = grl,
+ year = {1995},
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+}
+
+ at ARTICLE{IngTon69,
+ author = {K. A. Ingebrigtsen and A. Tonning},
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+}
+
+ at INPROCEEDINGS{InEl08,
+ author = {Inman, M. J. and Elsherbeni, A. Z.},
+ title = {Optimization and parameter exploration using {GPU} based {FDTD} solvers},
+ booktitle = {Proceedings of the 2008 IEEE MTT-S International Microwave Symposium},
+ year = {2008},
+ pages = {149-152},
+ address = {Atlanta, Georgia, USA},
+ month = {June},
+ doi = {10.1109/MWSYM.2008.4633125}
+}
+
+ at INPROCEEDINGS{InElMaBa07,
+ author = {Inman, M. J. and Elsherbeni, A. Z. and Maloney, J. G. and Baker,
+ B. N.},
+ title = {{GPU} based {FDTD} solver with {CPML} boundaries},
+ booktitle = {Proceedings of the 2007 IEEE Antennas and Propagation Society International
+ Symposium},
+ year = {2007},
+ pages = {5255-5258},
+ address = {Honolulu, Hawaii, USA},
+ month = {June},
+ doi = {10.1109/APS.2007.4396732}
+}
+
+ at INCOLLECTION{IsIgKa90,
+ author = {K. Ishihara and M. Iguchi and K. Kamo},
+ title = {Numerical simulation of lava flows on some volcanoes in {J}apan},
+ booktitle = {Lava flows and domes},
+ publisher = {Springer-Verlag},
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+ editor = {J. H. Fink},
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+}
+
+ at BOOK{Iss89,
+ title = {An Introduction to Applied Geostatistics},
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+}
+
+ at ARTICLE{IwHaKaIr96,
+ author = {T. Iwata and K. Hatayama and H. Kawase and K. Irikura},
+ title = {Site Amplification of Ground motions during aftershocks of the 1995
+ {H}yogo-ken {N}anbu earthquake in severely damaged zone - {A}rray
+ observation of ground motions at {H}igashinada {W}ard, {K}obe city,
+ {J}apan},
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+}
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+ at PHDTHESIS{Jon02,
+ author = {S. J\'onsson},
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+ interferometric observations},
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+ year = {2002},
+ address = {California}
+}
+
+ at ARTICLE{JaJiGeLo06,
+ author = {R. K. Jaiman and X. Jiao and P. H. Geubelle and E. Loth},
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+ non-matching meshes},
+ journal = jcp,
+ year = {2006},
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+ number = {1},
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+}
+
+ at OTHER{JaReNeGue2008,
+ author = {A. Jarvis and H.I. Reuter and A. Nelson and E. Guevara},
+ lastchecked = {2008},
+ title = {Hole-filled seamless SRTM data V4},
+ url = {http://srtm.csi.cgiar.org},
+ urldate = {http://srtm.csi.cgiar.org},
+ year = {2008}
+}
+
+ at ARTICLE{JaBe92,
+ author = {C. Jastram and A. Behle},
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+ journal = gp,
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+ at ARTICLE{JaTe92,
+ author = {C. Jastram and E. Tessmer},
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+ journal = gp,
+ year = {1992},
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+}
+
+ at BOOK{Jeffreys3,
+ title = {The {E}arth},
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+}
+
+ at INCOLLECTION{Jen75,
+ author = {P. Jennings},
+ title = {Fault map of {C}alifornia with volcanoes, thermal springs and thermal
+ wells at 1:750,000 scale},
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+ publisher = {California Division of Mines and Geology},
+ year = {1975},
+ address = {Sacramento, California}
+}
+
+ at BOOK{COA2011,
+ title = {Computational Ocean Acoustics},
+ publisher = {Springer},
+ year = {2011},
+ author = {F. B. Jensen and W. Kuperman and M. Porter and H. Schmidt},
+ edition = {2nd}
+}
+
+ at INPROCEEDINGS{Jensen2008,
+ author = {F. B. Jensen and P. L. Nielsen and M. Zampolli and M. D. Collins
+ and W. L. Siegmann},
+ title = {Benchmark scenarios for range-dependent seismo-acoustic models},
+ booktitle = {Proceedings of the 8th International Conference on Theoretical and
+ Computational Acoustics (ICTCA)},
+ year = {2007},
+ editor = {M. Taroudakis and P. Papadakis}
+}
+
+ at ARTICLE{JiHeWa04,
+ author = {Chen Ji and Don V. Helmberger and David J. Wald},
+ title = {A Teleseismic Study of the 2002 {D}enali Fault, {A}laska, Earthquake
+ and Implications for Rapid Strong-Motion Estimation},
+ journal = {Earthquake Spectra},
+ year = {2004},
+ volume = {20},
+ pages = {617-637},
+ number = {3}
+}
+
+ at ARTICLE{JiHeWa2000,
+ author = {C. Ji and D. V. Helmberger and D. J. Wald},
+ title = {Basin structure estimation by waveform modeling: forward and inverse
+ methods},
+ journal = bssa,
+ year = {2000},
+ volume = {90},
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+}
+
+ at ARTICLE{JiTsKoTr05,
+ author = {Chen Ji and Seiji Tsuboi and Dimitri Komatitsch and Jeroen Tromp},
+ title = {Rayleigh-Wave Multipathing along the West Coast of North America},
+ journal = bssa,
+ year = {2005},
+ volume = {95},
+ pages = {2115-2124},
+ number = {6},
+ doi = {10.1785/0120040180}
+}
+
+ at ARTICLE{Ji2002a,
+ author = {C. Ji and D. J. Wald and D. V. Helmberger},
+ title = {Source description of the 1999 {Hector Mine, California} earthquake;
+ {Part I: Wavelet} Domain Inversion Theory and Resolution Analysis},
+ journal = bssa,
+ year = {2002},
+ volume = {92},
+ pages = {1192-1207}
+}
+
+ at ARTICLE{Jia99,
+ author = {Zhang Jianfeng},
+ title = {Quadrangle-grid velocity-stress finite difference method for poroelastic
+ wave equations},
+ journal = gji,
+ year = {1999},
+ volume = {139},
+ pages = {171-182}
+}
+
+ at ARTICLE{JiWaBe95,
+ author = {W. Jiao and T. C. Wallace and S. L. Beck},
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+ earthquake},
+ journal = grl,
+ year = {1995},
+ volume = {22},
+ pages = {2285-2288},
+ number = {16}
+}
+
+ at ARTICLE{JiMcDe88,
+ author = {R. S. Jih and K. L. McLaughlin and Z. A Der},
+ title = {Free-boundary conditions of arbitrary polygonal topography in a two-dimensional
+ explicit elastic finite-difference scheme},
+ journal = geophysics,
+ year = {1988},
+ volume = {53},
+ pages = {1045-1055}
+}
+
+ at ARTICLE{JiMaViLa92,
+ author = {S. Jin and R. Madariaga and J. Virieux and G. Lambar\'e},
+ title = {Two dimensional asymptotic iterative elastic inversion},
+ journal = gji,
+ year = {1992},
+ volume = {108},
+ pages = {575-588}
+}
+
+ at ARTICLE{JoGaDiRo77,
+ author = {N. Jobert and R. Gaulon and A. Dieulin and G. Roult},
+ title = {Sur les ondes de tr\`es longue p\'eriode, caract\'eristiques du manteau
+ sup\'erieur},
+ journal = {Comptes rendus Acad. Sci. Paris},
+ year = {1977},
+ volume = {S\'erie B, 285},
+ pages = {49-51}
+}
+
+ at ARTICLE{JoHuMaJo92,
+ author = {Z. Johan and T. J. R. Hughes and K. K. Mathur and S. L. Johnsson},
+ title = {A data parallel finite element method for computational fluid dynamics
+ on the {C}onnection {M}achine system},
+ journal = cmame,
+ year = {1992},
+ volume = {99},
+ pages = {113-134}
+}
+
+ at ARTICLE{JoMaJoHu94,
+ author = {Z. Johan and K. K. Mathur and S. L. Johnsson and T. J. R. Hughes},
+ title = {An efficient communications strategy for finite element methods on
+ the {C}onnection {Machine} {CM-5} system},
+ journal = cmame,
+ year = {1994},
+ volume = {113},
+ pages = {363-387}
+}
+
+ at TECHREPORT{Jol95,
+ author = {P. Joly},
+ title = {R\'esolution de l'\'equation de {B}urgers par paquets d'ondelettes},
+ institution = {Laboratoire d'Analyse Num\'erique},
+ year = {1995},
+ address = {Universit\'e Pierre et Marie Curie, Paris}
+}
+
+ at INPROCEEDINGS{JoKoVi95,
+ author = {P. Joly and D. Komatitsch and J. P. Vilotte},
+ title = {Solution of the wave equation by a wavelet basis approximation},
+ booktitle = {Proceedings of the Enumath'1995 conference},
+ year = {1995},
+ pages = {12-24},
+ address = {Paris, France}
+}
+
+ at ARTICLE{JoMaPe94,
+ author = {P. Joly and Y. Maday and V. Perrier},
+ title = {Towards a method for solving partial differential equations by using
+ wavelet packet bases},
+ journal = cmame,
+ year = {1994},
+ volume = {116},
+ pages = {9999998-9999999}
+}
+
+ at ARTICLE{Jordan2,
+ author = {P. M. Jordan},
+ title = {{C}omment on \textit{{E}xact Constructions of Square-root {H}elmholtz
+ Operator Symbols: The Focusing Quadratic Profile}},
+ journal = {J. Math. Phys.},
+ year = {2000},
+ volume = {42},
+ pages = {4618-4623}
+}
+
+ at INPROCEEDINGS{JoJiLaGiCa03,
+ author = {Gabriele Jost and Haoquian Jin and Jesus Labarta and Judit Gim\'enez
+ and Jordi Caubet},
+ title = {Performance Analysis of Multilevel Parallel Applications on Shared
+ Memory Architectures},
+ booktitle = {Proceedings of the IPDPS'2003 International Parallel and Distributed
+ Processing Symposium},
+ year = {2003},
+ pages = {80.2},
+ address = {Nice, France},
+ month = apr,
+ bdsk-url-2 = {http://dx.doi.org/10.1109/IPDPS.2003.1213183},
+ doi = {10.1109/IPDPS.2003.1213183},
+ url = {www.cepba.upc.es/paraver}
+}
+
+ at ARTICLE{JoCh75,
+ author = {W. B. Joyner and T. F. Chen},
+ title = {Calculation of nonlinear ground response on earthquakes},
+ journal = bssa,
+ year = {1975},
+ volume = {65},
+ pages = {1315-1336}
+}
+
+ at ARTICLE{KaDu08,
+ author = {Martin K\"aser and Michael Dumbser},
+ title = {A Highly Accurate Discontinuous {G}alerkin Method for Complex Interfaces
+ Between Solids and Moving Fluids},
+ journal = geophysics,
+ year = {2008},
+ volume = {73},
+ pages = {T23-T35},
+ number = {3},
+ doi = {10.1190/1.2870081}
+}
+
+ at ARTICLE{KaDu06,
+ author = {M. K\"aser and M. Dumbser},
+ title = {An arbitrary high-order discontinuous {G}alerkin method for elastic
+ waves on unstructured meshes-{I}. {T}he two-dimensional isotropic
+ case with external source terms},
+ journal = gji,
+ year = {2006},
+ volume = {166},
+ pages = {855-877},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2006.03051.x}
+}
+
+ at ARTICLE{KaBi93,
+ author = {L. F. Kallivokas and J. Bielak},
+ title = {Time-domain analysis of transient structural acoustics problems based
+ on the finite element method and a novel boundary element},
+ journal = jasa,
+ year = {1993},
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+}
+
+ at ARTICLE{KaSgKi95,
+ author = {A. Kamel and P. Sguazzero and M. Kindelan},
+ title = {Cost-effective staggered schemes for the numerical simulation of
+ wave propagation},
+ journal = ijnme,
+ year = {1995},
+ volume = {38},
+ pages = {755-773}
+}
+
+ at ARTICLE{KaMaOrWe03,
+ author = {C. Kane and J. E. Marsden and M. Ortiz and M. West},
+ title = {Variational integrators and the {N}ewmark algorithm for conservative
+ and dissipative mechanical systems},
+ journal = ijnme,
+ year = {2003},
+ volume = {49},
+ pages = {1295-1325},
+ number = {10}
+}
+
+ at ARTICLE{KaBa04,
+ author = {Tae-Seob Kang and Chang-Eob Baag},
+ title = {Finite-Difference Seismic Simulation Combining Discontinuous Grids
+ with Locally Variable Timesteps},
+ journal = bssa,
+ year = {2004},
+ volume = {94},
+ pages = {207-219},
+ number = {1},
+ doi = {10.1785/0120030080}
+}
+
+ at ARTICLE{KapKuz99,
+ author = {A. V. Kaptsov and S. V. Kuznetsov},
+ title = {Spectral properties of {C}hristoffel equation for {R}ayleigh waves},
+ journal = {Compte Rendu de l'Academie des Sciences de Paris},
+ year = {1999},
+ volume = {327},
+ pages = {1123-1128},
+ number = {IIb}
+}
+
+ at ARTICLE{karato1993,
+ author = {S. Karato},
+ title = {Importance of anelasticity in the interpretation of seismic tomography},
+ journal = grl,
+ year = {1993},
+ volume = {20},
+ pages = {1623-1626}
+}
+
+ at ARTICLE{KaKu98a,
+ author = {George Karypis and Vipin Kumar},
+ title = {A Fast and High-Quality Multilevel Scheme for Partitioning Irregular
+ Graphs},
+ journal = {SIAM Journal on Scientific Computing},
+ year = {1998},
+ volume = {20},
+ pages = {359-392},
+ number = {1}
+}
+
+ at ARTICLE{KaKu98b,
+ author = {George Karypis and Vipin Kumar},
+ title = {Multilevel {$k$}-way Partitioning Scheme for Irregular Graphs},
+ journal = {Journal of Parallel and Distributed Computing},
+ year = {1998},
+ volume = {48},
+ pages = {96-129},
+ number = {1}
+}
+
+ at ARTICLE{KaKu98c,
+ author = {George Karypis and Vipin Kumar},
+ title = {A Parallel Algorithm for Multilevel Graph Partitioning and Sparse
+ Matrix Ordering},
+ journal = {Journal of Parallel and Distributed Computing},
+ year = {1998},
+ volume = {48},
+ pages = {71-85}
+}
+
+ at ARTICLE{KaWiTeSn87,
+ author = {Kass, M. and Witkin, A.P. and Terzopoulos, D. and Snakes},
+ title = {Active contour models},
+ journal = {Int. J. Comput. Vis.},
+ year = {1987},
+ volume = {1},
+ pages = {133-144},
+ number = {4}
+}
+
+ at INPROCEEDINGS{KaAn02,
+ author = {Theodoros K. Katsibas and Christos S. Antonopoulos},
+ title = {An efficient {PML} absorbing medium in {FDTD} simulations of acoustic
+ scattering in lossy media},
+ booktitle = {Proceedings of the 2002 IEEE ultrasonics symposium},
+ year = {2002},
+ volume = {1},
+ pages = {551-554},
+ address = {Munich, Germany},
+ month = {October},
+ organization = {IEEE}
+}
+
+ at ARTICLE{Kau92,
+ author = {E. Kausel},
+ title = {Physical interpretation and stability of paraxial boundary conditions},
+ journal = bssa,
+ year = {1992},
+ volume = {82},
+ pages = {898-913}
+}
+
+ at ARTICLE{KaTaGe06,
+ author = {K. Kawai and N. Takeuchi and R. J. Geller},
+ title = {Complete synthetic seismograms up to 2~{H}z for transversely-isotropic
+ spherically-symmetric media},
+ journal = gji,
+ year = {2006},
+ volume = {164},
+ pages = {411-424},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2005.02829.x}
+}
+
+ at ARTICLE{Kaw88,
+ author = {H. Kawase},
+ title = {Time-domain response of a semi-circular canyon for incident {{\it
+ SV}}, {{\it P}} and {R}ayleigh waves calculated by the discrete wavenumber
+ boundary element method},
+ journal = bssa,
+ year = {1988},
+ volume = {78},
+ pages = {1415-1437}
+}
+
+ at ARTICLE{KaAk90,
+ author = {H. Kawase and K. Aki},
+ title = {Topography effect at the critical {{\it SV}} wave incidence: possible
+ explanation of damage pattern by the {W}hittier {N}arrows, {C}alifornia,
+ earthquake of 1 {O}ctober 1987},
+ journal = bssa,
+ year = {1990},
+ volume = {80},
+ pages = {1-22}
+}
+
+ at ARTICLE{KaAk89,
+ author = {H. Kawase and K. Aki},
+ title = {A study on the response of a soft sedimentary basin for incident
+ {{\it S}}, {{\it P}} and {R}ayleigh waves, with special reference
+ to the long duration observed in {M}exico {C}ity},
+ journal = bssa,
+ year = {1989},
+ volume = {79},
+ pages = {1361-1382}
+}
+
+ at ARTICLE{KaKr99,
+ author = {I. Kay and E. S. Krebes},
+ title = {Applying finite element analysis to the memory variable formulation
+ of wave propagation in anelastic media},
+ journal = geophysics,
+ year = {1999},
+ volume = {64},
+ pages = {300-307}
+}
+
+ at ARTICLE{KeWaTrAl76,
+ author = {K. R. Kelly and R. W. Ward and S. Treitel and R. M. Alford},
+ title = {Synthetic seismograms: a Finite Difference approach},
+ journal = geophysics,
+ year = {1976},
+ volume = {41},
+ pages = {2-27}
+}
+
+ at ARTICLE{KeSi96,
+ author = {J. M. Kendall and P. G. Silver},
+ title = {Constraints from seismic anisotropy on the nature of the lowermost
+ mantle},
+ journal = {Nature},
+ year = {1996},
+ volume = {381},
+ pages = {409}
+}
+
+ at BOOK{Ken83,
+ title = {Seismic wave propagation in stratified media},
+ publisher = {Cambridge University Press},
+ year = {1983},
+ author = {B. L. N. Kennett},
+ address = {Cambridge}
+}
+
+ at ARTICLE{KeEn91,
+ author = {B. L. N. Kennett and E. R. Engdahl},
+ title = {Traveltimes for global earthquake location and phase identification},
+ journal = gji,
+ year = {1991},
+ volume = {105},
+ pages = {429-465}
+}
+
+ at ARTICLE{KeEnBu95,
+ author = {B. L. N. Kennett and E. R. Engdahl and R. Buland},
+ title = {Constraints on seismic velocities in the {E}arth from traveltimes},
+ journal = gji,
+ year = {1995},
+ volume = {122},
+ pages = {108-124}
+}
+
+ at ARTICLE{KhBoEn12,
+ author = {Khan, Samee and Bouvry, Pascal and Engel, Thomas},
+ title = {Energy-efficient high-performance parallel and distributed computing},
+ journal = {Journal of Supercomputing},
+ year = {2012},
+ volume = {60},
+ pages = {163-164},
+ number = {2},
+ doi = {10.1007/s11227-010-0485-0}
+}
+
+ at UNPUBLISHED{Khronos:2008:TOS,
+ author = {{Khronos OpenCL Working Group}},
+ title = {The {OpenCL} {S}pecification, Version 1.0},
+ note = {\url{http://www.khronos.org/opencl}},
+ month = dec,
+ year = {2008},
+ editor = {Aaftab Munshi}
+}
+
+ at ARTICLE{Khu85,
+ author = {M. J. Khun},
+ title = {A numerical study of {L}amb's problem},
+ journal = gp,
+ year = {1985},
+ volume = {33},
+ pages = {1103-1137}
+}
+
+ at ARTICLE{KiFe76,
+ author = {L. Kiefling and G. C. Feng},
+ title = {Fluid-structure finite-element vibrational analysis},
+ journal = {AIAA J.},
+ year = {1976},
+ volume = {14},
+ pages = {199-203},
+ number = {2}
+}
+
+ at MISC{KiYa2002,
+ author = {M. Kikuchi and Y. Yamanaka},
+ title = {Source rupture process of the central {A}laska earthquake of {N}ovember
+ 3, 2002, inferred from teleseismic body waves},
+ year = {2002},
+ note = {ERI, University of Tokyo, Japan, wwweic.eri.u-tokyo.ac.jp/EIC/EIC\_News/021103AL-e.html}
+}
+
+ at ARTICLE{KiPa93,
+ author = {J. Kim and A. Papageorgiou},
+ title = {Discrete wavenumber boundary element method for 3{D} scattering problems},
+ journal = {J. Eng. Mech. ASCE},
+ year = {1993},
+ volume = {119},
+ pages = {603-624}
+}
+
+ at INPROCEEDINGS{Kim08,
+ author = {Theodore Kim},
+ title = {Hardware-Aware Analysis and Optimization of `{S}table {F}luids'},
+ booktitle = {I3D '08: Proceedings of the 2008 symposium on Interactive 3D graphics
+ and games},
+ year = {2008},
+ pages = {99--106},
+ doi = {10.1145/1342250.1342265}
+}
+
+ at ARTICLE{KiSeSg89,
+ author = {M. Kindelan and G. Seriani and P. Sguazzero},
+ title = {Elastic modeling and its application to amplitude versus angle interpretation},
+ journal = gp,
+ year = {1989},
+ volume = {37},
+ pages = {3-30}
+}
+
+ at INPROCEEDINGS{KiEnShShArStPhHw09,
+ author = {Volodymyr V. Kindratenko and Jeremy J. Enos and Guochun Shi and Michael
+ T. Showerman and Galen W. Arnold and John E. Stone and James C. Phillips
+ and Wen{-}mei Hwu},
+ title = {{GPU} Clusters for High-Performance Computing},
+ booktitle = {Proceedings on the IEEE Cluster'2009 Workshop on Parallel Programming
+ on Accelerator Clusters (PPAC'09)},
+ year = {2009},
+ pages = {1-8},
+ address = {New Orleans, Louisiana, USA},
+ month = aug
+}
+
+ at BOOK{KiHw10,
+ title = {Programming Massively Parallel Processors: A Hands-on Approach},
+ publisher = {Morgan Kaufmann},
+ year = {2010},
+ author = {Kirk, David B. and Hwu, Wen-mei W.},
+ address = {Boston, Massachusetts, USA}
+}
+
+ at INPROCEEDINGS{kiyashchenkoplessix2005,
+ author = {D. A. Kiyashchenko and R. E. Plessix},
+ title = {True amplitude multi-one-way migration: comparison of different imaging
+ principles},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {2005},
+ note = {75th international meeting of the SEG}
+}
+
+ at ARTICLE{KlWaBrHe09,
+ author = {A. Kl\"ockner and T. Warburton and J. Bridge and J. S. Hesthaven},
+ title = {Nodal discontinuous {G}alerkin methods on graphics processors},
+ journal = jcp,
+ year = {2009},
+ volume = {228},
+ pages = {7863-7882},
+ doi = {10.1016/j.jcp.2009.06.041}
+}
+
+ at TECHREPORT{KlVi02,
+ author = {E. M. C. Klien and J. P. Vilotte},
+ title = {Perfectly matched layers in the spectral element method},
+ institution = {Lithos Scientific Report},
+ year = {2002},
+ number = {4},
+ note = {Unpublished}
+}
+
+ at ARTICLE{Kli96,
+ author = {L. Klimes},
+ title = {Accuracy of elastic finite differences in smooth media},
+ journal = pageoph,
+ year = {1996},
+ volume = {148},
+ pages = {39-76},
+ number = {1}
+}
+
+ at ARTICLE{Kno52,
+ author = {L. Knopoff},
+ title = {On {R}ayleigh wave velocities},
+ journal = {Bulletin of the Seismological Society of America},
+ year = {1952},
+ volume = {42},
+ pages = {307-308}
+}
+
+ at ARTICLE{Knu99,
+ author = {Patrick M. Knupp},
+ title = {Applications of mesh smoothing: copy, morph, and sweep on unstructured
+ quadrilateral meshes},
+ journal = ijnme,
+ year = {1999},
+ volume = {45},
+ pages = {37-45},
+ number = {1}
+}
+
+ at INCOLLECTION{Kob84,
+ author = {S. Kobayashi},
+ title = {Fundamentals of boundary integral equations methods in elastodynamics},
+ booktitle = {Boundary element research},
+ publisher = {Springer-Verlag},
+ year = {1984},
+ editor = {C. A. Brebbia},
+ volume = {2},
+ address = {New York}
+}
+
+ at BOOK{Kob87,
+ title = {Elastodynamics in boundary element methods in mechanics},
+ publisher = {North-Holland},
+ year = {1987},
+ author = {S. Kobayashi},
+ address = {Amsterdam, The Netherlands}
+}
+
+ at ARTICLE{KohnNir,
+ author = {J. J. Kohn and L. Nirenberg},
+ title = {On the Algebra of Pseudo-Differential Operators},
+ journal = {Comm. Pure Appl. Math.},
+ year = {1965},
+ volume = {18},
+ pages = {269-305}
+}
+
+ at ARTICLE{KolMaz93,
+ author = {Al. A. Kolomenskii and A. A. Maznev},
+ title = {Phonon-focusing effect with laser-generated ultrasonic surface waves},
+ journal = {Physical Review B},
+ year = {1993},
+ volume = {48},
+ pages = {14502-14512},
+ number = {19}
+}
+
+ at ARTICLE{Kom11,
+ author = {Dimitri Komatitsch},
+ title = {Fluid-solid coupling on a cluster of {GPU} graphics cards for seismic
+ wave propagation},
+ journal = {C. R. Acad. Sci., Ser. IIb Mec.},
+ year = {2011},
+ volume = {339},
+ pages = {125-135},
+ doi = {10.1016/j.crme.2010.11.007}
+}
+
+ at ARTICLE{Kom08,
+ author = {Dimitri Komatitsch},
+ title = {Comment on ``{M}ultidomain {P}seudospectral {T}ime-{D}omain ({PSTD})
+ method for acoustic waves in lossy media'' by {Y. Q. Zeng, Q. H.
+ Liu and G. Zhao, Journal of Computational Acoustics, vol. 12, no.
+ 3, pp 277-299 (2004)}},
+ journal = jca,
+ year = {2008},
+ volume = {16},
+ pages = {465-467},
+ number = {3}
+}
+
+ at PHDTHESIS{Kom03,
+ author = {Dimitri Komatitsch},
+ title = {Advanced numerical modeling in geophysics ({M}od\'elisation num\'erique
+ avanc\'ee pour la g\'eophysique)},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {2003},
+ address = {Pau, France},
+ month = {September},
+ note = {Habilitation Thesis (Habilitation \`a {D}iriger des {R}echerches,
+ {H.D.R.}), 114 pages}
+}
+
+ at PHDTHESIS{Kom97,
+ author = {Dimitri Komatitsch},
+ title = {M\'ethodes spectrales et \'el\'ements spectraux pour l'\'equation
+ de l'\'elastodynamique 2{D} et 3{D} en milieu h\'et\'erog\`ene ({S}pectral
+ and spectral-element methods for the 2{D} and 3{D} elastodynamics
+ equations in heterogeneous media)},
+ school = {Institut de Physique du Globe},
+ year = {1997},
+ address = {Paris, France},
+ month = {May},
+ note = {187 pages}
+}
+
+ at ARTICLE{KoBaTr00,
+ author = {D. Komatitsch and C. Barnes and J. Tromp},
+ title = {Wave propagation near a fluid-solid interface: a spectral element
+ approach},
+ journal = geophysics,
+ year = {2000},
+ volume = {65},
+ pages = {623-631},
+ number = {2},
+ doi = {10.1190/1.1444758}
+}
+
+ at ARTICLE{KoBaTr00b,
+ author = {D. Komatitsch and C. Barnes and J. Tromp},
+ title = {Simulation of anisotropic wave propagation based upon a spectral
+ element method},
+ journal = geophysics,
+ year = {2000},
+ volume = {65},
+ pages = {1251-1260},
+ number = {4},
+ doi = {10.1190/1.1444816}
+}
+
+ at ARTICLE{KoCaCaFa11,
+ author = {Dimitri Komatitsch and Jos\'e Carcione and Fabio Cavallini and Nathalie
+ Favretto-Cristini},
+ title = {Elastic surface waves in crystals: {P}art {II} : Cross-check of two
+ full-wave numerical modeling methods},
+ journal = {Ultrasonics},
+ year = {2011},
+ volume = {51},
+ pages = {878-889},
+ number = {8},
+ doi = {10.1016/j.ultras.2011.05.001}
+}
+
+ at ARTICLE{KoCoMo96,
+ author = {D. Komatitsch and F. Coutel and P. Mora},
+ title = {Tensorial formulation of the wave equation for modelling curved interfaces},
+ journal = gji,
+ year = {1996},
+ volume = {127},
+ pages = {156-168},
+ number = {1},
+ doi = {10.1111/j.1365-246X.1996.tb01541.x}
+}
+
+ at ARTICLE{KoErGoMi10,
+ author = {Dimitri Komatitsch and Gordon Erlebacher and Dominik G\"oddeke and
+ David Mich\'ea},
+ title = {High-order finite-element seismic wave propagation modeling with
+ {MPI} on a large {GPU} cluster},
+ journal = jcp,
+ year = {2010},
+ volume = {229},
+ pages = {7692-7714},
+ number = {20},
+ doi = {10.1016/j.jcp.2010.06.024}
+}
+
+ at ARTICLE{KoGoErMi10,
+ author = {Dimitri Komatitsch and Dominik G\"oddeke and Gordon Erlebacher and
+ David Mich\'ea},
+ title = {Modeling the propagation of elastic waves using spectral elements
+ on a cluster of 192 {GPU}s},
+ journal = {Computer Science Research and Development},
+ year = {2010},
+ volume = {25},
+ pages = {75-82},
+ number = {1-2},
+ doi = {10.1007/s00450-010-0109-1}
+}
+
+ at ARTICLE{KoLaMi08a,
+ author = {Dimitri Komatitsch and Jes\'us Labarta and David Mich\'ea},
+ title = {A simulation of seismic wave propagation at high resolution in the
+ inner core of the {E}arth on 2166 processors of {M}are{N}ostrum},
+ journal = lncs,
+ year = {2008},
+ volume = {5336},
+ pages = {364-377}
+}
+
+ at INPROCEEDINGS{KoLaMi08b,
+ author = {Dimitri Komatitsch and Jes\'us Labarta and David Mich\'ea},
+ title = {A 21 billion degrees of freedom, 2.5 terabyte simulation of seismic
+ wave propagation in the inner core of the {E}arth on {M}are{N}ostrum},
+ booktitle = {Proceedings of the 8th. World Congress on Computational Mechanics
+ (WCCM8) and the 5th. European Congress on Computational Methods in
+ Applied Sciences and Engineering (ECCOMAS 2008)},
+ year = {2008},
+ address = {Venice, Italy},
+ note = {30 June - 4 July 2008}
+}
+
+ at ARTICLE{KoLiTrSuStSh04,
+ author = {Dimitri Komatitsch and Qinya Liu and Jeroen Tromp and Peter S\"{u}ss
+ and Christiane Stidham and John H. Shaw},
+ title = {Simulations of Ground Motion in the {L}os {A}ngeles Basin based upon
+ the Spectral-Element Method},
+ journal = bssa,
+ year = {2004},
+ volume = {94},
+ pages = {187-206},
+ number = {1},
+ doi = {10.1785/0120030077}
+}
+
+ at ARTICLE{KoMa07,
+ author = {Dimitri Komatitsch and Roland Martin},
+ title = {An unsplit convolutional {P}erfectly {M}atched {L}ayer improved at
+ grazing incidence for the seismic wave equation},
+ journal = geophysics,
+ year = {2007},
+ volume = {72},
+ pages = {SM155-SM167},
+ number = {5},
+ doi = {10.1190/1.2757586}
+}
+
+ at ARTICLE{KoMaTrTaWi01,
+ author = {D. Komatitsch and R. Martin and J. Tromp and M. A. Taylor and B.
+ A. Wingate},
+ title = {Wave propagation in 2-{D} elastic media using a spectral element
+ method with triangles and quadrangles},
+ journal = jca,
+ year = {2001},
+ volume = {9},
+ pages = {703-718},
+ number = {2},
+ doi = {10.1142/S0218396X01000796}
+}
+
+ at ARTICLE{KoMiEr09,
+ author = {Dimitri Komatitsch and David Mich\'ea and Gordon Erlebacher},
+ title = {Porting a high-order finite-element earthquake modeling application
+ to {NVIDIA} graphics cards using {CUDA}},
+ journal = jpdc,
+ year = {2009},
+ volume = {69},
+ pages = {451-460},
+ number = {5},
+ doi = {10.1016/j.jpdc.2009.01.006}
+}
+
+ at ARTICLE{KoRiTr02,
+ author = {D. Komatitsch and J. Ritsema and J. Tromp},
+ title = {The Spectral-Element Method, {B}eowulf Computing, and Global Seismology},
+ journal = {Science},
+ year = {2002},
+ volume = {298},
+ pages = {1737-1742},
+ number = {5599},
+ doi = {10.1126/science.1076024}
+}
+
+ at INCOLLECTION{KoTr02c,
+ author = {D. Komatitsch and J. Tromp},
+ title = {Propagaci{\'o}n de ondas s{\'\i}smicas en modelos de tierra global
+ 3-{D} usando elementos espectrales},
+ booktitle = {M\'etodos num\'ericos en ingenieria y ciencias aplicadas},
+ publisher = {CIMNE},
+ year = {2002},
+ editor = {{E. O{\~{n}}ate et al.}},
+ pages = {676-686},
+ address = {Barcelona, Espa{\~{n}}a}
+}
+
+ at ARTICLE{KoTr03,
+ author = {D. Komatitsch and J. Tromp},
+ title = {A {P}erfectly {M}atched {L}ayer absorbing boundary condition for
+ the second-order seismic wave equation},
+ journal = gji,
+ year = {2003},
+ volume = {154},
+ pages = {146-153},
+ number = {1},
+ doi = {10.1046/j.1365-246X.2003.01950.x}
+}
+
+ at ARTICLE{KoTr02a,
+ author = {D. Komatitsch and J. Tromp},
+ title = {Spectral-Element Simulations of Global Seismic Wave Propagation{-I.
+ V}alidation},
+ journal = gji,
+ year = {2002},
+ volume = {149},
+ pages = {390-412},
+ number = {2},
+ doi = {10.1046/j.1365-246X.2002.01653.x}
+}
+
+ at ARTICLE{KoTr02b,
+ author = {D. Komatitsch and J. Tromp},
+ title = {Spectral-Element Simulations of Global Seismic Wave Propagation{-II.
+ 3-D} Models, Oceans, Rotation, and Self-Gravitation},
+ journal = gji,
+ year = {2002},
+ volume = {150},
+ pages = {303-318},
+ number = {1},
+ doi = {10.1046/j.1365-246X.2002.01716.x}
+}
+
+ at INPROCEEDINGS{KoTr01c,
+ author = {D. Komatitsch and J. Tromp},
+ title = {Modeling of seismic wave propagation at the scale of the {E}arth
+ on a large {B}eowulf},
+ booktitle = {SC'01: Proceedings of the 2001 ACM/IEEE conference on Supercomputing},
+ year = {2001},
+ pages = {33-41},
+ address = {Denver, Colorado, USA},
+ month = nov,
+ doi = {10.1109/SC.2001.10003}
+}
+
+ at ARTICLE{KoTr01d,
+ author = {D. Komatitsch and J. Tromp},
+ title = {Modeling Seismic Wave Propagation on a 156~{GB PC} Cluster},
+ journal = {Linux Journal},
+ year = {2001},
+ volume = {90},
+ pages = {38-45}
+}
+
+ at ARTICLE{KoTr99,
+ author = {D. Komatitsch and J. Tromp},
+ title = {Introduction to the spectral-element method for 3-{D} seismic wave
+ propagation},
+ journal = gji,
+ year = {1999},
+ volume = {139},
+ pages = {806-822},
+ number = {3},
+ doi = {10.1046/j.1365-246x.1999.00967.x}
+}
+
+ at INPROCEEDINGS{KoTsChTr03,
+ author = {Dimitri Komatitsch and Seiji Tsuboi and Chen Ji and Jeroen Tromp},
+ title = {A 14.6~billion degrees of freedom, 5~teraflops, 2.5~terabyte earthquake
+ simulation on the {E}arth~{S}imulator},
+ booktitle = {SC'03: Proceedings of the 2003 ACM/IEEE conference on Supercomputing},
+ year = {2003},
+ pages = {4-11},
+ address = {Phoenix, Arizona, USA},
+ month = nov,
+ note = {{G}ordon {B}ell {P}rize winner article},
+ doi = {10.1109/SC.2003.10023}
+}
+
+ at INCOLLECTION{KoTsTr05,
+ author = {D. Komatitsch and S. Tsuboi and J. Tromp},
+ title = {The Spectral-Element Method in Seismology},
+ booktitle = {Seismic Earth: Array Analysis of Broadband Seismograms},
+ publisher = {American Geophysical Union},
+ year = {2005},
+ editor = {Alan Levander and Guust Nolet},
+ volume = {157},
+ series = {Geophysical Monograph},
+ pages = {205-228},
+ address = {Washington DC, USA}
+}
+
+ at ARTICLE{KoVi98,
+ author = {D. Komatitsch and J. P. Vilotte},
+ title = {The spectral-element method: an efficient tool to simulate the seismic
+ response of 2{D} and 3{D} geological structures},
+ journal = bssa,
+ year = {1998},
+ volume = {88},
+ pages = {368-392},
+ number = {2}
+}
+
+ at ARTICLE{KoViVaCaSa99,
+ author = {D. Komatitsch and J. P. Vilotte and R. Vai and J. M. Castillo-Covarrubias
+ and F. J. S\'anchez-Sesma},
+ title = {The spectral-element method for elastic wave equations: application
+ to 2{D} and 3{D} seismic problems},
+ journal = ijnme,
+ year = {1999},
+ volume = {45},
+ pages = {1139-1164},
+ number = {9},
+ doi = {10.1002/(SICI)1097-0207(19990730)45:9<1139::AID-NME617>3.0.CO;2-T}
+}
+
+ at ARTICLE{KoViCh10,
+ author = {D. Komatitsch and L. P. Vinnik and S. Chevrot},
+ title = {{SH}diff/{SV}diff splitting in an isotropic {E}arth},
+ journal = jgr,
+ year = {2010},
+ volume = {115},
+ pages = {B07312},
+ number = {B7},
+ doi = {10.1029/2009JB006795}
+}
+
+ at ARTICLE{Komornik,
+ author = {V. Komornik},
+ title = {Stabilisation fronti\`ere des \'equations de {M}axwell},
+ journal = {C. R. Acad. Sci. Paris S\'er. I},
+ year = {1994},
+ volume = {318},
+ pages = {535-540}
+}
+
+ at ARTICLE{Kop06,
+ author = {D. A. Kopriva},
+ title = {Metric identities and the discontinuous spectral element method on
+ curvilinear meshes},
+ journal = {Journal of Scientific Computing},
+ year = {2006},
+ volume = {26},
+ pages = {301-327},
+ number = {3},
+ doi = {10.1007/s10915-005-9070-8}
+}
+
+ at ARTICLE{Kop96,
+ author = {D. A. Kopriva},
+ title = {A conservative staggered-grid {C}hebyshev multidomain method for
+ compressible flows: {P}art {II}, a semi-structured method},
+ journal = jcp,
+ year = {1996},
+ volume = {128},
+ pages = {475-488}
+}
+
+ at ARTICLE{Kop89,
+ author = {David A. Kopriva},
+ title = {Computation of Hyperbolic Equations on Complicated Domains with Patched
+ and Overset {C}hebyshev Grids},
+ journal = {SIAM Journal on Scientific and Statistical Computing},
+ year = {1989},
+ volume = {10},
+ pages = {120-132},
+ number = {1},
+ doi = {10.1137/0910010}
+}
+
+ at ARTICLE{Kop86,
+ author = {David A. Kopriva},
+ title = {A spectral multidomain method for the solution of hyperbolic systems},
+ journal = {Applied Numerical Mathematics},
+ year = {1986},
+ volume = {2},
+ pages = {221-241},
+ number = {3-5},
+ doi = {10.1016/0168-9274(86)90030-9}
+}
+
+ at ARTICLE{KoWoHu02,
+ author = {D. A. Kopriva and S. L. Woodruff and M. Y. Hussaini},
+ title = {Computation of electromagnetic scattering with a non-conforming discontinuous
+ spectral element method},
+ journal = ijnme,
+ year = {2002},
+ volume = {53},
+ pages = {105-122},
+ number = {1},
+ doi = {10.1002/nme.394}
+}
+
+ at ARTICLE{KosKosSyr85,
+ author = {A. M. Kosevich and Yu. A. Kosevich and E. S. Syrkin},
+ title = {Generalized {R}ayleigh waves and the geometry of isofrequency surfaces
+ of sound oscillation waves in crystals},
+ journal = {Soviet Physics - Journal of Experimental and Theoretical Physics},
+ year = {1985},
+ volume = {61},
+ pages = {639-644}
+}
+
+ at ARTICLE{KosSyr85,
+ author = {Yu. A. Kosevich and E. S. Syrkin},
+ title = {Existence criterion and properties of deeply penetrating {R}ayleigh
+ waves in crystals},
+ journal = {Soviet Physics - Journal of Experimental and Theoretical Physics},
+ year = {1985},
+ volume = {62},
+ pages = {1282-1286},
+ number = {6}
+}
+
+ at ARTICLE{KosSyrKos97,
+ author = {Yu. A. Kosevich and E. S. Syrkin and A. M. Kosevich},
+ title = {Vibrations localized near surfaces and interfaces in non-traditional
+ crystals},
+ journal = {Progress in Surface Science},
+ year = {1997},
+ volume = {55},
+ pages = {59-111},
+ number = {1}
+}
+
+ at ARTICLE{KoBa82,
+ author = {D. Kosloff and E. Baysal},
+ title = {Forward modeling by the {F}ourier method},
+ journal = geophysics,
+ year = {1982},
+ volume = {47},
+ pages = {1402-1412}
+}
+
+ at ARTICLE{KoKeFiTeBeSt90,
+ author = {D. Kosloff and D. Kessler and A. Q. Filho and E. Tessmer and A. Behle
+ and R. Strahilevitz},
+ title = {Solution of the equations of dynamic elasticity by a {C}hebychev
+ spectral method},
+ journal = geophysics,
+ year = {1990},
+ volume = {55},
+ pages = {734-748},
+ doi = {10.1190/1.1442885}
+}
+
+ at ARTICLE{KoReLo84,
+ author = {D. Kosloff and M. Reshef and D. Loewenthal},
+ title = {Elastic wave calculations by the {F}ourier method},
+ journal = bssa,
+ year = {1984},
+ volume = {74},
+ pages = {875-891}
+}
+
+ at ARTICLE{KoTa93,
+ author = {D. Kosloff and H. Tal-Ezer},
+ title = {A modified {C}hebyshev pseudospectral method with an {{$O(N^{-1})$}}
+ time step restriction},
+ journal = jcp,
+ year = {1993},
+ volume = {104},
+ pages = {457-469}
+}
+
+ at ARTICLE{KoYiTs99,
+ author = {T. I. Kosmanis and T. V. Yioultsis and T. D. Tsiboukis},
+ title = {Perfectly matched anisotropic layer for the numerical analysis of
+ unbounded eddy-current problems},
+ journal = {IEEE transactions on Magnetics},
+ year = {1999},
+ volume = {35},
+ pages = {4452-4458},
+ number = {6}
+}
+
+ at PHDTHESIS{Krueger:2006:AGF,
+ author = {Jens Kr{\"u}ger},
+ title = {A {GPU} Framework for Interactive Simulation and Rendering of Fluid
+ Effects},
+ school = {Technische Universit{\"a}t M{\"u}nchen, Germany},
+ year = {2006},
+ month = dec
+}
+
+ at ARTICLE{Krueger:2003:LAO,
+ author = {Jens Kr{\"u}ger and R{\"u}diger Westermann},
+ title = {Linear algebra operators for {GPU} implementation of numerical algorithms},
+ journal = {ACM Transactions on Graphics},
+ year = {2003},
+ volume = {22},
+ pages = {908--916},
+ number = {3},
+ month = jul,
+ doi = {10.1145/882262.882363}
+}
+
+ at INPROCEEDINGS{KrTuOk04a,
+ author = {Sean E. Krakiwsky and Laurence E. Turner and Michal M. Okoniewski},
+ title = {Graphics processor unit ({GPU}) acceleration of a finite-difference
+ time-domain ({FDTD}) algorithm},
+ booktitle = {Proceedings of the 2004 IEEE International Symposium on Circuits
+ and Systems},
+ year = {2004},
+ pages = {265-268},
+ address = {Vancouver, British Columbia, Canada}
+}
+
+ at ARTICLE{KrTuOk04b,
+ author = {S. E. Krakiwsky and L. E. Turner and M. M. Okoniewski},
+ title = {Acceleration of finite-difference time-domain ({FDTD}) using graphics
+ processor units ({GPU})},
+ journal = {IEEE 2004 MTT-S International Microwave Symposium Digest},
+ year = {2004},
+ volume = {2},
+ pages = {1033-1036},
+ doi = {10.1109/MWSYM.2004.1339160}
+}
+
+ at ARTICLE{Kra76,
+ author = {E. Kraut},
+ title = {Review of theories of scattering of elastic waves by cracks},
+ journal = {IEEE Trans. S. U.},
+ year = {1976},
+ volume = {3},
+ pages = {162-167}
+}
+
+ at ARTICLE{Kra63,
+ author = {E. A. Kraut},
+ title = {Advances in the theory of anisotropic elastic wave propagation},
+ journal = {Reviews of Geophysics},
+ year = {1963},
+ volume = {1},
+ pages = {401-448},
+ number = {3}
+}
+
+ at ARTICLE{Kre06,
+ author = {Steen Krenk},
+ title = {Energy conservation in {N}ewmark based time integration algorithms},
+ journal = cmame,
+ year = {2006},
+ volume = {195},
+ pages = {6110-6124},
+ number = {44-47},
+ doi = {10.1016/j.cma.2005.12.001}
+}
+
+ at ARTICLE{KrJiKoTr06a,
+ author = {Swaminathan Krishnan and Chen Ji and Dimitri Komatitsch and Jeroen
+ Tromp},
+ title = {Case Studies of Damage to Tall Steel Moment-Frame Buildings in {S}outhern
+ {C}alifornia during Large {S}an {A}ndreas Earthquakes},
+ journal = bssa,
+ year = {2006},
+ volume = {96},
+ pages = {1523-1537},
+ number = {4A},
+ doi = {10.1785/0120050145}
+}
+
+ at ARTICLE{KrJiKoTr06b,
+ author = {Swaminathan Krishnan and Chen Ji and Dimitri Komatitsch and Jeroen
+ Tromp},
+ title = {Performance of two 18-story steel moment-frame buildings in {S}outhern
+ {C}alifornia during two large simulated {S}an {A}ndreas Earthquakes},
+ journal = {Earthquake Spectra},
+ year = {2006},
+ volume = {22},
+ pages = {1035-1061},
+ number = {4},
+ doi = {10.1193/1.2360698}
+}
+
+ at INPROCEEDINGS{KrJiKoTr06c,
+ author = {Swaminathan Krishnan and Chen Ji and Dimitri Komatitsch and Jeroen
+ Tromp},
+ title = {Impact of a large {S}an {A}ndreas fault earthquake on tall buildings
+ in {S}outhern {C}alifornia},
+ booktitle = {Proceedings of the 8th U.S. National Conference on Earthquake Engineering},
+ year = {2006},
+ pages = {1-12},
+ month = {April 18-22},
+ note = {Paper No. 154, available on CD-ROM.}
+}
+
+ at ARTICLE{KrMo03,
+ author = {J. Kristek and P. Moczo},
+ title = {Seismic-Wave Propagation in Viscoelastic Media with Material Discontinuities:
+ {A 3D} Fourth-Order Staggered-Grid Finite-Difference Modeling},
+ journal = bssa,
+ year = {2003},
+ volume = {93},
+ pages = {2273-2280},
+ number = {5}
+}
+
+ at ARTICLE{KrMoGa09,
+ author = {Jozef Kristek and Peter Moczo and Martin Galis},
+ title = {A brief summary of some {PML} formulations and discretizations for
+ the velocity-stress equation of seismic motion},
+ journal = {Studia Geophysica et Geodaetica},
+ year = {2009},
+ volume = {53},
+ pages = {459-474},
+ number = {4},
+ doi = {10.1007/s11200-009-0034-6}
+}
+
+ at INCOLLECTION{KrMoIrIwSe99,
+ author = {J. Kristek and P. Moczo and K. Irikura and T. Iwata and H. Sekiguchi},
+ title = {The 1995 {K}obe mainshock simulated by {3D} finite differences},
+ booktitle = {The Effects of Surface Geology on Seismic Motion},
+ publisher = {Balkema},
+ year = {1999},
+ editor = {K. Irikura and K. Kudo and H. Okada and T. Sasatani},
+ volume = {3},
+ pages = {1361-1368},
+ address = {Rotterdam, The Netherlands}
+}
+
+ at ARTICLE{KrWeScSc95,
+ author = {F. Krueger and M. Weber and F. Scherbaum and J. Schlittenhardt},
+ title = {Evidence for normal and inhomogeneous lowermost mantle and core-mantle
+ boundary structure under the {A}rctic and northern {C}anada},
+ journal = gji,
+ year = {1995},
+ volume = {122},
+ pages = {637-657},
+ number = {2}
+}
+
+ at ARTICLE{KuAn69,
+ author = {M. Kumazawa and O. L. Anderson},
+ title = {Elastic Moduli, Pressure Derivates and Temperature Derivates of Single-Crystal
+ Olivine and Single-Crystal Forstite},
+ journal = jgr,
+ year = {1969},
+ volume = {74},
+ pages = {5961-5972}
+}
+
+ at INPROCEEDINGS{KuBe88,
+ author = {B. Kummer and A. Behle},
+ title = {Fast modeling of seismic waves in laterally inhomogeneous media},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1988},
+ pages = {1175-1177},
+ note = {58th international meeting of the SEG}
+}
+
+ at ARTICLE{KuDzEk06,
+ author = {B. Kustowski and A. M. Dziewo\'nski and G. Ekstrom},
+ title = {Modeling the anisotropic shear-wave velocity structure in the {E}arth's
+ mantle on global and regional scales},
+ journal = {EOS},
+ year = {2006},
+ volume = {87},
+ pages = {Abstract S41E-02},
+ number = {52},
+ note = {Fall Meet. Suppl.}
+}
+
+ at ARTICLE{Kuz02,
+ author = {S. V. Kuznetsov},
+ title = {"Forbidden" planes for {R}ayleigh waves},
+ journal = {Quarterly of Applied Mathematics},
+ year = {2002},
+ volume = {60},
+ pages = {87-97}
+}
+
+ at ARTICLE{KuMi96,
+ author = {M. Kuzuoglu and R. Mittra},
+ title = {Frequency dependence of the constitutive parameters of causal perfectly
+ matched anisotropic absorbers},
+ journal = {IEEE Microwave and Guided Wave Letters},
+ year = {1996},
+ volume = {6},
+ pages = {447-449},
+ number = {12}
+}
+
+ at ARTICLE{LaMaQu97,
+ author = {D. J. P. Lahaye and F. Maggio and A. Quarteroni},
+ title = {Hybrid finite element-spectral element approximation of wave propagation
+ problems},
+ journal = {East-West J. Numer. Math.},
+ year = {1997},
+ volume = {5},
+ pages = {265-289},
+ number = {4}
+}
+
+ at ARTICLE{Lak87,
+ author = {R. Lakes},
+ title = {Foam structures with a negative {P}oisson's ratio},
+ journal = {Science},
+ year = {1987},
+ volume = {235},
+ pages = {1038-1040}
+}
+
+ at BOOK{Lam52,
+ title = {Le\c cons sur la th\'eorie math\'ematique de l'\'elasticit\'e des
+ corps solides},
+ publisher = {Gauthier-Villars},
+ year = {1852},
+ author = {Gabriel Lam\'e},
+ address = {Paris}
+}
+
+ at ARTICLE{Lam04,
+ author = {H. Lamb},
+ title = {On the propagation of tremors over the surface of an elastic solid},
+ journal = {Phil. Trans. R. Soc. London. Ser. A},
+ year = {1904},
+ volume = {203},
+ pages = {1-42}
+}
+
+ at ARTICLE{LaViMaJi92,
+ author = {Gilles Lambar\'e and Jean Virieux and Raul Madariaga and Side Jin},
+ title = {Iterative asymptotic inversion in the acoustic approximation},
+ journal = geophysics,
+ year = {1992},
+ volume = {57},
+ pages = {1138-1154},
+ number = {9}
+}
+
+ at BOOK{LaLi53,
+ title = {Th\'eorie de l'\'elasticit\'e ({T}heory of {E}lasticity)},
+ publisher = {Mir},
+ year = {1953},
+ author = {L. Landau and E. Lifchitz},
+ address = {Moscow, Russia},
+ edition = {2nd}
+}
+
+ at BOOK{LaLi59,
+ title = {Fluid mechanics},
+ publisher = {Pergamon Press},
+ year = {1959},
+ author = {L. D. Landau and E. M. Lifshitz},
+ address = {New York}
+}
+
+ at ARTICLE{Lap61,
+ author = {E. R. Lapwood},
+ title = {The transmission of a {R}ayleigh pulse round a corner},
+ journal = {Geophys. J.},
+ year = {1961},
+ volume = {4},
+ pages = {174-196}
+}
+
+ at ARTICLE{LaAnDrStScLoRo97,
+ author = {S. Larsen and M. Antolik and D. Dreger and C. Stidham and C. Schultz
+ and A. Lomax and B. Romanowicz},
+ title = {3-{D} Models of Seismic Wave Propagation: Simulating Scenario Earthquakes
+ Along the {H}ayward Fault},
+ journal = {Seis. Res. Lett.},
+ year = {1997},
+ volume = {68},
+ pages = {328}
+}
+
+ at ARTICLE{LaMiTrTaKoCh05,
+ author = {Konstantin Latychev and Jerry X. Mitrovica and Jeroen Tromp and Mark
+ E. Tamisiea and Dimitri Komatitsch and Christina C. Christara},
+ title = {Glacial isostatic adjustment on 3-{D} {E}arth models: a finite-volume
+ formulation},
+ journal = gji,
+ year = {2005},
+ volume = {161},
+ pages = {421-444},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2005.02536.x}
+}
+
+ at ARTICLE{LayKanamoriAmmon2005,
+ author = {T. Lay and H. Kanamori and C.J. Ammon and M. Nettles and S. N. Ward
+ and R. C. Aster and S. L. Beck and S. L. Bilek and M. R. Brudzinski
+ and R. Butler and H. R. DeShon and G. Ekstrom and K. Satake and S.
+ Sipkin},
+ title = {The great {S}umatra-{A}ndaman earthquake of 26 {D}ecember 2004},
+ journal = {Science},
+ year = {2005},
+ volume = {3},
+ pages = {1127-1133},
+ number = {5725}
+}
+
+ at ARTICLE{LaYo91,
+ author = {T. Lay and C. Young},
+ title = {Analysis of seismic {SV} waves in the core's penumbra},
+ journal = grl,
+ year = {1991},
+ volume = {18},
+ pages = {1373-1376}
+}
+
+ at ARTICLE{LeLi07,
+ author = {Joon Ho Lee and Qing Huo Liu},
+ title = {A {3-D} Spectral-Element Time-Domain Method for Electromagnetic Simulation},
+ journal = {IEEE Transactions on Microwave Theory and Techniques},
+ year = {2007},
+ volume = {55},
+ pages = {983-991},
+ number = {5},
+ doi = {10.1109/TMTT.2007.895398}
+}
+
+ at ARTICLE{LeLi05,
+ author = {Joon Ho Lee and Qing Huo Liu},
+ title = {An efficient {3-D} spectral element method for {S}chr\"odinger equation
+ in nanodevice simulation},
+ journal = {IEEE Transactions on Computer-Aided Design of Integrated Circuits
+ and Systems},
+ year = {2005},
+ volume = {24},
+ pages = {1848-1858},
+ number = {12}
+}
+
+ at ARTICLE{LeChKoHuTr09,
+ author = {Shiann Jong Lee and Yu Chang Chan and Dimitri Komatitsch and Bor
+ Shouh Huang and Jeroen Tromp},
+ title = {Effects of realistic surface topography on seismic ground motion
+ in the {Y}angminshan region of {T}aiwan based upon the spectral-element
+ method and {LiDAR DTM}},
+ journal = bssa,
+ year = {2009},
+ volume = {99},
+ pages = {681-693},
+ number = {2A},
+ doi = {10.1785/0120080264}
+}
+
+ at ARTICLE{LeChLiKoHuTr08,
+ author = {Shiann Jong Lee and How Wei Chen and Qinya Liu and Dimitri Komatitsch
+ and Bor Shouh Huang and Jeroen Tromp},
+ title = {Three-Dimensional Simulations of Seismic Wave Propagation in the
+ {T}aipei Basin with Realistic Topography Based upon the Spectral-Element
+ Method},
+ journal = bssa,
+ year = {2008},
+ volume = {98},
+ pages = {253-264},
+ number = {1},
+ doi = {10.1785/0120070033}
+}
+
+ at ARTICLE{LeKoHuTr09,
+ author = {S. J. Lee and Dimitri Komatitsch and B. S. Huang and J. Tromp},
+ title = {Effects of topography on seismic wave propagation: An example from
+ northern {T}aiwan},
+ journal = bssa,
+ year = {2009},
+ volume = {99},
+ pages = {314-325},
+ number = {1},
+ doi = {10.1785/0120080020}
+}
+
+ at ARTICLE{LaWaBe05,
+ author = {A. Legay and H. W. Wang and T. Belytschko},
+ title = {Strong and weak arbitrary discontinuities in spectral finite elements},
+ journal = ijnme,
+ year = {2005},
+ volume = {64},
+ pages = {991-1008},
+ number = {8},
+ doi = {10.1002/nme.1388}
+}
+
+ at BOOK{LeCh85,
+ title = {M\'ecanique des mat\'eriaux solides},
+ publisher = {Dunod},
+ year = {1985},
+ author = {J. Lemaitre and J. L. Chaboche},
+ address = {Paris}
+}
+
+ at ARTICLE{Lem88,
+ author = {P. G. Lemari\'e},
+ title = {Ondelettes \`a localisation exponentielle},
+ journal = {Journal de Math\'ematiques Pures et Appliqu\'ees},
+ year = {1988},
+ volume = {67},
+ pages = {9999998-9999999}
+}
+
+ at PHDTHESIS{LeRousseau2001,
+ author = {J. H. {Le Rousseau}},
+ title = {Microlocal analysis of wave-equation imaging and generalized-screen
+ propagators},
+ school = {Center for Wave Phenomena, Colorado School of Mines},
+ year = {2001}
+}
+
+ at BOOK{Les97,
+ title = {Turbulence in fluids},
+ publisher = {Kluwer Academic Publishers},
+ year = {1997},
+ author = {M. Lesieur},
+ address = {Dordrecht}
+}
+
+ at ARTICLE{LeNiLeCh06,
+ author = {Alan Levander and Fenglin Niu and Cin-Ty A. Lee and Xin Cheng},
+ title = {Imag(in)ing the continental lithosphere},
+ journal = {Tectonophysics},
+ year = {2006},
+ volume = {416},
+ pages = {167-185},
+ number = {1-4},
+ doi = {10.1016/j.tecto.2005.11.018}
+}
+
+ at INCOLLECTION{LeNiSy05,
+ author = {A. Levander and F. Niu and W. W. Symes},
+ title = {Imaging teleseismic {P} to {S} scattered waves using the {K}irchhoff
+ integral},
+ booktitle = {Seismic Earth: Array Analysis of Broadband Seismograms},
+ publisher = {American Geophysical Union},
+ year = {2005},
+ editor = {Alan Levander and Guust Nolet},
+ volume = {157},
+ series = {Geophysical Monograph},
+ pages = {149-170},
+ address = {Washington DC, USA}
+}
+
+ at ARTICLE{Lev88,
+ author = {A. R. Levander},
+ title = {Fourth-order finite-difference {{\it P-SV}} seismograms},
+ journal = geophysics,
+ year = {1988},
+ volume = {53},
+ pages = {1425-1436}
+}
+
+ at ARTICLE{LeDaMaEaVe00,
+ author = {J. Lewis and S. M. Day and H. Magistrale and J. Eakins and F. L.
+ Vernon},
+ title = {Crustal thickness of the {P}eninsular {R}anges, southern {C}alifornia,
+ from teleseismic receiver functions},
+ journal = {Geology},
+ year = {2000},
+ volume = {28},
+ pages = {303-306}
+}
+
+ at INPROCEEDINGS{LiBiGa92,
+ author = {X. Li and J. Bielak and O. Ghattas},
+ title = {Three-dimensional earthquake response on a {CM}2},
+ booktitle = {Proc. 10th World Conf. Earthquake Eng.},
+ year = {1992},
+ pages = {959-964},
+ note = {Madrid, Spain}
+}
+
+ at ARTICLE{Li02,
+ author = {X. Li and V. F. Cormier},
+ title = {Frequency-dependent seismic attenuation in the inner core 1. {A}
+ viscoelastic interpretation},
+ journal = jgr,
+ year = {2002},
+ volume = {107},
+ pages = {2361-2380},
+ number = {B12},
+ doi = {10.1029/2002JB001795}
+}
+
+ at ARTICLE{LiRo95,
+ author = {X. D. Li and B. Romanowicz},
+ title = {Comparison of global waveform inversions with and without considering
+ cross-branch modal coupling},
+ journal = gji,
+ year = {1995},
+ volume = {121},
+ pages = {695-709}
+}
+
+ at ARTICLE{LiTa93,
+ author = {X. D. Li and T. Tanimoto},
+ title = {Waveforms of long-period body waves in a slightly aspherical {E}arth
+ model},
+ journal = gji,
+ year = {1993},
+ volume = {112},
+ pages = {92-102}
+}
+
+ at INCOLLECTION{LiPeTc92,
+ author = {J. Liandrat and V. Perrier and P. Tchamitchian},
+ title = {Numerical resolution of Nonlinear Partial Differential Equations
+ using the Wavelet approach},
+ booktitle = {Wavelets and their Applications},
+ publisher = {Edited by Ruskai, Jones and Barlett},
+ year = {1992},
+ address = {New York}
+}
+
+ at ARTICLE{LimFar69,
+ author = {T. C. Lim and G. W. Farnell},
+ title = {Character of pseudo-surface waves on anisotropic crystals},
+ journal = jasa,
+ year = {1969},
+ volume = {45},
+ pages = {845-851},
+ number = {4}
+}
+
+ at ARTICLE{LimFar68,
+ author = {T. C. Lim and G. W. Farnell},
+ title = {Search for forbidden directions of elastic surface wave propagation
+ in anisotropic crystals},
+ journal = {Journal of Applied Physics},
+ year = {1968},
+ volume = {39},
+ pages = {4319-4325},
+ number = {9}
+}
+
+ at ARTICLE{Lindholm:2008:NTA,
+ author = {Erik Lindholm and John Nickolls and Stuart Oberman and John Montrym},
+ title = {{NVIDIA} {T}esla: {A} Unified Graphics and Computing Architecture},
+ journal = {IEEE Micro},
+ year = {2008},
+ volume = {28},
+ pages = {39--55},
+ number = {2},
+ month = mar # {\slash } # apr,
+ doi = {10.1109/MM.2008.31}
+}
+
+ at ARTICLE{LiNeGi10,
+ author = {Joseph M. Lindquist and Beny Neta and Francis X. Giraldo},
+ title = {A spectral element solution of the {K}lein-{G}ordon equation with
+ high-order treatment of time and non-reflecting boundary},
+ journal = {Wave Motion},
+ year = {2010},
+ volume = {47},
+ pages = {289-298},
+ number = {5}
+}
+
+ at ARTICLE{LiAnKa76,
+ author = {H. P. Liu and D. L. Anderson and H. Kanamori},
+ title = {Velocity dispersion due to anelasticity: implications for seismology
+ and mantle composition},
+ journal = gjras,
+ year = {1976},
+ volume = {47},
+ pages = {41-58}
+}
+
+ at INPROCEEDINGS{liu_wang_zhang_2006,
+ author = {K. Liu and Xiao Bing Wang and Yang Zhang and Cheng Liao},
+ title = {Acceleration of Time-Domain Finite Element Method ({TD-FEM}) Using
+ {Graphics Processor Units (GPU)}},
+ booktitle = {Proceedings of the 7th International Symposium on Antennas, Propagation
+ \& EM Theory (ISAPE '06)},
+ year = {2006},
+ pages = {1-4},
+ address = {Guilin, China},
+ month = {October},
+ doi = {10.1109/ISAPE.2006.353223},
+ journal = {Antennas, Propagation and EM Theory}
+}
+
+ at ARTICLE{LiPoKoTr04,
+ author = {Qinya Liu and Jascha Polet and Dimitri Komatitsch and Jeroen Tromp},
+ title = {Spectral-element moment tensor inversions for earthquakes in {S}outhern
+ {C}alifornia},
+ journal = bssa,
+ year = {2004},
+ volume = {94},
+ pages = {1748-1761},
+ number = {5},
+ doi = {10.1785/012004038}
+}
+
+ at ARTICLE{LiTa97,
+ author = {Q. Liu and J. Tao},
+ title = {The perfectly matched layer for acoustic waves in absorptive media},
+ journal = jasa,
+ year = {1997},
+ volume = {102},
+ pages = {2072-2082},
+ number = {4}
+}
+
+ at ARTICLE{LiTr08,
+ author = {Q. Liu and J. Tromp},
+ title = {Finite-frequency sensitivity kernels for global seismic wave propagation
+ based upon adjoint methods},
+ journal = gji,
+ year = {2008},
+ volume = {174},
+ pages = {265-286},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2008.03798.x}
+}
+
+ at ARTICLE{LiTr06,
+ author = {Qinya Liu and Jeroen Tromp},
+ title = {Finite-Frequency Kernels Based on Adjoint Methods},
+ journal = bssa,
+ year = {2006},
+ volume = {96},
+ pages = {2383-2397},
+ number = {6},
+ doi = {10.1785/0120060041}
+}
+
+ at ARTICLE{Lo91,
+ author = {P. Lognonn\'{e}},
+ title = {Normal modes and seismograms in an anelastic rotating {E}arth},
+ journal = jgr,
+ year = {1991},
+ volume = {91},
+ pages = {20309-20319}
+}
+
+ at ARTICLE{LoRo90,
+ author = {P. Lognonn\'{e} and B. Romanowicz},
+ title = {Modeling of coupled normal modes of the {E}arth: the spectral method},
+ journal = gji,
+ year = {1990},
+ volume = {102},
+ pages = {365-395}
+}
+
+ at ARTICLE{LoPi04,
+ author = {B. Lombard and J. Piraux},
+ title = {Numerical treatment of two-dimensional interfaces for acoustic and
+ elastic waves},
+ journal = jcp,
+ year = {2004},
+ volume = {195},
+ pages = {90-116},
+ number = {1},
+ doi = {10.1016/j.jcp.2003.09.024}
+}
+
+ at ARTICLE{LoPiGeVi08,
+ author = {B. Lombard and J. Piraux and C. G\'elis and J. Virieux},
+ title = {Free and smooth boundaries in 2-{D} finite-difference schemes for
+ transient elastic waves},
+ journal = gji,
+ year = {2008},
+ volume = {172},
+ pages = {252-261},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2007.03620.x}
+}
+
+ at ARTICLE{loperlay1995,
+ author = {D. E. Loper and T. Lay},
+ title = {The core-mantle boundary region},
+ journal = {Journal of Geophysical Research-Solid Earth},
+ year = {1995},
+ volume = {100},
+ pages = {6397-6420}
+}
+
+ at ARTICLE{LotAls09,
+ author = {J. Lothe and V.I. Alshits},
+ title = {Surface waves, limiting waves and exceptional waves: David Barnett's
+ role in the development of the theory},
+ journal = {Mathematics and Mechanics of Solids},
+ year = {2009},
+ volume = {14},
+ pages = {16-37}
+}
+
+ at ARTICLE{LotAls77,
+ author = {J. Lothe and V. I. Alshits},
+ title = {Existence criterion for quasi-bulk surface waves},
+ journal = {Soviet Physics Crystallography},
+ year = {1977},
+ volume = {22},
+ pages = {519-525}
+}
+
+ at ARTICLE{LotBar76,
+ author = {J. Lothe and D. M. Barnett},
+ title = {On the existence of surface-wave solutions for anisotropic elastic
+ half-spaces with free surface},
+ journal = {Journal of Applied Physics},
+ year = {1976},
+ volume = {47},
+ pages = {428-433}
+}
+
+ at ARTICLE{LotWan95,
+ author = {J. Lothe and L. Wang},
+ title = {Self-orthogonal sextic formalism for anisotropic elastic media: spaces
+ of simple reflection and two-component surface waves},
+ journal = {Wave Motion},
+ year = {1995},
+ volume = {21},
+ pages = {163-181}
+}
+
+ at ARTICLE{LotWan94,
+ author = {J. Lothe and L. Wang},
+ title = {Properties of {T}ype 6 transonic states with respect to grazing incidence
+ reflection of bulk waves at planar free or clamped surfaces of half-infinite
+ elastically anisotropic media},
+ journal = {Wave Motion},
+ year = {1994},
+ volume = {20},
+ pages = {41-56}
+}
+
+ at BOOK{Lov11,
+ title = {Some problems of geodynamics},
+ publisher = {Cambridge University Press},
+ year = {1911},
+ author = {A. E. H. Love},
+ address = {Cambridge}
+}
+
+ at ARTICLE{lovelyetal06,
+ author = {P. Lovely and J. Shaw and Q. Liu and J. Tromp},
+ title = {A structural model of the {S}alton {T}rough and its implications
+ for seismic hazard},
+ journal = bssa,
+ year = {2006},
+ volume = {96},
+ pages = {1882-1896}
+}
+
+ at ARTICLE{LuPaXu05,
+ author = {Jing Lu and Jie Pan and Boling Xu},
+ title = {Time-domain calculation of acoustical wave propagation in discontinuous
+ media using acoustical wave propagator with mapped pseudospectral
+ method},
+ journal = jasa,
+ year = {2005},
+ volume = {118},
+ pages = {3408-3419},
+ number = {6},
+ doi = {10.1121/1.2114627}
+}
+
+ at ARTICLE{LuZh07,
+ author = {Y. Y. Lu and J. Zhu},
+ title = {Perfectly matched layer for acoustic waveguide modeling - {B}enchmark
+ calculations and perturbation analysis},
+ journal = cmes,
+ year = {2007},
+ volume = {22},
+ pages = {235-248},
+ number = {3}
+}
+
+ at BOOK{Lub90,
+ title = {Plasticity theory},
+ publisher = {Macmillan Publishing Company},
+ year = {1990},
+ author = {Jacob Lubliner},
+ address = {New York}
+}
+
+ at ARTICLE{LuBa95,
+ author = {J. E. Luco and F. C. P. de Barros},
+ title = {Three-dimensional response of a layered valley embedded in a layered
+ half-space},
+ journal = eesd,
+ year = {1995},
+ volume = {24},
+ pages = {109-125}
+}
+
+ at BOOK{LuPi96,
+ title = {Introduction au calcul scientifique},
+ publisher = {Masson},
+ year = {1996},
+ author = {Brigitte Lucquin and Olivier Pironneau},
+ address = {Paris}
+}
+
+ at ARTICLE{LuHu92,
+ author = {R. J. Luebbers and F. Hunsberger},
+ title = {{FDTD} for {N}th-Order Dispersive Media},
+ journal = {IEEE Transactions on Antennas and Propagation},
+ year = {1992},
+ volume = {40},
+ pages = {1297-1301},
+ number = {11}
+}
+
+ at ARTICLE{Luo01,
+ author = {Luo, S-N. and S. Ni and D. V. Helmberger},
+ title = {Evidence for a sharp lateral variation of velocity at the core-mantle
+ boundary from multipathed {PKP}ab},
+ journal = epsl,
+ year = {2001},
+ volume = {189},
+ pages = {155-164}
+}
+
+ at ARTICLE{LuSc90,
+ author = {Y. Luo and G. Schuster},
+ title = {Parsimonious staggered grid finite-differencing of the wave equation},
+ journal = grl,
+ year = {1990},
+ volume = {17},
+ pages = {155-158}
+}
+
+ at INCOLLECTION{LuHo87,
+ author = {B. P. Luyendyk and J. S. Hornafius},
+ title = {Neogene crustal rotations, fault slip and basin development in southern
+ {C}alifornia},
+ booktitle = {Cenozoic basin development of coastal {C}alifornia},
+ publisher = {Prentice-Hall},
+ year = {1987},
+ editor = {R. V. Ingersoll and W. G. Ernst},
+ pages = {259-283},
+ address = {Old Tappan, New Jersey}
+}
+
+ at ARTICLE{LuGiSaOr04,
+ author = {F. Luz\'on and S. A. Gil-Zepeda and F. J. S\'anchez-Sesma and C.
+ Ortiz-Alem\'an},
+ title = {Three-dimensional simulation of ground motion in the {Z}afarraya
+ basin (southern {S}pain) up to 1.335~{H}z under incident plane waves},
+ journal = gji,
+ year = {2004},
+ volume = {156},
+ pages = {584-594}
+}
+
+ at ARTICLE{LuSaRoPoGaMaRoNa97,
+ author = {F. Luz\'on and F. J. S\'anchez-Sesma and J. L. Rodr{\'\i}guez-Z\'u{\~{n}}iga
+ and A. M. Posadas and J. M. Garc{\'\i}a and J. Mart{\'\i}n and M.
+ D. Romacho and M. Navarro},
+ title = {Diffraction of {{\it P}}, {{\it S}} and {R}ayleigh waves by three-dimensional
+ topographies},
+ journal = gji,
+ year = {1997},
+ volume = {129},
+ pages = {571-578}
+}
+
+ at ARTICLE{Cools94,
+ author = {J. Lyness and R. Cools},
+ title = {A survey of numerical cubature over triangles},
+ journal = {Proceedings of Symposia in Applied Mathematics},
+ year = {1994},
+ volume = {48},
+ pages = {127-150}
+}
+
+ at INCOLLECTION{LyDr72,
+ author = {J. Lysmer and L. A. Drake},
+ title = {A finite element method for seismology},
+ booktitle = {Methods in Computational Physics},
+ publisher = {Academic Press},
+ year = {1972},
+ editor = {B. Alder and S. Fernbach and B. A. Bolt},
+ volume = {11},
+ chapter = {6},
+ pages = {181-216},
+ address = {New York, USA}
+}
+
+ at ARTICLE{LyKu69,
+ author = {J. Lysmer and R. L. Kuhlemeyer},
+ title = {Finite dynamic model for infinite media},
+ journal = {J. Eng. Mech. Div. ASCE 95 EM},
+ year = {1969},
+ volume = {4},
+ pages = {859-877}
+}
+
+ at ARTICLE{LyuSan75,
+ author = {V. N. Lyubimov and D. G. Sannikov},
+ title = {Surface quasi-bulk waves in the neighbourhood of exceptional directions
+ and surfaces in crystals},
+ journal = {Soviet Solid State Physics},
+ year = {1975},
+ volume = {17},
+ pages = {478-483},
+ number = {2}
+}
+
+ at ARTICLE{MeRo00,
+ author = {Charles M\'{e}gnin and Barabara Romanowicz},
+ title = {The 3{D} shear velocity structure of the mantle from the inversion
+ of body, surface and higher modes wave forms},
+ journal = gji,
+ year = {2000},
+ volume = {143},
+ pages = {709-728}
+}
+
+ at ARTICLE{Mul85,
+ author = {G. M\"{u}ller},
+ title = {The reflectivity method: a tutorial},
+ journal = {Journal of Geophysics},
+ year = {1985},
+ volume = {58},
+ pages = {153-174}
+}
+
+ at ARTICLE{MaLi06,
+ author = {Shuo Ma and Pengcheng Liu},
+ title = {Modeling of the Perfectly Matched Layer Absorbing Boundaries and
+ Intrinsic Attenuation in Explicit Finite-Element Methods},
+ journal = bssa,
+ year = {2006},
+ volume = {96},
+ pages = {1779-1794},
+ number = {5},
+ doi = {10.1785/0120050219}
+}
+
+ at INCOLLECTION{Mad83,
+ author = {R. Madariaga},
+ title = {Earthquake source theory: a review},
+ booktitle = {Earthquakes, Observation Theory and Interpretation},
+ publisher = {North-Holland},
+ year = {1983},
+ editor = {H. Kanamori and E. Boschi},
+ address = {Amsterdam},
+ note = {The Enrico Fermi Summer School of Physics, 55th course}
+}
+
+ at ARTICLE{Mad87,
+ author = {R. Madariaga},
+ title = {Seismology, theoretical},
+ journal = {Encyclopedia of Physical Science and Technology},
+ year = {1987},
+ volume = {12},
+ pages = {519-533}
+}
+
+ at ARTICLE{Mad76,
+ author = {R. Madariaga},
+ title = {Dynamics of an expanding circular fault},
+ journal = bssa,
+ year = {1976},
+ volume = {66},
+ pages = {639-666},
+ number = {3}
+}
+
+ at ARTICLE{MaMePaRo93,
+ author = {Y. Maday and D. Meiron and A. T. Patera and E. M. R{\o}nquist},
+ title = {Analysis of Iterative Methods for the Steady and Unsteady {S}tokes
+ Problem: Application to {S}pectral {E}lement Discretizations},
+ journal = {SIAM J. Sci. Stat. Comput.},
+ year = {1993},
+ volume = {14},
+ pages = {310-337}
+}
+
+ at INPROCEEDINGS{MaPa89,
+ author = {Y. Maday and A. T. Patera},
+ title = {Spectral-element methods for the incompressible {N}avier-{S}tokes
+ equations},
+ booktitle = {State of the art survey in computational mechanics},
+ year = {1989},
+ pages = {71-143},
+ note = {{A}. K. Noor and J. T. Oden editors}
+}
+
+ at ARTICLE{MaQu82,
+ author = {Y. Maday and A. Quarteroni},
+ title = {Approximation of {B}urgers equation by pseudospectral methods},
+ journal = {RAIRO Anal. Numer.},
+ year = {1982},
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+ pages = {375-404}
+}
+
+ at ARTICLE{MaRo90,
+ author = {Y. Maday and E. M. R{\o}nquist},
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+ coefficients and deformed geometries},
+ journal = cmame,
+ year = {1990},
+ volume = {80},
+ pages = {91-115}
+}
+
+ at PHDTHESIS{Mad09,
+ author = {Ronan Madec},
+ title = {M\'ethode des \'el\'ements spectraux pour la propagation d'ondes
+ sismiques en milieu g\'eologique fluide-solide avec pas de temps
+ locaux et couches absorbantes parfaitement adapt\'ees C-PML},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {2009},
+ address = {Pau, France},
+ month = {December}
+}
+
+ at ARTICLE{MaKoDi09,
+ author = {Ronan Madec and Dimitri Komatitsch and Julien Diaz},
+ title = {Energy-conserving local time stepping based on high-order finite
+ elements for seismic wave propagation across a fluid-solid interface},
+ journal = cmes,
+ year = {2009},
+ volume = {49},
+ pages = {163-189},
+ number = {2}
+}
+
+ at ARTICLE{Maggi2009,
+ author = {A. Maggi and C. Tape and M. Chen and D. Chao and J. Tromp},
+ title = {{An automated time-window selection algorithm for seismic tomography}},
+ journal = gji,
+ year = {2009},
+ volume = {178},
+ pages = {257-281}
+}
+
+ at ARTICLE{MaDaClGr2000,
+ author = {H. Magistrale and S. Day and R. W. Clayton and R. Graves},
+ title = {The {SCEC} {S}outhern {C}alifornia reference three-dimensional seismic
+ velocity model version~2},
+ journal = bssa,
+ year = {2000},
+ volume = {90},
+ pages = {S65-S76}
+}
+
+ at ARTICLE{MaMcDa96,
+ author = {H. Magistrale and K. McLaughlin and S. Day},
+ title = {A geology based 3-{D} velocity model of the {L}os {A}ngeles basin
+ sediments},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1161-1166}
+}
+
+ at ARTICLE{MaMoTa94,
+ author = {S. A. Magnier and P. Mora and A. Tarantola},
+ title = {Finite differences on minimal grids},
+ journal = geophysics,
+ year = {1994},
+ volume = {59},
+ pages = {1435-1443}
+}
+
+ at ARTICLE{Mah90,
+ author = {K. D. Mahrer},
+ title = {Numerical time step instability and {S}tacey's and {C}layton-{E}ngquist's
+ absorbing boundary conditions},
+ journal = bssa,
+ year = {1990},
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+ pages = {213-217}
+}
+
+ at ARTICLE{Mainprice08,
+ author = {Mainprice, D. and A. Tommasi and D. Ferre and P. Carrez and P. Cordier},
+ title = {Predicted glide systems and crystal preferred orientations of polycrystalline
+ silicate {M}g-Perovskite at high pressure: {I}mplications for the
+ seismic anisotropy in the lower mantle},
+ journal = epsl,
+ year = {2008},
+ volume = {271},
+ pages = {135--144}
+}
+
+ at ARTICLE{MaKn66,
+ author = {A. K. Mal and L. Knopoff},
+ title = {Transmission of {R}ayleigh waves at a corner},
+ journal = bssa,
+ year = {1966},
+ volume = {56},
+ pages = {455-466}
+}
+
+ at ARTICLE{Mal89,
+ author = {S. G. Mallat},
+ title = {Multiresolution approximation and wavelet orthonormal bases of ${L}^2({R})$},
+ journal = {Transactions of the AMS},
+ year = {1989},
+ volume = {135},
+ pages = {9999998-9999999}
+}
+
+ at ARTICLE{Mal88,
+ author = {S. G. Mallat},
+ title = {A theory for multiresolution signal decomposition: the wavelet representation},
+ journal = {Communications in Pure and Applied Mathematics},
+ year = {1988},
+ volume = {41},
+ pages = {9999998-9999999}
+}
+
+ at ARTICLE{Mal97,
+ author = {J. L. Mallet},
+ title = {Discrete modeling for natural objects},
+ journal = {Math. Geol.},
+ year = {1997},
+ volume = {29},
+ pages = {199-219}
+}
+
+ at ARTICLE{Mal92,
+ author = {J. L. Mallet},
+ title = {Discrete smooth interpolation in geometric modeling},
+ journal = {Computer-Aided Design},
+ year = {1992},
+ volume = {24},
+ pages = {178-191}
+}
+
+ at BOOK{MaBe88,
+ title = {Boundary element methods in elastodynamics},
+ publisher = {Umwin Hyman},
+ year = {1988},
+ author = {G. Manolis and D. E. Beskos},
+ address = {London}
+}
+
+ at ARTICLE{MaOl03,
+ author = {Carey Marcinkovich and Kim Bak Olsen},
+ title = {On the implementation of perfectly matched layers in a three-dimensional
+ fourth-order velocity-stress finite-difference scheme},
+ journal = jgr,
+ year = {2003},
+ volume = {108},
+ pages = {2276},
+ number = {B5},
+ doi = {10.1029/2002JB002235}
+}
+
+ at ARTICLE{Mar84,
+ author = {K. J. Marfurt},
+ title = {Accuracy of finite-difference and finite-element modeling of the
+ scalar and elastic wave equation},
+ journal = geophysics,
+ year = {1984},
+ volume = {49},
+ pages = {533-549},
+ number = {5}
+}
+
+ at ARTICLE{MaGu69,
+ author = {L. Martel and S. K. Gupta},
+ title = {{\`A} propos des ondes de {R}ayleigh sur une surface courbe},
+ journal = {Ann. G\'eophys.},
+ year = {1969},
+ volume = {25},
+ pages = {973-979},
+ number = {4}
+}
+
+ at ARTICLE{MaKo09,
+ author = {Roland Martin and Dimitri Komatitsch},
+ title = {An unsplit convolutional perfectly matched layer technique improved
+ at grazing incidence for the viscoelastic wave equation},
+ journal = gji,
+ year = {2009},
+ volume = {179},
+ pages = {333-344},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2009.04278.x}
+}
+
+ at ARTICLE{MaKo06,
+ author = {Roland Martin and Dimitri Komatitsch},
+ title = {An optimized Convolution-Perfectly Matched Layer {(C-PML)} absorbing
+ technique for {3D} seismic wave simulation based on a finite-difference
+ method},
+ journal = {Geophysical Research Abstracts},
+ year = {2006},
+ volume = {8},
+ pages = {03988},
+ month = {April},
+ note = {Abstract EGU06-A-03988, www.cosis.net/abstracts/EGU06/03988/EGU06-J-03988-1.pdf}
+}
+
+ at ARTICLE{MaKoBa05,
+ author = {Roland Martin and Dimitri Komatitsch and H\'el\`ene Barucq},
+ title = {An optimized Convolution-Perfectly Matched Layer {(C-PML)} absorbing
+ technique for {3D} seismic wave simulation based on a finite-difference
+ method},
+ journal = {Eos Trans. AGU},
+ year = {2005},
+ volume = {86},
+ pages = {Fall Meet. Suppl., Abstract NG43B-0574},
+ number = {52},
+ month = {December},
+ note = {www.agu.org/meetings/fm05/waisfm05.html}
+}
+
+ at ARTICLE{MaKoBlLe08,
+ author = {Roland Martin and Dimitri Komatitsch and C\'eline Blitz and Nicolas
+ {Le Goff}},
+ title = {Simulation of seismic wave propagation in an asteroid based upon
+ an unstructured {MPI} spectral-element method: blocking and non-blocking
+ communication strategies},
+ journal = lncs,
+ year = {2008},
+ volume = {5336},
+ pages = {350-363}
+}
+
+ at ARTICLE{MaKoEz08,
+ author = {Roland Martin and Dimitri Komatitsch and Abdela\^aziz Ezziani},
+ title = {An unsplit convolutional perfectly matched layer improved at grazing
+ incidence for seismic wave equation in poroelastic media},
+ journal = geophysics,
+ year = {2008},
+ volume = {73},
+ pages = {T51-T61},
+ number = {4},
+ doi = {10.1190/1.2939484}
+}
+
+ at ARTICLE{MaKoGe08,
+ author = {Roland Martin and Dimitri Komatitsch and Stephen D. Gedney},
+ title = {A variational formulation of a stabilized unsplit convolutional perfectly
+ matched layer for the isotropic or anisotropic seismic wave equation},
+ journal = cmes,
+ year = {2008},
+ volume = {37},
+ pages = {274-304},
+ number = {3}
+}
+
+ at ARTICLE{MaKoGeBr10,
+ author = {Roland Martin and Dimitri Komatitsch and Stephen D. Gedney and Emilien
+ Bruthiaux},
+ title = {A high-order time and space formulation of the unsplit perfectly
+ matched layer for the seismic wave equation using {Auxiliary Differential
+ Equations (ADE-PML)}},
+ journal = cmes,
+ year = {2010},
+ volume = {56},
+ pages = {17-42},
+ number = {1}
+}
+
+ at ARTICLE{MaPr07,
+ author = {Y. J. Masson and S. R. Pride},
+ title = {Poroelastic finite-difference modeling of seismic attenuation and
+ dispersion due to mesoscopic-scale heterogeneity},
+ journal = jgr,
+ year = {2007},
+ volume = {112},
+ pages = {B03204},
+ number = {B3},
+ doi = {10.1029/2006JB004592}
+}
+
+ at ARTICLE{Masson2006,
+ author = {Y. J. Masson and S. R. Pride and K. T. Nihei},
+ title = {Finite-difference modelling of {B}iot's poroelastic equations at
+ seismic frequencies},
+ journal = jgr,
+ year = {2006},
+ volume = {111},
+ pages = {B10305},
+ doi = {10.1029/2006JB004366}
+}
+
+ at ARTICLE{MaFe98,
+ author = {D. Massonnet and Kurt L. Feigl},
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+ surface},
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+ volume = {36},
+ pages = {441-500}
+}
+
+ at ARTICLE{MaSeGr96,
+ author = {E. Matzel and M. K. Sen and S. P. Grand},
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+ journal = grl,
+ year = {1996},
+ volume = {23},
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+ number = {18}
+}
+
+ at ARTICLE{Mat11,
+ author = {Ren\'e Matzen},
+ title = {An efficient finite element time-domain formulation for the elastic
+ second-order wave equation: {A} non-split complex frequency shifted
+ convolutional {PML}},
+ journal = ijnme,
+ year = {2011},
+ volume = {88},
+ pages = {951-973},
+ number = {10},
+ doi = {10.1002/nme.3205}
+}
+
+ at ARTICLE{Mau94,
+ author = {V. Maupin},
+ title = {On the possibility of anisotropy in the {D}'' layer as inferred from
+ the polarization of diffracted {S} waves},
+ journal = pepi,
+ year = {1994},
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+ pages = {1-32}
+}
+
+ at ARTICLE{MazEve97,
+ author = {A. A. Maznev and A. G. Every},
+ title = {Time-domain dynamic surface response of an anisotropic elastic solid
+ to an impulsive line force},
+ journal = {International Journal of Engineering Science},
+ year = {1997},
+ volume = {35},
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+ number = {4}
+}
+
+ at ARTICLE{MazEve95,
+ author = {A. A. Maznev and A. G. Every},
+ title = {Secluded supersonic surface waves in germanium},
+ journal = {Physics Letters},
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+ volume = {A197},
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+}
+
+ at ARTICLE{MazEve94,
+ author = {A. A. Maznev and A. G. Every},
+ title = {Ray surface and focusing of surface acoustic waves on the basal plane
+ of cubic crystals},
+ journal = {Acta Acustica},
+ year = {1994},
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+}
+
+ at ARTICLE{MazKolHes95,
+ author = {A. A. Maznev and Al. A. Kolomenskii and P. Hess},
+ title = {Time-resolved cuspidal structure in the wavefront of surface acoustic
+ pulses on (111) {G}allium {A}rsenide},
+ journal = {Physics Review Letters},
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+}
+
+ at ARTICLE{MazLomHesKol03,
+ author = {A.A. Maznev and A. M. Lomonosov and P. Hess and Al. A. Kolomenskii},
+ title = {Anisotropic effects in surface acoustic wave propagation from a point
+ source in a crystal},
+ journal = {The European Physical Journal B},
+ year = {2003},
+ volume = {35},
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+}
+
+ at BOOK{Mcc57,
+ title = {Applications of tensor analysis},
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+}
+
+ at ARTICLE{McCool:2004:SA,
+ author = {Michael McCool and Stefanus {Du Toit} and Tiberiu S. Popa and Bryan
+ Chan and Kevin Moule},
+ title = {Shader Algebra},
+ journal = {ACM Transactions on Graphics},
+ year = {2004},
+ volume = {23},
+ pages = {787--795},
+ number = {3},
+ month = aug,
+ doi = {10.1145/1015706.1015801}
+}
+
+ at ARTICLE{McInAhMoRoCu07,
+ author = {Patrick McCormick and Jeff Inman and James Ahrens and Jamaludin Mohd-Yusof
+ and Greg Roth and Sharen Cummins},
+ title = {Scout: a data-parallel programming language for graphics processors},
+ journal = {Parallel Computing},
+ year = {2007},
+ volume = {33},
+ pages = {648-662}
+}
+
+ at ARTICLE{McC60,
+ author = {T. H. McCulloh},
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+ {C}alifornia},
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+}
+
+ at ARTICLE{McAl67,
+ author = {A. McGarr and L. E. Alsop},
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+ journal = jgr,
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+}
+
+ at ARTICLE{McBaDaShSt92,
+ author = {K. L. McLaughlin and T. G. Barker and S. M. Day and B. Shkoller and
+ J. L. Stevens},
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+ year = {1992},
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+}
+
+ at ARTICLE{McDa94,
+ author = {K. L. McLaughlin and S. M. Day},
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+ journal = {Computers in Physics},
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+}
+
+ at ARTICLE{McJi88,
+ author = {K. L. McLaughlin and R. S. Jih},
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+ year = {1988},
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+}
+
+ at ARTICLE{MeViSa06,
+ author = {E. D. Mercerat and J. P. Vilotte and F. J. S\'anchez-Sesma},
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+ wave propagation using unstructured triangular grids},
+ journal = gji,
+ year = {2006},
+ volume = {166},
+ pages = {679-698},
+ number = {2}
+}
+
+ at ARTICLE{Merkel07,
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+ Miyagi and Y. Meng and T. S. Duffy and H. R. Wenk},
+ title = {Deformation of ({M}g,{F}e){S}i{O}3 post-perovskite and {D}'' anisotropy},
+ journal = {Science},
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+ volume = {316},
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+}
+
+ at ARTICLE{MeMuGr08,
+ author = {Peter Messmer and Paul J. Mullowney and Brian E. Granger},
+ title = {{GPULib: GPU} Computing in High-Level Languages},
+ journal = {Computing in Science and Engineering},
+ year = {2008},
+ volume = {10},
+ pages = {70-73},
+ number = {5},
+ doi = {10.1109/MCSE.2008.135}
+}
+
+ at TECHREPORT{Top500,
+ author = {H. W. Meuer and E. Strohmaier and J. J. Dongarra and H. D. Simon},
+ title = {Top500 list of Supercomputer Sites},
+ institution = {University of Mannheim},
+ year = {2002},
+ address = {Mannheim, Germany},
+ note = {{{\tt www.top500.org}}}
+}
+
+ at ARTICLE{Mey92,
+ author = {Y. Meyer},
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+}
+
+ at BOOK{Mey90,
+ title = {Ondelettes et op\'erateurs},
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+}
+
+ at TECHREPORT{Mey87,
+ author = {Y. Meyer},
+ title = {Ondelettes, fonctions splines et analyses gradu\'ees},
+ institution = {Ceremade 8703},
+ year = {1987},
+ address = {Universit\'e Paris Dauphine}
+}
+
+ at ARTICLE{MePa08,
+ author = {Kristel C. Meza-Fajardo and Apostolos S. Papageorgiou},
+ title = {A nonconvolutional, split-field, perfectly matched layer for wave
+ propagation in isotropic and anisotropic elastic media: Stability
+ analysis},
+ journal = bssa,
+ year = {2008},
+ volume = {98},
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+ number = {4},
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+}
+
+ at ARTICLE{MiKo10,
+ author = {David Mich\'{e}a and Dimitri Komatitsch},
+ title = {Accelerating a 3{D} finite-difference wave propagation code using
+ {GPU} graphics cards},
+ journal = gji,
+ year = {2010},
+ volume = {182},
+ pages = {389-402},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2010.04616.x}
+}
+
+ at INPROCEEDINGS{Mic09,
+ author = {Paulius Micikevicius},
+ title = {{3D} finite-difference computation on {GPUs} using {CUDA}},
+ booktitle = {GPGPU-2: Proceedings of the 2nd Workshop on General Purpose Processing
+ on Graphics Processing Units},
+ year = {2009},
+ pages = {79-84},
+ address = {Washington, DC, USA},
+ month = mar,
+ doi = {10.1145/1513895.1513905}
+}
+
+ at ARTICLE{MieFu04,
+ author = {A. Mielke and Y. B. Fu},
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+ of the {S}troh formalism},
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+}
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+ at BOOK{Mik78,
+ title = {The theory of elastic waves and waveguides},
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+}
+
+ at ARTICLE{Min02,
+ author = {Susan E. Minkoff},
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+ Wave Propagation Code},
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+ year = {2002},
+ volume = {24},
+ pages = {1-19},
+ number = {1},
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+ publisher = {SIAM}
+}
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+ at INCOLLECTION{Mi96,
+ author = {S. Mitchell},
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+ editor = {Puech, Claude and Reischuk, R{\"u}diger},
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+}
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+ at ARTICLE{MiPe91,
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+}
+
+ at ARTICLE{Moc89,
+ author = {P. Moczo},
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+ irregular grids, application to the seismic response problem},
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+ year = {1989},
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+}
+
+ at ARTICLE{MoByKrCaBo97,
+ author = {P. Moczo and E. Bystrick{\'y} and J. Kristek and J. M. Carcione and
+ M. Bouchon},
+ title = {Hybrid modeling of {{\it P-SV}} seismic motion at inhomogeneous viscoelastic
+ topographic structures},
+ journal = bssa,
+ year = {1997},
+ volume = {87},
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+}
+
+ at ARTICLE{MoKr05,
+ author = {P. Moczo and J. Kristek},
+ title = {On the rheological models used for time-domain methods of seismic
+ wave propagation},
+ journal = grl,
+ year = {2005},
+ volume = {32},
+ pages = {L01306},
+ doi = {10.1029/2004GL021598}
+}
+
+ at ARTICLE{MoKrBy01,
+ author = {P. Moczo and J. Kristek and E. Bystrick{\'y}},
+ title = {Efficiency and optimization of the {3-D} finite-difference modeling
+ of seismic ground motion},
+ journal = jca,
+ year = {2001},
+ volume = {9},
+ pages = {593-609},
+ number = {2}
+}
+
+ at ARTICLE{MoKrHa2000,
+ author = {P. Moczo and J. Kristek and L. Halada},
+ title = {3-{D} fourth-order staggered-grid finite-difference schemes: stability
+ and grid dispersion},
+ journal = bssa,
+ year = {2000},
+ volume = {90},
+ pages = {587-603},
+ number = {3},
+ doi = {10.1785/0119990119}
+}
+
+ at INCOLLECTION{MoRoEi07,
+ author = {P. Moczo and J. Robertsson and L. Eisner},
+ title = {The Finite-difference Time-domain method for Modeling of Seismic
+ Wave Propagation},
+ booktitle = {Advances in wave propagation in heterogeneous media},
+ publisher = {Elsevier - Academic Press, London, UK},
+ year = {2007},
+ editor = {Ru-Shan Wu and Val\'erie Maupin},
+ volume = {48},
+ series = {Advances in Geophysics},
+ chapter = {8},
+ pages = {421-516}
+}
+
+ at PHDTHESIS{Mod86,
+ author = {H. Modaressi},
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+ year = {1986},
+ address = {Paris}
+}
+
+ at ARTICLE{MoBe94,
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+}
+
+ at ARTICLE{MoRi05,
+ author = {Peter Monk and Gerard R. Richter},
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+ Systems in Inhomogeneous Media},
+ journal = {Journal of Scientific Computing},
+ year = {2005},
+ volume = {22-23},
+ pages = {443-477},
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+}
+
+ at ARTICLE{montagner2002,
+ author = {J. P. Montagner},
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+ at ARTICLE{montagner1998,
+ author = {J.-P. Montagner},
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+ In boundary layers \ldots},
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+}
+
+ at ARTICLE{boutet,
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+
+ at ARTICLE{MoGaLaWi04,
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+ Williams},
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+ journal = jgr,
+ year = {2004},
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+}
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+ at ARTICLE{MoTr08,
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+}
+
+ at ARTICLE{MouDesCas96,
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+ half-space},
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+
+ at ARTICLE{MuDeEtNi92,
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+ journal = geophysics,
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+
+ at ARTICLE{MuBe82,
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+ two-dimensional wave equation},
+ journal = ijnme,
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+
+ at ARTICLE{MuHiSaOhKa04,
+ author = {M. K. Murakami and K. Hirose and N. Sata and Y. Ohishi and K. Kawamura},
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+ journal = {Science},
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+}
+
+ at BOOK{Mus70,
+ title = {Crystal {A}coustics - {I}ntroduction to the study of elastic waves
+ and vibrations in crystals},
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+
+ at TECHREPORT{NaDa92,
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+}
+
+ at ARTICLE{nataf2000,
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+}
+
+ at ARTICLE{Nau96,
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+
+ at ARTICLE{NaNeHu02,
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+ water equation models: the split equation approach},
+ journal = {Monthly Weather Review},
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+
+ at BOOK{jn,
+ title = {Les m\'ethodes directes en th\'eorie des \'equations elliptiques},
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+ at INPROCEEDINGS{New59,
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+
+ at ARTICLE{nietal2000,
+ author = {S. D. Ni and X. M. Ding and D. V. Helmberger},
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+ journal = gji,
+ year = {2000},
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+}
+
+ at ARTICLE{nietal2002,
+ author = {S. D. Ni and E. Tan and M. Gurnis and D. V. Helmberger},
+ title = {Sharp sides to the African superplume},
+ journal = {Science},
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+}
+
+ at ARTICLE{Nickolls:2008:SPP,
+ author = {John Nickolls and Ian Buck and Michael Garland and Kevin Skadron},
+ title = {Scalable Parallel Programming with {CUDA}},
+ journal = {ACM Queue},
+ year = {2008},
+ volume = {6},
+ pages = {40--53},
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+ doi = {10.1145/1365490.1365500}
+}
+
+ at ARTICLE{Nicetal2002,
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+ r\'ecent: apports nouveaux du forage {GMB}1 (1999) dans la r\'egion
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+
+ at ARTICLE{NiIfBeSk94,
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+ journal = gji,
+ year = {2007},
+ volume = {168},
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+}
+
+ at ARTICLE{NiFoDa08,
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+ title = {A 2-{D} spectral-element method for computing spherical-earth seismograms
+ - {II. W}aves in solid-fluid media},
+ journal = gji,
+ year = {2008},
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+}
+
+ at ARTICLE{NiFoDa07,
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+ title = {A two-dimensional spectral-element method for computing spherical-earth
+ seismograms - {I. M}oment-tensor source},
+ journal = gji,
+ year = {2007},
+ volume = {168},
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+}
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+ inner core},
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+ at TECHREPORT{Etopo5,
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+ model},
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+}
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+
+ at MANUAL{CUDAmanual,
+ title = {{NVIDIA CUDA} Programming Guide version 2.3},
+ author = {{NVIDIA Corporation}},
+ address = {Santa Clara, California, USA},
+ month = jul,
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+ note = {139 pages},
+ url = {http://www.nvidia.com/cuda}
+}
+
+ at TECHREPORT{NVIDIA:2009:FERMI,
+ author = {{NVIDIA Corporation}},
+ title = {{NVIDIA's} Next Generation {CUDA} Compute Architecture: {FERMI}},
+ institution = {NVIDIA},
+ year = {2009},
+ address = {Santa Clara, California, USA},
+ month = sep,
+ note = {22 pages},
+ url = {http://www.nvidia.com/object/fermi\_architecture.html}
+}
+
+ at TECHREPORT{nvidia_280_specs,
+ author = {{NVIDIA Corporation}},
+ title = {{NVIDIA} {G}e{F}orce {GTX} 200 {GPU} Architectural Overview, Second-Generation
+ Unified {GPU} Architecture for Visual Computing},
+ institution = {NVIDIA},
+ year = {2008},
+ pages = {1-23},
+ url = {www.nvidia.com/docs/IO/55506/GeForce\_GTX\_200\_GPU\_Technical\_Brief.pdf}
+}
+
+ at INCOLLECTION{NyHaPr07,
+ author = {Lars Nyland and Mark Harris and Jan Prins},
+ title = {Fast {N}-body simulation with {CUDA}},
+ booktitle = {GPU Gems 3},
+ publisher = {Addison-Wesley Professional, Boston, MA, USA},
+ year = {2007},
+ chapter = {31},
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+}
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+ and M. Faerman and R. Moore and P. Maechling and T. Jordan},
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+}
+
+ at ARTICLE{OlPeSc95,
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+ at INPROCEEDINGS{Owens:2005:ASO,
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+ J. Harris and Jens Kr{\"{u}}ger and Aaron E. Lefohn and Timothy J.
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+}
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+ at ARTICLE{owens_luebke_govindaraju_2007,
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+ J. Harris AND Jens Kr{\"u}ger AND Aaron E. Lefohn AND Timothy J.
+ Purcell},
+ title = {A Survey of General-Purpose Computation on Graphics Hardware},
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+ title = {Elastic wave propagation in transversely isotropic media},
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+ at PHDTHESIS{Ped94,
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+ th\'eorique et applications},
+ school = {Universit\'e Joseph Fourier},
+ year = {1994},
+ address = {Grenoble}
+}
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+ year = {1994},
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+ title = {Regular versus irregular meshing for complicated models and their
+ effect on synthetic seismograms},
+ journal = {Geophys. J. Int.},
+ year = {2010},
+ volume = {183},
+ pages = {1031-1051}
+}
+
+ at ARTICLE{Pel90,
+ author = {R. B. Pelz},
+ title = {Pseudospectral methods on massively parallel computers},
+ journal = cmame,
+ year = {1990},
+ volume = {80},
+ pages = {493-503}
+}
+
+ at ARTICLE{PeTo95,
+ author = {C. B. Peng and M. Nafi T\"oksoz},
+ title = {An optimal absorbing boundary condition for elastic wave modeling},
+ journal = geophysics,
+ year = {1995},
+ volume = {60},
+ pages = {296-301}
+}
+
+ at ARTICLE{PeBa89,
+ author = {V. Perrier and C. Basdevant},
+ title = {La d\'ecomposition en ondelettes p\'eriodiques, un outil pour l'analyse
+ de champs inhomog\`enes},
+ journal = {La Recherche A\'erospatiale},
+ year = {1989},
+ volume = {3},
+ pages = {99999998-99999999}
+}
+
+ at ARTICLE{PeKoLuMaLeCaLeMaLiBlNiBaTr11,
+ author = {Daniel Peter and Dimitri Komatitsch and Yang Luo and Roland Martin
+ and Nicolas {Le Goff} and Emanuele Casarotti and Pieyre {Le Loher}
+ and Federica Magnoni and Qinya Liu and C\'eline Blitz and Tarje Nissen-Meyer
+ and Piero Basini and Jeroen Tromp},
+ title = {Forward and adjoint simulations of seismic wave propagation on fully
+ unstructured hexahedral meshes},
+ journal = gji,
+ year = {2011},
+ volume = {186},
+ pages = {721-739},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2011.05044.x}
+}
+
+ at INPROCEEDINGS{PeBo06,
+ author = {E. Petit and F. Bodin},
+ title = {Extracting Threads Using Traces for System on a Chip},
+ booktitle = {Proceedings of the Compilers for Parallel Computers (CPC'2006)},
+ year = {2006},
+ address = {La Coru{\~{n}}a, Spain},
+ month = {January}
+}
+
+ at ARTICLE{PeOlMa2001,
+ author = {S. Peyrat and K. B. Olsen and R. Madariaga},
+ title = {Dynamic modeling of the 1992 {L}anders earthquake},
+ journal = jgr,
+ year = {2001},
+ volume = {106},
+ pages = {26467-26482}
+}
+
+ at INPROCEEDINGS{Phillips:2009:RAP,
+ author = {Everett H. Phillips and Yao Zhang and Roger L. Davis and John D.
+ Owens},
+ title = {Rapid Aerodynamic Performance Prediction on a Cluster of Graphics
+ Processing Units},
+ booktitle = {Proceedings of the 47th {AIAA} Aerospace Sciences Meeting},
+ year = {2009},
+ pages = {1-11},
+ month = jan
+}
+
+ at INPROCEEDINGS{PhStSc08,
+ author = {James C. Phillips and John E. Stone and Klaus Schulten},
+ title = {Adapting a message-driven parallel application to {GPU}-accelerated
+ clusters},
+ booktitle = {SC '08: Proceedings of the 2008 ACM/IEEE conference on Supercomputing},
+ year = {2008},
+ pages = {1--9},
+ address = {Austin, Texas, USA},
+ month = nov,
+ doi = {10.1145/1413370.1413379}
+}
+
+ at ARTICLE{Phinney66,
+ author = {Phinney, R. A and Alexander, S. S.},
+ title = {P wave diffraction theory and the structure of the core-mantle boundary},
+ journal = jgr,
+ year = {1966},
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+}
+
+ at ARTICLE{PhBu73,
+ author = {R. A. Phinney and R. Burridge},
+ title = {Representation of Elastic-Gravitational Excitation of a Spherical
+ {E}arth Model by Generalized Spherical Harmonics},
+ journal = gjras,
+ year = {1973},
+ volume = {34},
+ pages = {451-487}
+}
+
+ at ARTICLE{Phung,
+ author = {K. D. Phung},
+ title = {Controllability and stabilization of electromagnetic waves},
+ journal = {ESAIM Control Optim. Calc. Var.},
+ year = {2000},
+ volume = {5},
+ pages = {87-137}
+}
+
+ at BOOK{Pil79,
+ title = {Elastic waves in the {E}arth},
+ publisher = {Elsevier Scientific Publishing Company},
+ year = {1979},
+ author = {Walter L. Pilant},
+ volume = {11 of "Developments in Solid Earth Geophysics" Series},
+ address = {Amsterdam, The Netherlands}
+}
+
+ at ARTICLE{PiKnSc64,
+ author = {W. L. Pilant and L. Knopoff and F. Schwab},
+ title = {Transmission and reflection of surface waves at a corner, part 3:
+ {R}ayleigh waves (experimental)},
+ journal = jgr,
+ year = {1964},
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+}
+
+ at ARTICLE{PiIr96a,
+ author = {A. Pitarka and K. Irikura},
+ title = {Modeling 3{D} surface topography by a finite-difference method: {K}obe-{JMA}
+ station site, {J}apan, case study},
+ journal = grl,
+ year = {1996},
+ volume = {23},
+ pages = {2729-2732}
+}
+
+ at ARTICLE{PiIr96b,
+ author = {A. Pitarka and K. Irikura},
+ title = {Basin structure effects on long period strong motions in the {S}an
+ {F}ernando valley and the {L}os {A}ngeles basin from the 1994 {N}orthridge
+ earthquake and aftershocks},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {S126-S137},
+ number = {1B}
+}
+
+ at ARTICLE{PiIrIwKa96,
+ author = {A. Pitarka and K. Irikura and T. Iwata and T. Kagawa},
+ title = {Basin structure effects in the {K}obe area inferred from modelling
+ of ground motions from two aftershocks of the {J}anuary 17, 1995,
+ {H}yogo-ken {N}anbu earthquake},
+ journal = {J. Phys. Earth},
+ year = {1996},
+ volume = {44},
+ pages = {563-576}
+}
+
+ at ARTICLE{PiIrIw98,
+ author = {A. Pitarka and K. Irikura and T. Iwata and H. Sekiguchi},
+ title = {Three-dimensional simulation of the near-fault ground motion for
+ the 1995 {H}yogo-ken {N}anbu ({K}obe), {J}apan, earthquake},
+ journal = bssa,
+ year = {1998},
+ volume = {88},
+ pages = {428-440}
+}
+
+ at ARTICLE{PlBaAyLa09,
+ author = {Judit Planas and Rosa M. Badia and Eduard Ayguad\'{e} and Jesus Labarta},
+ title = {Hierarchical Task-Based Programming With {StarSs}},
+ journal = {International Journal of High Performance Computing Applications},
+ year = {2009},
+ volume = {23},
+ pages = {284-299},
+ number = {3},
+ doi = {10.1177/1094342009106195}
+}
+
+ at ARTICLE{PlSh88,
+ author = {B. J. Plohr and D. H. Sharp},
+ title = {A conservative {E}ulerian formulation of the equations for elastic
+ flow},
+ journal = {Advances in Applied Mathematics},
+ year = {1988},
+ volume = {9},
+ pages = {481-499}
+}
+
+ at ARTICLE{Poin00,
+ author = {T. Pointer and E. Liu and J. A. Hudson},
+ title = {Seismic wave propagation in cracked porous media},
+ journal = gji,
+ year = {2000},
+ volume = {141},
+ pages = {199-231}
+}
+
+ at ARTICLE{Poin98,
+ author = {T. Pointer and E. Liu and J. A. Hudson},
+ title = {Numerical modelling of seismic waves scattered by hydrofractures:
+ application of the indirect boundary method},
+ journal = gji,
+ year = {1998},
+ volume = {135},
+ pages = {289-303}
+}
+
+ at ARTICLE{PonDesEveAud01,
+ author = {O. Poncelet and M. Deschamps and A.G. Every and B. Audoin},
+ title = {Extension to cuspidal edges of wave surfaces of anisotropic solids:
+ treatment of near cusp behavior},
+ journal = {Review of Progress in Quantitative Nondestructive Evaluation},
+ year = {2001},
+ volume = {20},
+ pages = {51-58}
+}
+
+ at ARTICLE{PoWe91,
+ author = {D. J. Ponti and R. E. Wells},
+ title = {Off-fault ground ruptures in the {S}anta-{C}ruz mountains, {C}alifornia:
+ ridge-top spreading versus tectonic extension during the 1989 {L}oma
+ {P}rieta earthquake},
+ journal = bssa,
+ year = {1991},
+ volume = {81},
+ pages = {1480-1510}
+}
+
+ at ARTICLE{Poupinet83,
+ author = {G. Poupinet and R. Pillet and A. Souriau},
+ title = {Possible heterogeneity of the {E}arth's core deduced from {PKIKP}
+ travel times},
+ journal = {Nature},
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+}
+
+ at PHDTHESIS{prat2005,
+ author = {F. Prat},
+ title = {Analyse du Generalized Screen Propagator},
+ school = {Universit\'{e} de Pau et des Pays de l'Adour},
+ year = {2005}
+}
+
+ at ARTICLE{Pra99,
+ author = {R. Gerhard Pratt},
+ title = {Seismic waveform inversion in the frequency domain, {P}art 1: Theory
+ and verification in a physical scale model},
+ journal = geophysics,
+ year = {1999},
+ volume = {64},
+ pages = {888-901},
+ number = {3}
+}
+
+ at ARTICLE{PrCh92,
+ author = {R. G. Pratt and C. Chapman},
+ title = {Traveltime tomography in anisotropic media -{II}: Application},
+ journal = gji,
+ year = {1992},
+ volume = {109},
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+}
+
+ at ARTICLE{PrShHi98,
+ author = {R. Gerhard Pratt and Changsoo Shin and G. J. Hicks},
+ title = {Gauss-{N}ewton and full {N}ewton methods in frequency-space seismic
+ waveform inversion},
+ journal = geophysics,
+ year = {1998},
+ volume = {133},
+ pages = {341-362},
+ number = {2},
+ doi = {10.1046/j.1365-246X.1998.00498.x}
+}
+
+ at ARTICLE{PrSh99,
+ author = {R. Gerhard Pratt and Richard M. Shipp},
+ title = {Seismic waveform inversion in the frequency domain, {P}art 2: Fault
+ delineation in sediments using crosshole data},
+ journal = geophysics,
+ year = {1999},
+ volume = {64},
+ pages = {902-914},
+ number = {3}
+}
+
+ at ARTICLE{PrViPaSc09,
+ author = {Tobias Preis and Peter Virnau and Wolfgang Paul and Johannes J. Schneider},
+ title = {{GPU} accelerated {M}onte {C}arlo simulation of the {2D} and {3D}
+ {I}sing model},
+ journal = jcp,
+ year = {2009},
+ volume = {228},
+ pages = {4468-4477},
+ doi = {10.1016/j.jcp.2009.03.018}
+}
+
+ at BOOK{PrTeWeFl94,
+ title = {Numerical recipes: the art of scientific computing},
+ publisher = {Cambridge University Press},
+ year = {1994},
+ author = {W. H. Press and S. A. Teukolsky and W. T. Vetterling and B. P. Flannery},
+ address = {Cambridge, USA}
+}
+
+ at INCOLLECTION{PrHuKe07,
+ author = {Daniel K. Price and John R. Humphrey and Eric J. Kelmelis},
+ title = {{GPU}-based accelerated {2D} and {3D FDTD} solvers},
+ booktitle = {Proceedings of the SPIE Physics and Simulation of Optoelectronic
+ Devices XV Conference},
+ publisher = {SPIE and the International Society for Optical Engineering},
+ year = {2007},
+ volume = {6468},
+ address = {San Jose, California, USA},
+ doi = {10.1117/12.715044}
+}
+
+ at ARTICLE{Pride2004,
+ author = {S. R. Pride and J. G. Berryman and J. M. Harris},
+ title = {Seismic attenuation due to wave-induced flow},
+ journal = jgr,
+ year = {2004},
+ volume = {109},
+ pages = {681-693}
+}
+
+ at ARTICLE{PrCaSe94,
+ author = {E. Priolo and J. M. Carcione and G. Seriani},
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+ techniques},
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+}
+
+ at ARTICLE{PuAmKa09,
+ author = {de la Puente, J. and Ampuero, J. P. and K\"aser, M.},
+ title = {Dynamic rupture modeling on unstructured meshes using a discontinuous
+ {G}alerkin method},
+ journal = jgr,
+ year = {2009},
+ volume = {114},
+ pages = {B10302},
+ doi = {10.1029/2008JB006271}
+}
+
+ at ARTICLE{PuSe98,
+ author = {Jay Pulliam and Mrinal K. Sen},
+ title = {Seismic anisotropy in the core-mantle transition zone},
+ journal = gji,
+ year = {1998},
+ volume = {135},
+ pages = {113-128},
+ number = {1}
+}
+
+ at ARTICLE{QiGe98,
+ author = {Q. Qi and T. L. Geers},
+ title = {Evaluation of the {P}erfectly {M}atched {L}ayer for computational
+ acoustics},
+ journal = jcp,
+ year = {1998},
+ volume = {139},
+ pages = {166-183},
+ number = {1}
+}
+
+ at ARTICLE{sympl1,
+ author = {Qin, M.-Z. and Chen, J.-B},
+ title = {Maslov asymptotic theory and symplectic algorithm},
+ journal = {Chinese J. Geophys.},
+ year = {2000},
+ volume = {43},
+ pages = {556-567},
+ number = {4}
+}
+
+ at ARTICLE{QuTaZa98,
+ author = {A. Quarteroni and A. Tagliani and E. Zampieri},
+ title = {Generalized {G}alerkin approximations of elastic waves with absorbing
+ boundary conditions},
+ journal = cmame,
+ year = {1998},
+ volume = {163},
+ pages = {323-341}
+}
+
+ at ARTICLE{Quiroga2005,
+ author = {G. Quiroga-Goode and S. Jim\'enez-Hern\'andez and M. A. P\'erez-Flores
+ and R. Padilla-Hern\'andez},
+ title = {Computational study of seismic waves in homogeneous dynamic-porosity
+ media with thermal and fluid relaxation: {G}auging {B}iot theory},
+ journal = jgr,
+ year = {2005},
+ volume = {110},
+ pages = {B07303},
+ doi = {10.1029/2004JB003347}
+}
+
+ at ARTICLE{Ron96,
+ author = {E. M. R{\o}nquist},
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+ journal = {Int. J. Num. Meth. Fluids},
+ year = {1996},
+ volume = {22},
+ pages = {241-264}
+}
+
+ at PHDTHESIS{Ron88,
+ author = {E. M. R{\o}nquist},
+ title = {Optimal spectral element methods for the unsteady three-dimensional
+ incompressible {N}avier-{S}tokes equations},
+ school = {Massachussets Institute of Technology},
+ year = {1988},
+ address = {Massachussets}
+}
+
+ at INPROCEEDINGS{RoPa88,
+ author = {E. M. R{\o}nquist and A. T. Patera},
+ title = {A {L}egendre Spectral-Element Method for the Incompressible {N}avier-{S}tokes
+ Equations},
+ booktitle = {Proc. of the Seventh GAMM Conference on Numerical Methods in Fluid
+ Mechanics},
+ year = {1988},
+ editor = {M. Deville},
+ pages = {318-326},
+ address = {Louvain-la-Neuve, Belgium}
+}
+
+ at ARTICLE{RoPa87,
+ author = {E. M. R{\o}nquist and A. T. Patera},
+ title = {A {L}egendre {S}pectral {E}lement Method for the {S}tefan Problem},
+ journal = ijnme,
+ year = {1987},
+ volume = {24},
+ pages = {2273-2299}
+}
+
+ at ARTICLE{RuRy00,
+ author = {G. R\"umpker and T. Ryberg},
+ title = {New "Fresnel-zone" estimates for shear-wave splitting observations
+ from finite-difference modeling},
+ journal = grl,
+ year = {2000},
+ volume = {27},
+ pages = {2005-2008}
+}
+
+ at ARTICLE{RaNaLi09,
+ author = {Nikunj Raghuvanshi and Rahul Narain and Ming C. Lin},
+ title = {Efficient and Accurate Sound Propagation Using Adaptive Rectangular
+ Decomposition},
+ journal = {IEEE Transactions on Visualization and Computer Graphics},
+ year = {2009},
+ volume = {15},
+ pages = {789-801},
+ number = {5},
+ doi = {10.1109/TVCG.2009.28}
+}
+
+ at ARTICLE{Rah04,
+ author = {A. N. Rahmouni},
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+ ({A} well-posed {PML} model for anisotropic elastodynamics)},
+ journal = {C. R. Acad. Sci. Paris, Ser. I},
+ year = {2004},
+ volume = {338},
+ pages = {963-968}
+}
+
+ at PHDTHESIS{Rah00,
+ author = {A. N. Rahmouni},
+ title = {Des mod\`eles {PML} bien pos\'es pour divers probl\`emes hyperboliques
+ ({S}ome well-posed {PML} models for several hyperbolic problems)},
+ school = {University of Paris XIII, France},
+ year = {2000}
+}
+
+ at BOOK{Ray45,
+ title = {The theory of sound},
+ publisher = {Dover Publications},
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+ edition = {2nd}
+}
+
+ at ARTICLE{Ray10,
+ author = {L. J. W. S. Rayleigh},
+ title = {The problem of the whispering gallery},
+ journal = {Philosophical Magazine Ser. 6},
+ year = {1910},
+ volume = {20},
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+}
+
+ at ARTICLE{Ray87,
+ author = {Lord J. W. S. Rayleigh},
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+ journal = {Proc. London Math. Soc.},
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+}
+
+ at TECHREPORT{ReHi73,
+ author = {W. H. Reed and T. R. Hill},
+ title = {Triangular mesh methods for the neutron transport equation},
+ institution = {Los Alamos Scientific Laboratory},
+ year = {1973},
+ number = {LA-UR-73-479},
+ address = {Los Alamos, USA}
+}
+
+ at ARTICLE{reidetal2001,
+ author = {F. J. L. Reid and J. H. Woodhouse and H. J. van Heijst},
+ title = {Upper mantle attenuation and velocity structure from measurements
+ of differential S phases},
+ journal = gji,
+ year = {2001},
+ volume = {145},
+ pages = {615-630}
+}
+
+ at ARTICLE{ReKoEdHs88,
+ author = {M. Reshef and D. Kosloff and M. Edwards and C. Hsiung},
+ title = {Three dimensional acoustic modeling by the {F}ourier method},
+ journal = geophysics,
+ year = {1988},
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+}
+
+ at ARTICLE{Ria96,
+ author = {J. A. Rial},
+ title = {The anomalous seismic response of the ground at the {T}arzana {H}ill
+ site during the {N}orthridge 1994 {S}outhern {C}alifornia earthquake:
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+ year = {1996},
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+}
+
+ at ARTICLE{rial1978,
+ author = {J. A. Rial},
+ title = {On the focusing of seismic body waves at the epicenter's antipode},
+ journal = gjras,
+ year = {1978},
+ volume = {55},
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+}
+
+ at ARTICLE{rial&cormier1980,
+ author = {J. A. Rial and V. F. Cormier},
+ title = {Seismic waves at the epicenter's antipode},
+ journal = jgr,
+ year = {1980},
+ volume = {85},
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+}
+
+ at ARTICLE{RiMeGrBr05,
+ author = {J. E. Richardson and H. J. Melosh and R. J. Greenberg and D. P. O'Brien},
+ title = {The global effects of impact-induced seismic activity on fractured
+ asteroid surface morphology},
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+}
+
+ at ARTICLE{Ric94,
+ author = {G. R. Richter},
+ title = {An explicit finite element method for the wave equation},
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+ volume = {16},
+ pages = {65-80}
+}
+
+ at PHDTHESIS{Rio97,
+ author = {Bruno Riollet},
+ title = {Simulation num\'erique de la propagation d'ondes sismiques en milieu
+ fractur\'e ({N}umerical simulation of wave propagation in media with
+ cracks)},
+ school = {Universit\'e Paris {\sc VII} Jussieu},
+ year = {1997},
+ address = {Paris}
+}
+
+ at INCOLLECTION{Rit05,
+ author = {J. Ritsema},
+ title = {Global seismic structure maps},
+ booktitle = {Plates, Plumes, and Paradigms},
+ publisher = {Geological Soc. Amer. special paper},
+ year = {2005},
+ editor = {G. R. Foulger and J. H. Natland and D. C. Presnall and D. L. Anderson},
+ volume = {388},
+ pages = {11-18},
+ doi = {10.1130/2005.2388}
+}
+
+ at ARTICLE{RiDeVaWo10,
+ author = {J. Ritsema and A. Deuss and H. J. {Van Heijst} and J. H. Woodhouse},
+ title = {{S40RTS}: a degree-40 shear-velocity model for the mantle from new
+ Rayleigh wave dispersion, teleseismic traveltime and normal-mode
+ splitting function measurements},
+ journal = gji,
+ year = {2011},
+ volume = {184},
+ pages = {1223-1236},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2010.04884.x}
+}
+
+ at ARTICLE{ritsemavanheijst2002,
+ author = {J. Ritsema and H. J. van Heijst},
+ title = {Constraints on the correlation of P- and S-wave velocity heterogeneity
+ in the mantle from P, PP, PPP, and PKPab traveltimes},
+ journal = gji,
+ year = {2002},
+ volume = {149},
+ pages = {482-489}
+}
+
+ at ARTICLE{RiLaGaBe98,
+ author = {J. Ritsema and T. Lay and E. J. Garnero and H. Benz},
+ title = {Seismic anisotropy in the lowermost mantle beneath the {P}acific},
+ journal = grl,
+ year = {1998},
+ volume = {25},
+ pages = {1229-1232}
+}
+
+ at ARTICLE{RiRiKoTrHe02,
+ author = {J. Ritsema and L. A. Rivera and D. Komatitsch and J. Tromp and H.
+ J. van Heijst},
+ title = {The effects of crust and mantle heterogeneity on {PP/P} and {SS/S}
+ amplitude ratios},
+ journal = grl,
+ year = {2002},
+ volume = {29},
+ pages = {1430},
+ number = {10},
+ doi = {10.1029/2001GL013831}
+}
+
+ at ARTICLE{RiVa00,
+ author = {J. Ritsema and H. J. {Van Heijst}},
+ title = {Seismic imaging of structural heterogeneity in {E}arth's mantle:
+ Evidence for large-scale mantle flow},
+ journal = {Science Progress},
+ year = {2000},
+ volume = {83},
+ pages = {243-259}
+}
+
+ at ARTICLE{RiVaWo99,
+ author = {J. Ritsema and H. J. {Van Heijst} and J. H. Woodhouse},
+ title = {Complex shear velocity structure imaged beneath {A}frica and {I}celand},
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+}
+
+ at ARTICLE{ritzwollerlavely1995,
+ author = {M. H. Ritzwoller and E. M. Lavely},
+ title = {Three-dimensional models of the {E}arth's mantle},
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+ year = {1995},
+ volume = {33},
+ pages = {1-66}
+}
+
+ at ARTICLE{RiWh03,
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+}
+
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+ year = {1994},
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+ pages = {1444-1456}
+}
+
+ at ARTICLE{RoThVeMuWi02,
+ author = {M. S. Robinson and P. C. Thomas and J. Veverka and S. L. Murchie
+ and B. B. Wilcox},
+ title = {The geology of 433 Eros},
+ journal = {Meteoritics and Planetary Sciences},
+ year = {2002},
+ volume = {37},
+ pages = {1651-1684}
+}
+
+ at ARTICLE{RoGe00,
+ author = {J. A. Roden and S. D. Gedney},
+ title = {Convolution {PML} ({CPML}): {A}n Efficient {FDTD} Implementation
+ of the {CFS}-{PML} for Arbitrary Media},
+ journal = {Microwave and Optical Technology Letters},
+ year = {2000},
+ volume = {27},
+ pages = {334-339},
+ number = {5},
+ doi = {10.1002/1098-2760(20001205)27:5<334::AID-MOP14>3.0.CO;2-A}
+}
+
+ at PHDTHESIS{Rod04,
+ author = {Jer\'onimo Rodr\'{\i}guez},
+ title = {Raffinement de maillage spatio-temporel pour les \'equations de l'\'elastodynamique},
+ school = {Universit\'e Paris IX-Dauphine},
+ year = {2004},
+ address = {Paris, France}
+}
+
+ at ARTICLE{RoSaLuMa06,
+ author = {A. Rodr\'{\i}guez-Castellanos and F.J. S\'anchez-Sesma and F. Luz\'on
+ and R. Martin},
+ title = {Multiple scattering of elastic waves by subsurface fractures and
+ cavities},
+ journal = bssa,
+ year = {2006},
+ volume = {96},
+ pages = {1359-1374},
+ number = {4A}
+}
+
+ at INPROCEEDINGS{RoHaStScHw08,
+ author = {Christopher I. Rodrigues and David J. Hardy and John E. Stone and
+ Klaus Schulten and Wen{-}mei W. Hwu},
+ title = {{GPU} acceleration of cutoff pair potentials for molecular modeling
+ applications},
+ booktitle = {Proceedings of the 2008 conference on Computing Frontiers},
+ year = {2008},
+ pages = {273--282},
+ address = {New York, USA},
+ publisher = {ACM}
+}
+
+ at PHDTHESIS{Rod93,
+ author = {Dominique Rodrigues},
+ title = {Simulation de la propagation d'ondes sismiques sur machine massivement
+ parall\`ele},
+ school = {\'Ecole Centrale de Paris},
+ year = {1993},
+ address = {Paris, France}
+}
+
+ at INPROCEEDINGS{RoMo93,
+ author = {D. Rodrigues and P. Mora},
+ title = {Implementation of the free surface boundary condition in 2-{D} and
+ 3-{D} elastic cases},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1993},
+ pages = {215-217},
+ note = {63rd international meeting of the SEG}
+}
+
+ at INPROCEEDINGS{RoMo92,
+ author = {D. Rodrigues and P. Mora},
+ title = {Analysis of a finite difference solution to 3-{D} elastic wave propagation},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1992},
+ pages = {1247-1250},
+ note = {62nd international meeting of the SEG}
+}
+
+ at ARTICLE{RoVaHelene,
+ author = {A. A. Rodriguez and A. Valli},
+ title = {Domain Decomposition Algorithms for Time-harmonic {M}axwell Equations
+ with Damping},
+ journal = {Mathematical Modelling and Numerical Analysis},
+ year = {2001},
+ volume = {35},
+ pages = {825-848},
+ number = {4}
+}
+
+ at ARTICLE{RoLaGaRu04,
+ author = {J. M. Rokosky and T. Lay and E. J. Garnero and S. A. Russel},
+ title = {High-resolution investigation of shear wave anisotropy in {D}'' beneath
+ the {C}ocos plate},
+ journal = grl,
+ year = {2004},
+ volume = {31},
+ pages = {L07605},
+ doi = {10.1029/2003GL018902}
+}
+
+ at ARTICLE{Rol68,
+ author = {F. R. {Rollins Jr}},
+ title = {Ultrasonic examination of liquid-solid boundaries using a right-angle
+ reflector technique},
+ journal = jasa,
+ year = {1968},
+ volume = {44},
+ pages = {431-434},
+ number = {2}
+}
+
+ at ARTICLE{RolLimFar68,
+ author = {F. R. {Rollins Jr} and T. C. Lim and G. W. Farnell},
+ title = {Ultrasonic reflectivity and surface wave phenomena on surfaces of
+ copper single crystals},
+ journal = {Applied Physics Letters},
+ year = {1968},
+ volume = {12},
+ pages = {236-238},
+ number = {7}
+}
+
+ at ARTICLE{Romanowicz08,
+ author = {B. Romanowicz},
+ title = {Using seismic waves to image {E}arth's internal structure},
+ journal = {Nature},
+ year = {2008},
+ volume = {451},
+ pages = {266-268}
+}
+
+ at ARTICLE{romanowicz1998,
+ author = {B. Romanowicz},
+ title = {Attenuation tomography of the {E}arth's mantle: a review of current
+ status},
+ journal = pageoph,
+ year = {1998},
+ volume = {153},
+ pages = {257-272}
+}
+
+ at ARTICLE{romanowiczgung2002,
+ author = {B. Romanowicz and Y. C. Gung},
+ title = {Superplumes from the core-mantle boundary to the lithosphere: implications
+ for heat flux},
+ journal = {Science},
+ year = {2002},
+ volume = {296},
+ pages = {513-516}
+}
+
+ at ARTICLE{RoIaPa96,
+ author = {C. Ronchi and R. Ianoco and P. S. Paolucci},
+ title = {The ``{C}ubed {S}phere'': a new method for the solution of partial
+ differential equations in spherical geometry},
+ journal = jcp,
+ year = {1996},
+ volume = {124},
+ pages = {93-114}
+}
+
+ at INCOLLECTION{RoBoFi05,
+ author = {S. Rondenay and M. G. Bostock and K. M. Fischer},
+ title = {Multichannel inversion of scattered teleseismic body waves: practical
+ considerations},
+ booktitle = {Seismic Earth: Array Analysis of Broadband Seismograms},
+ publisher = {American Geophysical Union},
+ year = {2005},
+ editor = {Alan Levander and Guust Nolet},
+ volume = {157},
+ series = {Geophysical Monograph},
+ pages = {187-204},
+ address = {Washington DC, USA}
+}
+
+ at ARTICLE{RoHiRi03,
+ author = {S\'everine Rosat and Jacques Hinderer and Luis Rivera},
+ title = {First observation of ${}_2{S}_1$ and study of the splitting of the
+ football mode ${}_0{S}_2$ after the {J}une 2001 {P}eru earthquake
+ of magnitude 8.4},
+ journal = grl,
+ year = {2003},
+ volume = {30},
+ pages = {2111},
+ number = {21},
+ doi = {10.1029/2003GL018304}
+}
+
+ at ARTICLE{RoBeCoKo10,
+ author = {Diego Rossinelli and Michael Bergdorf and Georges-Henri Cottet and
+ Petros Koumoutsakos},
+ title = {{GPU} accelerated simulations of bluff body flows using vortex particle
+ methods},
+ journal = jcp,
+ year = {2010},
+ volume = {229},
+ pages = {3316-3333},
+ number = {9},
+ doi = {10.1016/j.jcp.2010.01.004}
+}
+
+ at ARTICLE{Roy08,
+ author = {D. Royer},
+ title = {Stresses and displacements for some Rayleigh-type surface acoustic
+ waves propagating on an anisotropic half space (L)},
+ journal = jasa,
+ year = {2008},
+ volume = {123},
+ pages = {599-601},
+ number = {2}
+}
+
+ at BOOK{RoyDie96,
+ title = {Ondes elastiques dans les solides},
+ publisher = {Masson (Paris)},
+ year = {1996},
+ author = {D. Royer and E. Dieulesaint},
+ volume = {1. Propagation libre et guid\'ee}
+}
+
+ at ARTICLE{RoyDie84,
+ author = {D. Royer and E. Dieulesaint},
+ title = {Rayleigh wave velocity and displacement in orthorhombic, tetragonal,
+ hexagonal, and cubic crystals},
+ journal = jasa,
+ year = {1984},
+ volume = {76},
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+}
+
+ at ARTICLE{Rul69,
+ author = {B. Rulf},
+ title = {Rayleigh waves on curved surfaces},
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+ year = {1969},
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+}
+
+ at INPROCEEDINGS{rumpf_strzodka_2006,
+ author = {M. Rumpf and R. Strzodka},
+ title = {Graphics {P}rocessor {U}nits: {N}ew prospects for parallel computing},
+ booktitle = {Numerical Solution to Partial Differential Equations on Parallel
+ Computers},
+ year = {2006},
+ volume = {51},
+ series = {Lecture Notes in Computational Science and Engineering},
+ pages = {89-134},
+ address = {Germany},
+ publisher = {Springer-Verlag}
+}
+
+ at INPROCEEDINGS{Rumpf:2001:NLD,
+ author = {Martin Rumpf and Robert Strzodka},
+ title = {Nonlinear Diffusion in Graphics Hardware},
+ booktitle = {{Proceedings of EG/IEEE TCVG Symposium on Visualization (VisSym '01)}},
+ year = {2001},
+ pages = {75--84},
+ month = may
+}
+
+ at ARTICLE{RuLaGa99,
+ author = {S. A. Russell and T. Lay and E. J. Garnero},
+ title = {Small-scale lateral shear velocity and anisotropy heterogeneity near
+ the core-mantle boundary beneath the central {P}acific imaged using
+ broadband {ScS} waves},
+ journal = jgr,
+ year = {1999},
+ volume = {104},
+ pages = {13,183-13,199},
+ number = {B6}
+}
+
+ at ARTICLE{Rya71,
+ author = {R. L. Ryan},
+ title = {Pulse propagation in a transversely isotropic half-space},
+ journal = {Journal of Sound and Vibration},
+ year = {1971},
+ volume = {14},
+ pages = {511-524},
+ number = {4}
+}
+
+ at ARTICLE{RyLe83,
+ author = {G. Ryskin and L. G. Leal},
+ title = {Orthogonal mapping},
+ journal = jcp,
+ year = {1983},
+ volume = {50},
+ pages = {71-100}
+}
+
+ at ARTICLE{SesmaViv01,
+ author = {F. J. S{\'a}nchez-Sesma and U. Iturrar{\'a}n-Viveros},
+ title = {Scattering and diffraction of {$SH$} waves by a finite crack: an
+ analytical solution},
+ journal = gji,
+ year = {2001},
+ volume = {145},
+ pages = {749-758}
+}
+
+ at INCOLLECTION{San97,
+ author = {F. J. S\'anchez-Sesma},
+ title = {Strong ground motion and site effects},
+ booktitle = {Computer Analysis and Design of Earthquake resistant structures},
+ publisher = {Comp. Mech. Publications},
+ year = {1997},
+ editor = {D.E. Beskos and S.A. Angnostopoulos},
+ pages = {201-239},
+ address = {Southampton}
+}
+
+ at ARTICLE{San83,
+ author = {F. J. S\'anchez-Sesma},
+ title = {Diffraction of elastic waves by three-dimensional surface irregularities},
+ journal = bssa,
+ year = {1983},
+ volume = {73},
+ pages = {1621-1636},
+ number = {6}
+}
+
+ at INPROCEEDINGS{SaBeBi96,
+ author = {F. J. S\'anchez-Sesma and R. Benites and J. Bielak},
+ title = {The assessment of strong ground motion: what lies ahead?},
+ booktitle = {Proceedings of the 11th World Conference on Earthquake Engineering},
+ year = {1996},
+ pages = {1-19},
+ note = {Acapulco, Mexico, June 1996}
+}
+
+ at ARTICLE{SaCa93,
+ author = {F. J. S\'anchez-Sesma and M. Campillo},
+ title = {Topographic effects for incident {{\it P, SV}} and {R}ayleigh waves},
+ journal = {Tectonophysics},
+ year = {1993},
+ volume = {218},
+ pages = {113-125}
+}
+
+ at ARTICLE{SaCa91,
+ author = {F. J. S\'anchez-Sesma and M. Campillo},
+ title = {Diffraction of {{\it P}}, {{\it SV}} and {R}ayleigh waves by topographic
+ features: a boundary integral formulation},
+ journal = bssa,
+ year = {1991},
+ volume = {81},
+ pages = {2234-2253}
+}
+
+ at ARTICLE{SaLu96,
+ author = {F. J. S\'anchez-Sesma and F. Luz\'on},
+ title = {Can horizontal {{\it P}} waves be trapped and resonate in a shallow
+ sedimentary basin?},
+ journal = gji,
+ year = {1996},
+ volume = {124},
+ pages = {209-214}
+}
+
+ at ARTICLE{SaRaCa93,
+ author = {F. J. S\'anchez-Sesma and J. Ramos-Martinez and M. Campillo},
+ title = {An indirect boundary element method applied to simulate the seismic
+ response of alluvial valleys for incident {{\it P, SV}} and {R}ayleigh
+ waves},
+ journal = eesd,
+ year = {1993},
+ volume = {22},
+ pages = {279-295}
+}
+
+ at ARTICLE{SaRo79,
+ author = {F. J. S\'anchez-Sesma and E. Rosenblueth},
+ title = {Ground motion at canyons of arbitrary shape under incident {{\it
+ SH}} waves},
+ journal = eesd,
+ year = {1979},
+ volume = {7},
+ pages = {441-450}
+}
+
+ at ARTICLE{SuSh03,
+ author = {M. P. S\"uss and J. H. Shaw},
+ title = {P wave seismic velocity structure derived from sonic logs and industry
+ reflection data in the {L}os {A}ngeles basin, {C}alifornia},
+ journal = jgr,
+ year = {2003},
+ volume = {108},
+ pages = {2170},
+ number = {B3},
+ doi = {10.1029/2001JB001628}
+}
+
+ at ARTICLE{SaKiLeLe95,
+ author = {Z. S. Sacks and D. M. Kingsland and R. Lee and J. F. Lee},
+ title = {A {P}erfectly {M}atched anisotropic absorber for use as an absorbing
+ boundary condition},
+ journal = {IEEE transactions on Antennas and Propagation},
+ year = {1995},
+ volume = {43},
+ pages = {1460-1463},
+ number = {12}
+}
+
+ at ARTICLE{Sad72,
+ author = {R. Sadourny},
+ title = {Conservative finite-difference approximations of the primitive equations
+ on quasi-uniform spherical grids},
+ journal = {Monthly Weather Review},
+ year = {1972},
+ volume = {100},
+ pages = {136-144}
+}
+
+ at ARTICLE{SaBo04,
+ author = {Erik H. Saenger and Thomas Bohlen},
+ title = {Finite-difference modeling of viscoelastic and anisotropic wave propagation
+ using the rotated staggered grid},
+ journal = geophysics,
+ year = {2004},
+ volume = {69},
+ pages = {583-591},
+ number = {2},
+ doi = {10.1190/1.1707078}
+}
+
+ at ARTICLE{SaGoSh00,
+ author = {E. H. Saenger and N. Gold and S. A. Shapiro},
+ title = {Modeling the propagation of elastic waves using a modified finite-difference
+ grid},
+ journal = {Wave Motion},
+ year = {2000},
+ volume = {31},
+ pages = {77-92(16)},
+ number = {1}
+}
+
+ at ARTICLE{SaSh02,
+ author = {E. H. Saenger and S. A. Shapiro},
+ title = {Effective velocities in fractured media: a numerical study using
+ the rotated staggered finite-difference grid},
+ journal = {Geophysical Prospecting},
+ year = {2002},
+ volume = {50},
+ pages = {183-194}
+}
+
+ at ARTICLE{SaOd93,
+ author = {A. Safjan and J. T. Oden},
+ title = {High-order {T}aylor-{G}alerkin and adaptative {\it h-p} methods for
+ second-order hyperbolic systems: application to elastodynamics},
+ journal = cmame,
+ year = {1993},
+ volume = {103},
+ pages = {187-230}
+}
+
+ at ARTICLE{ks,
+ author = {K. Salkauskas},
+ title = {{$C^1$} splines for interpolation of rapidly varying data},
+ journal = {Rocky Mountain J. Math.},
+ year = {1974},
+ volume = {14},
+ pages = {239-250}
+}
+
+ at ARTICLE{SaKaSaPi01,
+ author = {Toshimi Satoh and Hiroshi Kawase and Toshiaki Sato and Arben Pitarka},
+ title = {Three-Dimensional Finite-Difference Waveform Modeling of Strong Motions
+ Observed in the {S}endai Basin, {J}apan},
+ journal = bssa,
+ year = {2001},
+ volume = {91},
+ pages = {365-380}
+}
+
+ at ARTICLE{SaKoTr10,
+ author = {Brian Savage and Dimitri Komatitsch and Jeroen Tromp},
+ title = {Effects of {3D} attenuation on seismic wave amplitude and phase measurements},
+ journal = bssa,
+ year = {2010},
+ volume = {100},
+ pages = {1241-1251},
+ number = {3},
+ doi = {10.1785/0120090263}
+}
+
+ at INPROCEEDINGS{SavWiTr05,
+ author = {Savage, B. and D. A. Wiens and J. Tromp},
+ title = {Effects of 3{D} Velocity and Attenuation in the {T}onga-{F}iji Subduction
+ Zone},
+ booktitle = {Expanded abstracts of the American Geophysical Union},
+ year = {Fall Meeting 2005},
+ note = {abstract T31D-04}
+}
+
+ at ARTICLE{ScHuYeHu96,
+ author = {C. L. Schneider and C. Hummon and R. S. Yeats and G. J. Huftile},
+ title = {Structural evolution of the northern {L}os {A}ngeles basin, {C}alifornia,
+ based on growth strata},
+ journal = {Tectonics},
+ year = {1996},
+ volume = {15},
+ pages = {341-355}
+}
+
+ at ARTICLE{ScMu89,
+ author = {M. Schoenberg and F. Muir},
+ title = {A calculus for finely layered anisotropic media},
+ journal = geophysics,
+ year = {1989},
+ volume = {54},
+ pages = {581-589},
+ number = {5}
+}
+
+ at INPROCEEDINGS{Schroeder:2009:DEI,
+ author = {Bianca Schroeder and Eduardo Pinheiro and Wolf-Dietrich Weber},
+ title = {{DRAM} errors in the wild: {A} large-scale field study},
+ booktitle = {SIGMETRICS/Performance '09: Proceedings of the 2009 Joint International
+ Conference on Measurement \& Modeling of Computer Systems},
+ year = {2009},
+ pages = {193--204},
+ month = jun,
+ doi = {10.1145/1555349.1555372}
+}
+
+ at TECHREPORT{Sch03,
+ author = {B. Schubert},
+ title = {The spectral-element method for seismic wave propagation: theory,
+ implementation and comparison to finite-difference methods},
+ institution = {University of Munich},
+ year = {2003},
+ address = {Germany},
+ note = {unpublished report, 165 p.}
+}
+
+ at ARTICLE{Ser04,
+ author = {G. Seriani},
+ title = {Double-grid {C}hebyshev spectral elements for acoustic wave modeling},
+ journal = {Wave Motion},
+ year = {2004},
+ volume = {39},
+ pages = {351-360}
+}
+
+ at ARTICLE{Ser98,
+ author = {G\'eza Seriani},
+ title = {3-{D} large-scale wave propagation modeling by a spectral element
+ method on a {C}ray {T3E} multiprocessor},
+ journal = cmame,
+ year = {1998},
+ volume = {164},
+ pages = {235-247}
+}
+
+ at ARTICLE{Ser97,
+ author = {G\'eza Seriani},
+ title = {A parallel spectral element method for acoustic wave modeling},
+ journal = jca,
+ year = {1997},
+ volume = {5},
+ pages = {53-69}
+}
+
+ at ARTICLE{SeOl08,
+ author = {G. Seriani and S. P. Oliveira},
+ title = {Dispersion analysis of spectral-element methods for elastic wave
+ propagation},
+ journal = {Wave Motion},
+ year = {2008},
+ volume = {45},
+ pages = {729-744},
+ doi = {10.1016/j.wavemoti.2007.11.007}
+}
+
+ at ARTICLE{SePr94,
+ author = {G. Seriani and E. Priolo},
+ title = {A spectral element method for acoustic wave simulation in heterogeneous
+ media},
+ journal = {Finite Elements in Analysis and Design},
+ year = {1994},
+ volume = {16},
+ pages = {337-348}
+}
+
+ at INPROCEEDINGS{SePr91,
+ author = {G. Seriani and E. Priolo},
+ title = {High-order spectral element method for acoustic wave modeling},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1991},
+ series = {61st international meeting of the SEG},
+ pages = {1561-1564},
+ address = {Houston, Texas, USA}
+}
+
+ at INPROCEEDINGS{SePrCaPa92,
+ author = {G. Seriani and E. Priolo and J. M. Carcione and E. Padovani},
+ title = {High-order spectral element method for elastic wave modeling},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1992},
+ series = {62nd international meeting of the SEG},
+ pages = {1285-1288},
+ address = {New-Orleans, Louisiana, USA}
+}
+
+ at INPROCEEDINGS{SePrPr95,
+ author = {G. Seriani and E. Priolo and A. Pregarz},
+ title = {Modelling waves in anisotropic media by a spectral element method},
+ booktitle = {Proceedings of the third international conference on mathematical
+ and numerical aspects of wave propagation},
+ year = {1995},
+ editor = {G. Cohen},
+ pages = {289-298},
+ publisher = {SIAM, Philadephia, PA}
+}
+
+ at ARTICLE{SeOl07,
+ author = {G{\'e}za Seriani and Saulo P. Oliveira},
+ title = {Optimal blended spectral-element operators for acoustic wave modeling},
+ journal = geophysics,
+ year = {2007},
+ volume = {72},
+ pages = {SM95-SM106},
+ number = {5},
+ doi = {10.1190/1.2750715}
+}
+
+ at ARTICLE{ShOlSi02,
+ author = {Nikolai M. Shapiro and Kim B. Olsen and Shri K. Singh},
+ title = {On the duration of seismic motion incident onto the Valley of {M}exico
+ for subduction zone earthquakes},
+ journal = gji,
+ year = {2002},
+ volume = {151},
+ pages = {501-510}
+}
+
+ at ARTICLE{Sha07,
+ author = {M. D. Sharma},
+ title = {Spatial dispersion of surface waves at the free surface of a general
+ anisotropic elastic medium},
+ journal = {Journal of Seismology},
+ year = {2007},
+ volume = {11},
+ pages = {187-197}
+}
+
+ at INPROCEEDINGS{ShSuRi99,
+ author = {J. H. Shaw and P. S\"uss and C. Rivero},
+ title = {Structural and seismologic investigations of concealed earthquake
+ sources in the {L}os {A}ngeles metropolitan area},
+ booktitle = {SCEC Annual Meeting},
+ year = {1999},
+ address = {Palm Springs, California}
+}
+
+ at ARTICLE{ShSh99,
+ author = {J. H. Shaw and P. Shearer},
+ title = {An elusive blind-thrust fault beneath metropolitan {L}os {A}ngeles},
+ journal = {Science},
+ year = {1999},
+ volume = {283},
+ pages = {1516-1518}
+}
+
+ at ARTICLE{ShSu96,
+ author = {John H. Shaw and J. Suppe},
+ title = {Earthquake hazards of active blind-thrust faults under the central
+ {L}os {A}ngeles basin, {C}alifornia},
+ journal = jgr,
+ year = {1996},
+ volume = {101},
+ pages = {8623-8642}
+}
+
+ at INPROCEEDINGS{Sheaffer:2007:AHR,
+ author = {Jeremy W. Sheaffer and David P. Luebke and Kevin Skadron},
+ title = {A Hardware Redundancy and Recovery Mechanism for Reliable Scientific
+ Computation on Graphics Processors},
+ booktitle = {Graphics Hardware 2007},
+ year = {2007},
+ editor = {Timo Aila and Mark Segal},
+ pages = {55--64},
+ month = aug
+}
+
+ at ARTICLE{Shearer94,
+ author = {P. M. Shearer},
+ title = {Constraints on inner core anisotropy from {PKP(DF)} travel times},
+ journal = jgr,
+ year = {1994},
+ volume = {99},
+ pages = {19647-19659}
+}
+
+ at ARTICLE{ShTuBaOr06,
+ author = {Dong-Hoon Sheen and Kagan Tuncay and Chang-Eob Baag and Peter J.
+ Ortoleva},
+ title = {Parallel implementation of a velocity-stress staggered-grid finite-difference
+ method for 2-{D} poroelastic wave propagation},
+ journal = {Computers and Geosciences},
+ year = {2006},
+ volume = {32},
+ pages = {1182-1191},
+ doi = {10.1016/j.cageo.2005.11.001}
+}
+
+ at ARTICLE{ShJo06,
+ author = {J. F. Shepherd and Ch. R. Johnson},
+ title = {Hexahedral mesh generation constraints},
+ journal = {Engineering with Computers},
+ year = {2008},
+ volume = {24},
+ pages = {195 - 213},
+ number = {3},
+ doi = {10.1007/s00366-008-0091-4}
+}
+
+ at BOOK{ShGe82,
+ title = {Exploration seismology: history, theory and data acquisition},
+ publisher = {Cambridge University Press},
+ year = {1982},
+ author = {R. E. Sheriff and L. P. Geldart},
+ address = {Cambridge}
+}
+
+ at ARTICLE{ShKarn95,
+ author = {S. J. Sherwin and G. E. Karniadakis},
+ title = {A triangular spectral element method: applications to the incompressible
+ {N}avier-{S}tokes equations},
+ journal = cmame,
+ year = {1995},
+ volume = {123},
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+}
+
+ at INPROCEEDINGS{Shinguetal2002,
+ author = {Satoru Shingu and Hiroshi Takahara and Hiromitsu Fuchigami and Masayuki
+ Yamada and Yoshinori Tsuda and Wataru Ohfuchi and Yuji Sasaki and
+ Kazuo Kobayashi and Takashi Hagiwara and Shin-Ichi Habata and Mitsuo
+ Yokokawa and Hiroyuki Itoh and Kiyoshi Otsuka},
+ title = {A 26.58 teraflops Global Atmospheric Simulation with the Spectral
+ Transform Method on the {E}arth {S}imulator},
+ booktitle = {SC'02: Proceedings of the 2002 ACM/IEEE conference on Supercomputing},
+ year = {2002},
+ month = nov
+}
+
+ at ARTICLE{Shu02,
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+ title = {Erratum: {O}n the theory of plane inhomogeneous waves in anisotropic
+ elastic media},
+ journal = {Wave Motion},
+ year = {2002},
+ volume = {36},
+ pages = {305}
+}
+
+ at ARTICLE{Shu01,
+ author = {A. L. Shuvalov},
+ title = {On the theory of plane inhomogeneous waves in anisotropic elastic
+ media},
+ journal = {Wave Motion},
+ year = {2001},
+ volume = {34},
+ pages = {401-429}
+}
+
+ at ARTICLE{ShuEve00,
+ author = {A. L. Shuvalov and A. G. Every},
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+ symmetry planes and associated phonon focusing cusps},
+ journal = jasa,
+ year = {2000},
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+ number = {5}
+}
+
+ at ARTICLE{ShuEve97,
+ author = {A. L. Shuvalov and A. G. Every},
+ title = {Shape of the acoustic slowness surface of anisotropic solids near
+ points of conical degeneracy},
+ journal = jasa,
+ year = {1997},
+ volume = {101},
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+ number = {4}
+}
+
+ at ARTICLE{ShuPonDes05,
+ author = {A. L. Shuvalov and O. Poncelet and M. Deschamps},
+ title = {Plane inhomogeneous elastic waves in transversely isotropic media:
+ explicit analysis of different types of degeneracy},
+ journal = {Mathematics and Mechanics of Solids},
+ year = {2005},
+ volume = {10},
+ pages = {249-279}
+}
+
+ at ARTICLE{SiLiTrTr07a,
+ author = {Anne Sieminski and Qinya Liu and Jeannot Trampert and Jeroen Tromp},
+ title = {Finite-frequency sensitivity of surface waves to anisotropy based
+ upon adjoint methods},
+ journal = gji,
+ year = {2007},
+ volume = {168},
+ pages = {1153-1174},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2006.03261.x}
+}
+
+ at ARTICLE{SiLiTrTr07b,
+ author = {Anne Sieminski and Qinya Liu and Jeannot Trampert and Jeroen Tromp},
+ title = {Finite-frequency sensitivity of body waves to anisotropy based upon
+ adjoint methods},
+ journal = gji,
+ year = {2007},
+ volume = {171},
+ pages = {368-389},
+ doi = {10.1111/j.1365-246X.2007.03528.x}
+}
+
+ at ARTICLE{silver1996,
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+ geology},
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+}
+
+ at ARTICLE{Sim92,
+ author = {J. C. Simo},
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+ preserve the classical return mapping schemes of the infinitesimal
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+ journal = cmame,
+ year = {1992},
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+}
+
+ at ARTICLE{SiTaWo92,
+ author = {J. C. Simo and N. Tarnow and K. K. Wong},
+ title = {Exact energy-momentum conserving algorithms and symplectic schemes
+ for nonlinear dynamics},
+ journal = cmame,
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+}
+
+ at ARTICLE{simonsetal2002,
+ author = {F. J. Simons and R. D. van der Hilst and J. P. Montagner and A. Zielhuis},
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+ anisotropy of the {A}ustralian upper mantle},
+ journal = gji,
+ year = {2002},
+ volume = {151},
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+}
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+}
+
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+}
+
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+ title = {Guided elastic waves and perfectly matched layers},
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+}
+
+ at ARTICLE{smith&dahlen73,
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+ R. Overfelt and Hans F. Schwaiger},
+ title = {Elastic Wave Propagation in Variable Media using a Discontinuous
+ Galerkin Method},
+ journal = {SEG Technical Program Expanded Abstracts},
+ year = {2010},
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+ doi = {10.1190/1.3513466},
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+}
+
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+ explicit and implicit multi-domain decomposition techniques},
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+ year = {2009},
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+}
+
+ at ARTICLE{SoMa05,
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+ Interaction Problems},
+ journal = cmes,
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+}
+
+ at ARTICLE{SoMaLi07,
+ author = {Soares Jr., D. and W. J. Mansur and D. L. Lima},
+ title = {An Explicit Multi-Level Time-Step Algorithm to Model the Propagation
+ of Interacting Acoustic-Elastic Waves Using Finite-Element/Finite-Difference
+ Coupled Procedures},
+ journal = cmes,
+ year = {2007},
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+}
+
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+}
+
+ at ARTICLE{Song93b,
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+
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+
+ at ARTICLE{SoRo97,
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+ the nature of the solid core},
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+ year = {1997},
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+}
+
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+ title = {Tensor Calculus},
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+
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+ title = {Physics of the Earth},
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+
+ at TECHREPORT{Ste00,
+ author = {T. L. Sterling},
+ title = {Petaflops Computing: looking Back at the Future},
+ institution = {California Institute of Technology},
+ year = {2000},
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+ 2000}
+}
+
+ at BOOK{StMe95,
+ title = {Enabling technologies for {P}etaflops computing},
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+}
+
+ at BOOK{StSaBeSa99,
+ title = {How to build a {B}eowulf, a guide to the implementation and application
+ of {PC} clusters},
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+}
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+}
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+ of the 1989 {L}oma {P}rieta Earthquake},
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+ year = {1999},
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+}
+
+ at INPROCEEDINGS{StSuSh01,
+ author = {C. Stidham and M. P. S\"uss and J. H. Shaw},
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+}
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+}
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+ author = {M. Strengert and C. M\"uller and C. Dachsbacher and T. Ertl},
+ title = {{CUDASA}: {C}ompute {U}nified {D}evice {A}nd {S}ystems {A}rchitecture},
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+ and Visualization (EGPGV'08)},
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+}
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+ at INPROCEEDINGS{Stuart:2009:MPO,
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+ Processing Symposium},
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+}
+
+ at ARTICLE{StPaIg09,
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+ by a High-Performance Spectral Element Code},
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+}
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+ year = {2000},
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+ at ARTICLE{Sukum00,
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+ year = {2000},
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+}
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+ at ARTICLE{Sul97,
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+}
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+ at ARTICLE{SuTsCh10,
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+ title = {Finite Element analysis},
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+ year = {2000},
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+ at ARTICLE{TaCo87,
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+ at ARTICLE{TaLiMaTr2010,
+ author = {Carl Tape and Qinya Liu and Alessia Maggi and Jeroen Tromp},
+ title = {Seismic tomography of the southern {C}alifornia crust based on spectral-element
+ and adjoint methods},
+ journal = gji,
+ year = {2010},
+ volume = {180},
+ pages = {433-462}
+}
+
+ at ARTICLE{TaLiMaTr09,
+ author = {Carl Tape and Qinya Liu and Alessia Maggi and Jeroen Tromp},
+ title = {Adjoint tomography of the southern {C}alifornia crust},
+ journal = {Science},
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+
+ at ARTICLE{TaLiTr07,
+ author = {Carl Tape and Qinya Liu and Jeroen Tromp},
+ title = {Finite-frequency tomography using adjoint methods - {M}ethodology
+ and examples using membrane surface waves},
+ journal = gji,
+ year = {2007},
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+ at ARTICLE{Tar84,
+ author = {A. Tarantola},
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+ author = {A. Tarantola and B. Valette},
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+ author = {Natalya Tatarchuk and Jeremy Shopf and Christopher DeCoro},
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+}
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+ at ARTICLE{TaWi00,
+ author = {M. A. Taylor and B. A. Wingate},
+ title = {A generalized diagonal mass matrix spectral element method for non-quadrilateral
+ elements},
+ journal = {Appl. Num. Math.},
+ year = {2000},
+ volume = {33},
+ pages = {259-265}
+}
+
+ at ARTICLE{TaWiVi00,
+ author = {M. A. Taylor and B. A. Wingate and R. E. Vincent},
+ title = {An Algorithm for Computing {F}ekete Points in the Triangle},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {2000},
+ volume = {38},
+ pages = {1707-1720},
+ number = {5}
+}
+
+ at ARTICLE{TaTrIs97,
+ author = {M. Taylor and J. Tribbia and M. Iskandarani},
+ title = {The spectral element method for the shallow water equation on the
+ sphere},
+ journal = jcp,
+ year = {1997},
+ volume = {130},
+ pages = {92-108}
+}
+
+ at BOOK{Tay81,
+ title = {Pseudodifferential operators},
+ publisher = {Princeton University Press},
+ year = {1981},
+ author = {M. E. Taylor},
+ address = {Princeton, New-Jersey, USA}
+}
+
+ at ARTICLE{taylor_cheng_ourselin_2008,
+ author = {Z. A. Taylor and M. Cheng and S. Ourselin},
+ title = {High-Speed Nonlinear Finite Element Analysis for Surgical Simulation
+ Using {Graphics Processing Units}},
+ journal = {IEEE Transactions on Medical Imaging},
+ year = {2008},
+ volume = {27},
+ pages = {650-663},
+ number = {5},
+ doi = {10.1109/TMI.2007.913112}
+}
+
+ at ARTICLE{TeCh99,
+ author = {F. L. Teixeira and W. C. Chew},
+ title = {On causality and dynamic stability of {P}erfectly {M}atched {L}ayers
+ for {FDTD} simulations},
+ journal = {IEEE transactions on Microwave Theory and Techniques},
+ year = {1999},
+ volume = {47},
+ pages = {775-785},
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+}
+
+ at ARTICLE{EUCrust07,
+ author = {M. Tesauro and M. K. Kaban and S. A. P. L. Cloetingh},
+ title = {EuCrust-07: A new reference model for the {European} crust},
+ journal = grl,
+ year = {2008},
+ volume = {35},
+ pages = {L05313},
+ doi = {10.1029/2007GL032244}
+}
+
+ at ARTICLE{Tes00,
+ author = {Ekkehart Tessmer},
+ title = {Seismic finite-difference modeling with spatially varying time steps},
+ journal = geophysics,
+ year = {2000},
+ volume = {65},
+ pages = {1290-1293},
+ number = {4},
+ doi = {10.1190/1.1444820}
+}
+
+ at ARTICLE{Tes95,
+ author = {E. Tessmer},
+ title = {3-{D} seismic modelling of general material anisotropy in the presence
+ of the free surface by a {C}hebyshev spectral method},
+ journal = gji,
+ year = {1995},
+ volume = {121},
+ pages = {557-575}
+}
+
+ at ARTICLE{TeKeKo92,
+ author = {E. Tessmer and D. Kessler and D. Kosloff and A. Behle},
+ title = {Multi-domain {C}hebyshev-{F}ourier method for the solution of the
+ equations of motion of dynamic elasticity},
+ journal = jcp,
+ year = {1992},
+ volume = {100},
+ pages = {355-363}
+}
+
+ at ARTICLE{TeKo94,
+ author = {E. Tessmer and D. Kosloff},
+ title = {3-{D} elastic modeling with surface topography by a {C}hebyshev spectral
+ method},
+ journal = geophysics,
+ year = {1994},
+ volume = {59},
+ pages = {464-473},
+ number = {3}
+}
+
+ at ARTICLE{TeKoBe92,
+ author = {E. Tessmer and D. Kosloff and A. Behle},
+ title = {Elastic wave propagation simulation in the presence of surface topography},
+ journal = gji,
+ year = {1992},
+ volume = {108},
+ pages = {621-632}
+}
+
+ at ARTICLE{Tew04,
+ author = {V. K. Tewary},
+ title = {Green's function method for modeling surface acoustic wave dispersion
+ in anisotropic material systems and determination of material parameters},
+ journal = {Wave Motion},
+ year = {2004},
+ volume = {40},
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+}
+
+ at ARTICLE{TewFor96a,
+ author = {V. K. Tewary and C. M. Fortunko},
+ title = {Surface waves in three-dimensional half-space tetragonal solids},
+ journal = jasa,
+ year = {1996},
+ volume = {100},
+ pages = {86-88},
+ number = {1}
+}
+
+ at ARTICLE{TewFor96b,
+ author = {V. K. Tewary and C. M. Fortunko},
+ title = {Theory of elastic waves in three-dimensional anisotropic plates},
+ journal = jasa,
+ year = {1996},
+ volume = {100},
+ pages = {2964-2968},
+ number = {5}
+}
+
+ at ARTICLE{TewFor92,
+ author = {V. K. Tewary and C. M. Fortunko},
+ title = {A computationally efficient representation for propagation of elastic
+ waves in anisotropic solids},
+ journal = jasa,
+ year = {1992},
+ volume = {91},
+ pages = {1888-1896},
+ number = {4}
+}
+
+ at INPROCEEDINGS{ThSe09,
+ author = {Julien C. Thibault and Inanc Senocak},
+ title = {{CUDA} Implementation of a {N}avier-{S}tokes Solver on Multi-{GPU}
+ Desktop Platforms for Incompressible Flows},
+ booktitle = {Proceedings of the 47th AIAA Aerospace Sciences Meeting},
+ year = {2009},
+ pages = {1-15}
+}
+
+ at ARTICLE{Toetal00,
+ author = {C. Thomas and H. Igel and M. Weber and F Scherbaum},
+ title = {Acoustic simulation of {P}-wave propagation in a heterogeneous spherical
+ {E}arth: numerical method and application to precursor waves to {PKP}df},
+ journal = gji,
+ year = {2000},
+ volume = {141},
+ pages = {6441-6464}
+}
+
+ at ARTICLE{ThKe02,
+ author = {C. Thomas and J. M. Kendall},
+ title = {The lowermost mantle beneath northern {A}sia-{II}. {E}vidence for
+ lower-mantle anisotropy},
+ journal = gji,
+ year = {2002},
+ volume = {151},
+ pages = {296-308},
+ number = {1}
+}
+
+ at BOOK{ThWaMa85,
+ title = {Numerical Grid Generation - Foundations and Applications},
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+ address = {New York, USA}
+}
+
+ at PHDTHESIS{Tho94,
+ author = {L. L. Thompson},
+ title = {Design and analysis of space-time and {G}alerkin-{L}east-{S}quares
+ finite element methods for fluid-structure interactions in exterior
+ domains},
+ school = {Stanford University},
+ year = {1994},
+ address = {California}
+}
+
+ at ARTICLE{ThPi96a,
+ author = {L. L. Thompson and P. Pinsky},
+ title = {A space-time finite element method for structural acoustics in infinite
+ domains. Part 1: formulation, stability and convergence},
+ journal = cmame,
+ year = {1996},
+ volume = {132},
+ pages = {195-227}
+}
+
+ at ARTICLE{ThPi96b,
+ author = {L. L. Thompson and P. Pinsky},
+ title = {A space-time finite element method for structural acoustics in infinite
+ domains. Part 2: Exact time-dependent non-reflecting boundary conditions},
+ journal = cmame,
+ year = {1996},
+ volume = {132},
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+}
+
+ at ARTICLE{Tho86,
+ author = {L. Thomsen},
+ title = {Weak elastic anisotropy},
+ journal = geophysics,
+ year = {1986},
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+}
+
+ at ARTICLE{Thorne04,
+ author = {Thorne, M. S. and E. J. Garnero and S. P. Grand},
+ title = {Geographic correlation between hot spots and deep mantle lateral
+ shear-wave velocity gradients},
+ journal = pepi,
+ year = {2004},
+ volume = {146},
+ pages = {47--63}
+}
+
+ at ARTICLE{Thouvetal03,
+ author = {Fran\c{c}ois Thouvenot and Julien Fr\'echet and Liliane Jenatton
+ and Jean-Fran\c{c}ois Gamond},
+ title = {The {B}elledonne Border Fault: identification of an active seismic
+ strike-slip fault in the western {A}lps},
+ journal = gji,
+ year = {2003},
+ volume = {155},
+ pages = {174-192},
+ number = {1}
+}
+
+ at ARTICLE{Tin09,
+ author = {T.C.T. Ting},
+ title = {Explicit conditions for the existence of exceptional body waves and
+ subsonic waves in anisotropic elastic solids},
+ journal = {Wave Motion},
+ year = {2009},
+ volume = {46},
+ pages = {323-335}
+}
+
+ at ARTICLE{Tin02,
+ author = {T.C.T. Ting},
+ title = {Explicit secular equations for surface waves in monoclinic materials
+ with the symmetry plane $x1=0$, $x2=0$ or $x3=0$},
+ journal = {Proc. R. Soc. London Ser. A},
+ year = {2002},
+ volume = {458},
+ pages = {1017-1031}
+}
+
+ at INCOLLECTION{Tin04a,
+ author = {T. C. T. Ting},
+ title = {Explicit secular equations for surface waves in an anisotropic elastic
+ half-space from {R}ayleigh to today},
+ booktitle = {Surface waves in anisotropic and laminated bodies and defects detection},
+ publisher = {Kluwer Academic Publishers, Dordrecht, The Netherlands},
+ year = {2004},
+ editor = {Goldstein, R.V. and Maugin, G.A.},
+ pages = {95-116}
+}
+
+ at ARTICLE{Tin04b,
+ author = {T. C. T. Ting},
+ title = {The polarization vector and secular equation for surface waves in
+ anisotropic elastic half-space},
+ journal = {International Journal of Solids and Structures},
+ year = {2004},
+ volume = {41},
+ pages = {2065-2083}
+}
+
+ at BOOK{Tin96,
+ title = {Anisotropic elasticity: theory and applications},
+ publisher = {Oxford University Press, United Kingdom},
+ year = {1996},
+ author = {T. C. T. Ting}
+}
+
+ at ARTICLE{Tin92,
+ author = {T. C. T. Ting},
+ title = {The motion of one-component surface waves},
+ journal = {Journal of the Mechanics and Physics of Solids},
+ year = {1992},
+ volume = {40},
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+}
+
+ at ARTICLE{TinBar97,
+ author = {T. C. T. Ting and D. M. Barnett},
+ title = {Classifications of surface waves in anisotropic elastic materials},
+ journal = {Wave Motion},
+ year = {1997},
+ volume = {26},
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+}
+
+ at ARTICLE{To05,
+ author = {To, A. and B. Romanowicz and Y. Capdeville and N. Takeuchi},
+ title = {3{D} effects of sharp boundaries at the borders of the {A}frican
+ and {P}acific superplumes: {O}bservations and modeling},
+ journal = epsl,
+ year = {2005},
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+}
+
+ at ARTICLE{ToIrKa95,
+ author = {K. Toki and K. Irikura and T. Kagawa},
+ title = {Strong motion records in the source area of the {H}yogo-ken {N}anbu
+ earthquake, {J}anuary 17, 1995},
+ journal = {J. Nat. Disast. Sci.},
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+}
+
+ at PHDTHESIS{Tor95,
+ author = {Nathalie Tordjman},
+ title = {{\'E}l\'ements finis d'ordre \'elev\'e avec condensation de masse
+ pour l'\'equation des ondes ({H}igh-order finite elements with mass
+ lumping for the wave equation)},
+ school = {Universit\'e Paris {\sc IX} Dauphine},
+ year = {1995},
+ address = {Paris, France}
+}
+
+ at PHDTHESIS{jjt,
+ author = {J. J. Torrens},
+ title = {Interpolaci\'on de superficies param\'etricas con discontinuidades
+ mediante, elementos finitos, aplicaciones},
+ school = {Universidad de Zaragoza},
+ year = {1991},
+ address = {Zaragoza, Espa{\~{n}}a},
+ note = {186 p.}
+}
+
+ at ARTICLE{ToOh92,
+ author = {Takumi Toshinawa and Tatsuo Ohmachi},
+ title = {Love-wave propagation in a three-dimensional sedimentary basin},
+ journal = bssa,
+ year = {1992},
+ volume = {82},
+ pages = {1661-1677},
+ number = {4}
+}
+
+ at BOOK{treves80,
+ title = {Introduction to pseudodifferential and {F}ourier Integral operators},
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+ volume = {1},
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+}
+
+ at ARTICLE{Tri73,
+ author = {M. D. Trifunac},
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+ year = {1973},
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+}
+
+ at ARTICLE{Tri71,
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+}
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+ author = {J. Tromp},
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+ journal = {Nature},
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+
+ at INCOLLECTION{TrKo00,
+ author = {J. Tromp and D. Komatitsch},
+ title = {Spectral-element simulations of wave propagation in a laterally homogeneous
+ {E}arth model},
+ booktitle = {Problems in Geophysics for the New Millennium},
+ publisher = {INGV},
+ year = {2000},
+ editor = {E. Boschi and G. Ekstr\"{o}m and A. Morelli},
+ pages = {351-372},
+ address = {Roma, Italy}
+}
+
+ at ARTICLE{TrKoHjLiZhPeBoMcFrTrHu10,
+ author = {Tromp, Jeroen and Komatitsch, Dimitri and Hjoerleifsdottir, Vala
+ and Liu, Qinya and Zhu, Hejun and Peter, Daniel and Bozdag, Ebru
+ and McRitchie, Dennis and Friberg, Paul and Trabant, Chad and Hutko,
+ Alex},
+ title = {Near real-time simulations of global {CMT} earthquakes},
+ journal = gji,
+ year = {2010},
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+ number = {1},
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+}
+
+ at ARTICLE{TrKoLi08,
+ author = {Jeroen Tromp and Dimitri Komatitsch and Qinya Liu},
+ title = {Spectral-Element and Adjoint Methods in Seismology},
+ journal = {Communications in Computational Physics},
+ year = {2008},
+ volume = {3},
+ pages = {1-32},
+ number = {1}
+}
+
+ at ARTICLE{trompetal2010,
+ author = {Jeroen Tromp and Yang Luo and Shravan Hanasoge and Daniel Peter},
+ title = {Noise Cross-Correlation Sensitivity Kernels},
+ journal = gji,
+ year = {2010},
+ volume = {183},
+ pages = {791-819},
+ doi = {10.1111/j.1365-246X.2010.04721.x}
+}
+
+ at ARTICLE{TrMi99,
+ author = {J. Tromp and J. X. Mitrovica},
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+ journal = gji,
+ year = {1999},
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+}
+
+ at ARTICLE{TrTaLi05,
+ author = {Jeroen Tromp and Carl Tape and Qinya Liu},
+ title = {Seismic tomography, adjoint methods, time reversal and banana-doughnut
+ kernels},
+ journal = gji,
+ year = {2005},
+ volume = {160},
+ pages = {195-216},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2004.02453.x}
+}
+
+ at ARTICLE{TrRoFl02,
+ author = {A. Tryggvason and S. T. R\"ognvaldsson and O. G. Fl\'ovenz},
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+ year = {2002},
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+}
+
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+}
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+ author = {Seiji Tsuboi and Dimitri Komatitsch and Chen Ji and Jeroen Tromp},
+ title = {Broadband modeling of the 2002 {D}enali fault earthquake on the {E}arth
+ {S}imulator},
+ journal = pepi,
+ year = {2003},
+ volume = {139},
+ pages = {305-313},
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+}
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+ Time-Domain method},
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+ Prefecture, {J}apan, earthquake of 1984},
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+ map},
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+ author = {R. Vai and J. M. Castillo-Covarrubias and F. J. S\'anchez-Sesma and
+ D. Komatitsch and J. P. Vilotte},
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+}
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+ at INPROCEEDINGS{VaDeZh08,
+ author = {Valcarce, A. and De La Roche, G. and Jie Zhang},
+ title = {A {GPU} approach to {FDTD} for radio coverage prediction},
+ booktitle = {Proceedings of the 11th IEEE International Conference on Communication
+ Systems},
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+}
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+}
+
+ at PHDTHESIS{Val87,
+ author = {B. Valette},
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+ et g\'eophysiques ({S}pectrum of the free oscillations of the {E}arth:
+ mathematical and geophysical aspects)},
+ school = {Universit\'e Paris {\sc VI} Jussieu},
+ year = {1987},
+ address = {Paris},
+ note = {th\`ese d'\'etat}
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+ institution = {LGGE, IPSN/CNRS, Universit\'e Joseph Fourier},
+ year = {1999},
+ pages = {33}
+}
+
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+}
+
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+ author = {J. C. Veihl and R. Mittra},
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+}
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+}
+
+ at ARTICLE{ViBrRo98,
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+ at INCOLLECTION{ViKoMa84,
+ author = {L. Vinnik and G. L. Kosarev and L. I. Makeyeva},
+ title = {Lithospheric anisotropy as indicated by {SKS} and {SKKS} waves},
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+}
+
+ at ARTICLE{ZhCa96,
+ author = {L. Zhao and A. C. Cangellaris},
+ title = {{GT-PML}: generalized theory of {P}erfectly {M}atched {L}ayers and
+ its application to the reflectionless truncation of {F}inite-{D}ifference
+ {T}ime-{D}omain grids},
+ journal = {IEEE transactions on Microwave Theory and Techniques},
+ year = {1996},
+ volume = {44},
+ pages = {2555-2563},
+ number = {12},
+ doi = {10.1109/22.554601}
+}
+
+ at ARTICLE{zhaoetal2000,
+ author = {L. Zhao and T. H. Jordan and C. H. Chapman},
+ title = {Three-dimensional Fr\'echet differential kernels for seismic delay
+ times},
+ journal = gji,
+ year = {2000},
+ volume = {141},
+ pages = {558-576}
+}
+
+ at ARTICLE{zhu&kanamori2000,
+ author = {L. Zhu and H. Kanamori},
+ title = {Moho depth variation in southern {C}alifornia from teleseismic receiver
+ functions},
+ journal = jgr,
+ year = {2000},
+ volume = {105},
+ pages = {2969-2980}
+}
+
+ at ARTICLE{zhumcmechan91,
+ author = {X. Zhu and G. A. McMechan},
+ title = {Finite-difference modelling of the seismic response of fluid-saturated,
+ porous, elastic media using {B}iot theory},
+ journal = geophysics,
+ year = {1991},
+ volume = {56},
+ pages = {328-339}
+}
+
+ at BOOK{Zie77,
+ title = {The finite element method in engineering science},
+ publisher = {McGraw-Hill},
+ year = {1977},
+ author = {Olgierd Cecil Zienkiewicz},
+ address = {New York},
+ edition = {3rd}
+}
+
+ at ARTICLE{ZiBe78,
+ author = {O. C. Zienkiewicz and P. Bettess},
+ title = {Fluid-structure dynamic interaction and wave forces, an introduction
+ to numerical treatment},
+ journal = ijnme,
+ year = {1978},
+ volume = {13},
+ pages = {1-16}
+}
+
+ at BOOK{ZiTa89,
+ title = {The finite element method: v.2, solid and fluid mechanics},
+ publisher = {McGraw-Hill},
+ year = {1989},
+ author = {Olgierd Cecil Zienkiewicz and R. L. Taylor},
+ address = {New York},
+ edition = {4th}
+}
+
+ at ARTICLE{Zin00,
+ author = {David W. Zingg},
+ title = {Comparison of High-Accuracy Finite-Difference Methods for Linear
+ Wave Propagation},
+ journal = {SIAM Journal on Scientific Computing},
+ year = {2000},
+ volume = {22},
+ pages = {476-502},
+ number = {2},
+ doi = {10.1137/S1064827599350320}
+}
+
+ at ARTICLE{ZiLoJu96,
+ author = {David W. Zingg and Harvard Lomax and Henry Jurgens},
+ title = {High-Accuracy Finite-Difference Schemes for Linear Wave Propagation},
+ journal = {SIAM Journal on Scientific Computing},
+ year = {1996},
+ volume = {17},
+ pages = {328-346},
+ number = {2},
+ doi = {10.1137/S1064827594267173}
+}
+
+ at MISC{notedegreesfreedom,
+ note = {The cost of calculation is due to the fact that the mesh contains
+ 498 million degrees of freedom.}
+}
+
+ at MISC{notedownlaod,
+ note = {We encourage interested research groups to download the SEM software
+ package from the `Theoretical and Computational Seismology' webpage
+ of the Seismological Laboratory at Caltech (www.gps.caltech.edu/research/jtromp).}
+}
+
+ at MISC{notehonormesh,
+ note = {It is important to honor the major discontinuities in the velocity
+ model when creating a mesh of the structure, to avoid numerical diffraction
+ by a staircase discretization of the complex-shaped interfaces in
+ the case of a regular grid.}
+}
+
+ at MISC{notePMLnotused,
+ note = {More accurate absorbing boundary conditions such as the Perfectly
+ Matched Layer (PML)~\cite{CoTs01} could be used instead, but because
+ we use a large mesh, simpler paraxial conditions are sufficient.}
+}
+
+ at MISC{notesciencevsrho,
+ note = {Shear-wave velocity $V_s$ is defined by dividing $V_p$ by a coefficient
+ that varies linearly from 1.732 in the deepest part of the basin
+ (i.e., Poisson's coefficient of 0.25) to 2 in the shallow sediments
+ near the surface(i.e., Poisson's coefficient of 0.33). Based upon
+ well-log information, density is defined by $\rho = V_p/3 + 1280$,
+ imposing a minimum of 2000~kg.m$^{-3}$ and maximum of 3000~kg.m$^{-3}$.}
+}
+
+ at MISC{notesmallevents,
+ note = {The SEM is not limited to point sources: a finite size source can
+ be used by summing individual contributions from points located along
+ the fault plane. To obtain the source mechanism for this event we
+ performed a 3D centroid-moment tensor inversion based upon the basin
+ model and the SEM. The solution is in excellent agreement with first-motion
+ and surface-wave estimates.}
+}
+
+ at MISC{notestationcorrection,
+ note = {The shear-wave speed ($V_s$) model is based upon a simple scaling
+ relation to compressional-wave speed ($V_p)$~\cite{notesciencevsrho}.
+ Rather than trying to determine an optimal scaling relation, or an
+ independent shear-wave speed model, we choose to use such a simple
+ scaling, but allow for deficiencies in the $V_s$ model by introducing
+ a station correction. These corrections are generally small, typically
+ less than plus or minus one~second}
+}
+
Added: seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/compile_LaTeX_paper.sh
===================================================================
--- seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/compile_LaTeX_paper.sh (rev 0)
+++ seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/compile_LaTeX_paper.sh 2012-08-07 23:03:13 UTC (rev 20558)
@@ -0,0 +1,39 @@
+#!/bin/sh
+
+file=notes_about_CPML_for_SPECFEM3D
+
+# clean up
+/bin/rm -rf *.dvi > /dev/null
+/bin/rm -rf *.log > /dev/null
+/bin/rm -rf *.out > /dev/null
+/bin/rm -rf *.aux > /dev/null
+/bin/rm -rf *.toc > /dev/null
+/bin/rm -rf *.blg > /dev/null
+/bin/rm -rf *.bbl > /dev/null
+/bin/rm -rf *.lof > /dev/null
+/bin/rm -rf *.lot > /dev/null
+/bin/rm -rf *.plt > /dev/null
+/bin/rm -rf *.fff > /dev/null
+/bin/rm -rf *.ttt > /dev/null
+/bin/rm -rf *.tit > /dev/null
+/bin/rm -rf *.spl > /dev/null
+
+# latex the document
+pdflatex $file && bibtex $file && pdflatex $file && pdflatex $file && pdflatex $file && pdflatex $file
+
+# clean up again
+/bin/rm -rf *.dvi > /dev/null
+/bin/rm -rf *.log > /dev/null
+/bin/rm -rf *.out > /dev/null
+/bin/rm -rf *.aux > /dev/null
+/bin/rm -rf *.toc > /dev/null
+/bin/rm -rf *.blg > /dev/null
+/bin/rm -rf *.bbl > /dev/null
+/bin/rm -rf *.lof > /dev/null
+/bin/rm -rf *.lot > /dev/null
+/bin/rm -rf *.plt > /dev/null
+/bin/rm -rf *.fff > /dev/null
+/bin/rm -rf *.ttt > /dev/null
+/bin/rm -rf *.tit > /dev/null
+/bin/rm -rf *.spl > /dev/null
+
Property changes on: seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/compile_LaTeX_paper.sh
___________________________________________________________________
Name: svn:executable
+ *
Added: seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji.bst
===================================================================
--- seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji.bst (rev 0)
+++ seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji.bst 2012-08-07 23:03:13 UTC (rev 20558)
@@ -0,0 +1,1659 @@
+%%
+%% This is file `gji.bst',
+%% ----------------------------------------
+%% *** For Geophysical Journal International ***
+%% based on egs.bst
+ %-------------------------------------------------------------------
+ % The original source file contains the following version information:
+ % \ProvidesFile{merlin.mbs}[1996/09/18 3.81 (PWD)]
+ %
+ % NOTICE:
+ % This file may be used for non-profit purposes.
+ % It may not be distributed in exchange for money,
+ % other than distribution costs.
+ %
+ % The author provides it `as is' and does not guarantee it in any way.
+ %
+ % Copyright (C) 1994, 1995, 1996 Patrick W. Daly
+ % modified by B.L.N. Kennett, 1998
+ %-------------------------------------------------------------------
+ % For use with BibTeX version 0.99a or later
+ %-------------------------------------------------------------------
+ % This bibliography style file is intended for texts in ENGLISH
+ % This is an author-year citation style bibliography. As such, it is
+ % non-standard LaTeX, and requires a special package file to function properly.
+ % Such a package is natbib.sty by Patrick W. Daly
+ % The form of the \bibitem entries is
+ % \bibitem[Jones et al.(1990)]{key}...
+ % \bibitem[Jones et al.(1990)Jones, Baker, and Smith]{key}...
+ % The essential feature is that the label (the part in brackets) consists
+ % of the author names, as they should appear in the citation, with the year
+ % in parentheses following. There must be no space before the opening
+ % parenthesis!
+ % With natbib v5.3, a full list of authors may also follow the year.
+ % In natbib.sty, it is possible to define the type of enclosures that is
+ % really wanted (brackets or parentheses), but in either case, there must
+ % be parentheses in the label.
+ % The \cite command functions as follows:
+ % \cite{key} ==>> Jones et al. (1990)
+ % \cite[]{key} ==>> (Jones et al., 1990)
+ % \cite[chap. 2]{key} ==>> (Jones et al., 1990, chap. 2)
+ % \cite[e.g.][]{key} ==>> (e.g. Jones et al., 1990)
+ % \cite[e.g.][p. 32]{key} ==>> (e.g. Jones et al., p. 32)
+ % \citeauthor{key} Jones et al.
+ % \citefullauthor{key} Jones, Baker, and Smith
+ % \citeyear{key} 1990
+ %---------------------------------------------------------------------
+
+ENTRY
+ { address
+ author
+ booktitle
+ chapter
+ edition
+ editor
+ howpublished
+ institution
+ journal
+ key
+ month
+ note
+ number
+ organization
+ pages
+ publisher
+ school
+ series
+ title
+ type
+ volume
+ year
+ }
+ {}
+ { label extra.label sort.label short.list }
+
+INTEGERS { output.state before.all mid.sentence after.sentence after.block }
+
+FUNCTION {init.state.consts}
+{ #0 'before.all :=
+ #1 'mid.sentence :=
+ #2 'after.sentence :=
+ #3 'after.block :=
+}
+
+STRINGS { s t }
+
+FUNCTION {output.nonnull}
+{ 's :=
+ output.state mid.sentence =
+ { ", " * write$ }
+ { output.state after.block =
+ { add.period$ write$
+ newline$
+ "\newblock " write$
+ }
+ { output.state before.all =
+ 'write$
+ { add.period$ " " * write$ }
+ if$
+ }
+ if$
+ mid.sentence 'output.state :=
+ }
+ if$
+ s
+}
+
+FUNCTION {output}
+{ duplicate$ empty$
+ 'pop$
+ 'output.nonnull
+ if$
+}
+
+FUNCTION {output.check}
+{ 't :=
+ duplicate$ empty$
+ { pop$ "empty " t * " in " * cite$ * warning$ }
+ 'output.nonnull
+ if$
+}
+
+FUNCTION {fin.entry}
+{ add.period$
+ write$
+ newline$
+}
+
+FUNCTION {fin.year}
+{ add.period$
+ write$
+ newline$
+}
+
+FUNCTION {new.block}
+{ output.state before.all =
+ 'skip$
+ { after.block 'output.state := }
+ if$
+}
+
+FUNCTION {new.sentence}
+{ output.state after.block =
+ 'skip$
+ { output.state before.all =
+ 'skip$
+ { after.sentence 'output.state := }
+ if$
+ }
+ if$
+}
+
+FUNCTION {add.blank}
+{ " " * before.all 'output.state :=
+}
+
+FUNCTION {date.block}
+{
+ skip$
+}
+
+FUNCTION {not}
+{ { #0 }
+ { #1 }
+ if$
+}
+
+FUNCTION {and}
+{ 'skip$
+ { pop$ #0 }
+ if$
+}
+
+FUNCTION {or}
+{ { pop$ #1 }
+ 'skip$
+ if$
+}
+
+FUNCTION {non.stop}
+{ duplicate$
+ "}" * add.period$
+ #-1 #1 substring$ "." =
+}
+
+FUNCTION {new.block.checkb}
+{ empty$
+ swap$ empty$
+ and
+ 'skip$
+ 'new.block
+ if$
+}
+
+FUNCTION {field.or.null}
+{ duplicate$ empty$
+ { pop$ "" }
+ 'skip$
+ if$
+}
+
+FUNCTION {emphasize}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "{\em " swap$ * "\/}" * }
+ if$
+}
+
+FUNCTION {italics}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "{\it " swap$ * "\/}" * }
+ if$
+}
+
+FUNCTION {bold}
+{ duplicate$ empty$
+ { pop$ "" }
+ { "{\bf " swap$ * "}" * }
+ if$
+}
+
+FUNCTION {capitalize}
+{ "u" change.case$ "t" change.case$ }
+
+FUNCTION {space.word}
+{ " " swap$ * " " * }
+
+ % Here are the language-specific definitions for explicit words.
+ % Each function has a name bbl.xxx where xxx is the English word.
+ % The language selected here is ENGLISH
+FUNCTION {bbl.and}
+{ "\&"}
+
+FUNCTION {bbl.editors}
+{ "eds." }
+
+FUNCTION {bbl.editor}
+{ "ed." }
+
+FUNCTION {bbl.edby}
+{ "edited by" }
+
+FUNCTION {bbl.edition}
+{ "edn." }
+
+FUNCTION {bbl.volume}
+{ "vol." }
+
+FUNCTION {bbl.of}
+{ "of" }
+
+FUNCTION {bbl.number}
+{ "no." }
+
+FUNCTION {bbl.nr}
+{ "no." }
+
+FUNCTION {bbl.in}
+{ "in" }
+
+FUNCTION {bbl.pages}
+{ "pp." }
+
+FUNCTION {bbl.page}
+{ "p." }
+
+FUNCTION {bbl.chapter}
+{ "chap." }
+
+FUNCTION {bbl.techrep}
+{ "Tech. Rep." }
+
+FUNCTION {bbl.mthesis}
+{ "Master's thesis" }
+
+FUNCTION {bbl.phdthesis}
+{ "Ph.D. thesis" }
+
+FUNCTION {bbl.first}
+{ "1st" }
+
+FUNCTION {bbl.second}
+{ "2nd" }
+
+FUNCTION {bbl.third}
+{ "3rd" }
+
+FUNCTION {bbl.fourth}
+{ "4th" }
+
+FUNCTION {bbl.fifth}
+{ "5th" }
+
+FUNCTION {bbl.st}
+{ "st" }
+
+FUNCTION {bbl.nd}
+{ "nd" }
+
+FUNCTION {bbl.rd}
+{ "rd" }
+
+FUNCTION {bbl.th}
+{ "th" }
+
+MACRO {jan} {"Jan."}
+
+MACRO {feb} {"Feb."}
+
+MACRO {mar} {"Mar."}
+
+MACRO {apr} {"Apr."}
+
+MACRO {may} {"May"}
+
+MACRO {jun} {"Jun."}
+
+MACRO {jul} {"Jul."}
+
+MACRO {aug} {"Aug."}
+
+MACRO {sep} {"Sep."}
+
+MACRO {oct} {"Oct."}
+
+MACRO {nov} {"Nov."}
+
+MACRO {dec} {"Dec."}
+
+FUNCTION {eng.ord}
+{ duplicate$ "1" swap$ *
+ #-2 #1 substring$ "1" =
+ { bbl.th * }
+ { duplicate$ #-1 #1 substring$
+ duplicate$ "1" =
+ { pop$ bbl.st * }
+ { duplicate$ "2" =
+ { pop$ bbl.nd * }
+ { "3" =
+ { bbl.rd * }
+ { bbl.th * }
+ if$
+ }
+ if$
+ }
+ if$
+ }
+ if$
+}
+
+ %-------------------------------------------------------------------
+ % The original source file contains the following version information:
+ % \ProvidesFile{physjour.mbs}[1996/06/26 2.0 (PWD)]
+ % Copyright (C) 1994--96 Patrick W. Daly
+ %-------------------------------------------------------------------
+MACRO {aph} {"Acta Phys."}
+MACRO {advp} {"Adv. Phys."}
+MACRO {ajp} {"Amer. J. Phys."}
+MACRO {ajm} {"Amer. J. Math."}
+MACRO {amsci} {"Amer. Sci."}
+MACRO {anofd} {"Ann. Fluid Dyn."}
+MACRO {am} {"Ann. Math."}
+MACRO {ap} {"Ann. Phys. (NY)"}
+MACRO {adp} {"Ann. Phys. (Leipzig)"}
+MACRO {ao} {"Appl. Opt."}
+MACRO {apl} {"Appl. Phys. Lett."}
+MACRO {app} {"Astroparticle Phys."}
+MACRO {apj} {"Astrophys. J."}
+MACRO {baps} {"Bull. Amer. Phys. Soc."}
+MACRO {cmp} {"Comm. Math. Phys."}
+MACRO {cpam} {"Commun. Pure Appl. Math."}
+MACRO {cppcf} {"Comm. Plasma Phys. \& Controlled Fusion"}
+MACRO {cpc} {"Comp. Phys. Comm."}
+MACRO {cqg} {"Class. Quant. Grav."}
+MACRO {cra} {"C. R. Acad. Sci. A"}
+MACRO {fed} {"Fusion Eng. \& Design"}
+MACRO {ft} {"Fusion Tech."}
+MACRO {grg} {"Gen. Relativ. Gravit."}
+MACRO {ieeens} {"IEEE Trans. Nucl. Sci."}
+MACRO {ieeeps} {"IEEE Trans. Plasma Sci."}
+MACRO {ijimw} {"Interntl. J. Infrared \& Millimeter Waves"}
+MACRO {ip} {"Infrared Phys."}
+MACRO {irp} {"Infrared Phys."}
+MACRO {jap} {"J. Appl. Phys."}
+MACRO {jasa} {"J. Acoust. Soc. America"}
+MACRO {jcp} {"J. Comp. Phys."}
+MACRO {jetp} {"Sov. Phys.--JETP"}
+MACRO {jfe} {"J. Fusion Energy"}
+MACRO {jfm} {"J. Fluid Mech."}
+MACRO {jmp} {"J. Math. Phys."}
+MACRO {jne} {"J. Nucl. Energy"}
+MACRO {jnec} {"J. Nucl. Energy, C: Plasma Phys., Accelerators, Thermonucl. Res."}
+MACRO {jnm} {"J. Nucl. Mat."}
+MACRO {jpc} {"J. Phys. Chem."}
+MACRO {jpp} {"J. Plasma Phys."}
+MACRO {jpsj} {"J. Phys. Soc. Japan"}
+MACRO {jsi} {"J. Sci. Instrum."}
+MACRO {jvst} {"J. Vac. Sci. \& Tech."}
+MACRO {nat} {"Nature"}
+MACRO {nature} {"Nature"}
+MACRO {nedf} {"Nucl. Eng. \& Design/Fusion"}
+MACRO {nf} {"Nucl. Fusion"}
+MACRO {nim} {"Nucl. Inst. \& Meth."}
+MACRO {nimpr} {"Nucl. Inst. \& Meth. in Phys. Res."}
+MACRO {np} {"Nucl. Phys."}
+MACRO {npb} {"Nucl. Phys. B"}
+MACRO {nt/f} {"Nucl. Tech./Fusion"}
+MACRO {inc} {"Nouvo Cimento"}
+MACRO {nc} {"Nouvo Cimento"}
+MACRO {pf} {"Phys. Fluids"}
+MACRO {pfa} {"Phys. Fluids A: Fluid Dyn."}
+MACRO {pfb} {"Phys. Fluids B: Plasma Phys."}
+MACRO {pl} {"Phys. Lett."}
+MACRO {pla} {"Phys. Lett. A"}
+MACRO {plb} {"Phys. Lett. B"}
+MACRO {prep} {"Phys. Rep."}
+MACRO {pnas} {"Proc. Nat. Acad. Sci. USA"}
+MACRO {pp} {"Plasma Phys."}
+MACRO {ppcf} {"Plasma Phys. \& Controlled Fusion"}
+MACRO {phitrsl} {"Philos. Trans. Roy. Soc. London"}
+MACRO {prl} {"Phys. Rev. Lett."}
+MACRO {pr} {"Phys. Rev."}
+MACRO {physrev} {"Phys. Rev."}
+MACRO {pra} {"Phys. Rev. A"}
+MACRO {prb} {"Phys. Rev. B"}
+MACRO {prc} {"Phys. Rev. C"}
+MACRO {prd} {"Phys. Rev. D"}
+MACRO {pre} {"Phys. Rev. E"}
+MACRO {ps} {"Phys. Scripta"}
+MACRO {procrsl} {"Proc. Roy. Soc. London"}
+MACRO {rmp} {"Rev. Mod. Phys."}
+MACRO {rsi} {"Rev. Sci. Inst."}
+MACRO {science} {"Science"}
+MACRO {sciam} {"Sci. Am."}
+MACRO {sam} {"Stud. Appl. Math."}
+MACRO {sjpp} {"Sov. J. Plasma Phys."}
+MACRO {spd} {"Sov. Phys.--Doklady"}
+MACRO {sptp} {"Sov. Phys.--Tech. Phys."}
+MACRO {spu} {"Sov. Phys.--Uspeki"}
+ % End of journal definition file
+
+ %-------------------------------------------------------------------
+ % The original source file contains the following version information:
+ % \ProvidesFile{geojour.mbs}[1996/06/26 2.0 (PWD)]
+ % Copyright (C) 1994--96 Patrick W. Daly
+ %-------------------------------------------------------------------
+MACRO {aisr} {"Adv. Space Res."}
+MACRO {ag} {"Ann. Geophys."}
+MACRO {anigeo} {"Ann. Geofis."}
+MACRO {angl} {"Ann. Glaciol."}
+MACRO {andmet} {"Ann. d. Meteor."}
+MACRO {andgeo} {"Ann. d. Geophys."}
+MACRO {andphy} {"Ann. d. Phys."}
+MACRO {afmgb} {"Arch. Meteor. Geophys. Bioklimatol."}
+MACRO {atph} {"Atm\'osphera"}
+MACRO {aao} {"Atmos.-Ocean"}
+MACRO {atenv} {"Atmos. Environ."}
+MACRO {aujag} {"Aust. J. Agric. Res."}
+MACRO {aumet} {"Aust. Meteor. Mag."}
+MACRO {blmet} {"Bound.-Layer Meteor."}
+MACRO {bams} {"Bull. Amer. Meteor. Soc."}
+MACRO {cch} {"Clim. Change"}
+MACRO {cdyn} {"Climate Dyn."}
+MACRO {cbul} {"Climatol. Bull."}
+MACRO {cap} {"Contrib. Atmos. Phys."}
+MACRO {dsr} {"Deep-Sea Res."}
+MACRO {dhz} {"Dtsch. Hydrogr. Z."}
+MACRO {dao} {"Dyn. Atmos. Oceans"}
+MACRO {eco} {"Ecology"}
+MACRO {envres} {"Environ. Res."}
+MACRO {envst} {"Environ. Sci. Technol."}
+MACRO {ecms} {"Estuarine Coastal Mar. Sci."}
+MACRO {geoint} {"Geofis. Int."}
+MACRO {geopub} {"Geofys. Publ."}
+MACRO {geogeo} {"Geol. Geofiz."}
+MACRO {gafd} {"Geophys. Astrophys. Fluid Dyn."}
+MACRO {gfd} {"Geophys. Fluid Dyn."}
+MACRO {geomag} {"Geophys. Mag."}
+MACRO {georl} {"Geophys. Res. Letters"}
+MACRO {grl} {"Geophys. Res. Letters"}
+MACRO {ga} {"Geophysica"}
+MACRO {gs} {"Geophysics"}
+MACRO {ieeetap} {"IEEE Trans. Antennas Propag."}
+MACRO {ijawp} {"Int. J. Air Water Pollut."}
+MACRO {ijc} {"Int. J. Climatol."}
+MACRO {ijrs} {"Int. J. Remote Sensing"}
+MACRO {jam} {"J. Appl. Meteor."}
+MACRO {jaot} {"J. Atmos. Ocean. Technol."}
+MACRO {jatp} {"J. Atmos. Terr. Phys."}
+MACRO {jce} {"J. Climate"}
+MACRO {jcam} {"J. Climate Appl. Meteor."}
+MACRO {jcm} {"J. Climate Meteor."}
+MACRO {jcy} {"J. Climatol."}
+MACRO {jgr} {"J. Geophys. Res."}
+MACRO {jga} {"J. Glaciol."}
+MACRO {jh} {"J. Hydrol."}
+MACRO {jmr} {"J. Mar. Res."}
+MACRO {jmrj} {"J. Meteor. Res. Japan"}
+MACRO {jm} {"J. Meteor."}
+MACRO {jpo} {"J. Phys. Oceanogr."}
+MACRO {jra} {"J. Rech. Atmos."}
+MACRO {jaes} {"J. Aeronaut. Sci."}
+MACRO {japca} {"J. Air Pollut. Control Assoc."}
+MACRO {jas} {"J. Atmos. Sci."}
+MACRO {jmts} {"J. Mar. Technol. Soc."}
+MACRO {jmsj} {"J. Meteor. Soc. Japan"}
+MACRO {josj} {"J. Oceanogr. Soc. Japan"}
+MACRO {jwm} {"J. Wea. Mod."}
+MACRO {lao} {"Limnol. Oceanogr."}
+MACRO {mwl} {"Mar. Wea. Log"}
+MACRO {mau} {"Mausam"}
+MACRO {meteor} {"``Meteor'' Forschungsergeb."}
+MACRO {map} {"Met. Atmos. Phys."}
+MACRO {metmag} {"Meteor. Mag."}
+MACRO {metmon} {"Meteor. Monogr."}
+MACRO {metrun} {"Meteor. Rundsch."}
+MACRO {metzeit} {"Meteor. Z."}
+MACRO {metgid} {"Meteor. Gidrol."}
+MACRO {mwr} {"Mon. Wea. Rev."}
+MACRO {nwd} {"Natl. Wea. Dig."}
+MACRO {nzjmfr} {"N. Z. J. Mar. Freshwater Res."}
+MACRO {npg} {"Nonlin. Proc. Geophys."}
+MACRO {om} {"Oceanogr. Meteor."}
+MACRO {ocac} {"Oceanol. Acta"}
+MACRO {oceanus} {"Oceanus"}
+MACRO {paleoc} {"Paleoceanography"}
+MACRO {pmg} {"Pap. Meteor. Geophys."}
+MACRO {ppom} {"Pap. Phys. Oceanogr. Meteor."}
+MACRO {physzeit} {"Phys. Z."}
+MACRO {pps} {"Planet. Space Sci."}
+MACRO {pag} {"Pure Appl. Geophys."}
+MACRO {qjrms} {"Quart. J. Roy. Meteor. Soc."}
+MACRO {quatres} {"Quat. Res."}
+MACRO {rsci} {"Radio Sci."}
+MACRO {rse} {"Remote Sens. Environ."}
+MACRO {rgeo} {"Rev. Geophys."}
+MACRO {rgsp} {"Rev. Geophys. Space Phys."}
+MACRO {rdgeo} {"Rev. Geofis."}
+MACRO {revmeta} {"Rev. Meteor."}
+MACRO {ssr} {"Space Sci. Rev."}
+MACRO {tellus} {"Tellus"}
+MACRO {tac} {"Theor. Appl. Climatol."}
+MACRO {tagu} {"Trans. Am. Geophys. Union (EOS)"}
+MACRO {wrr} {"Water Resour. Res."}
+MACRO {weather} {"Weather"}
+MACRO {wafc} {"Wea. Forecasting"}
+MACRO {ww} {"Weatherwise"}
+MACRO {wmob} {"WMO Bull."}
+MACRO {zeitmet} {"Z. Meteor."}
+ % End of journal definition file
+
+MACRO {acmcs} {"ACM Comput. Surv."}
+
+MACRO {acta} {"Acta Inf."}
+
+MACRO {cacm} {"Commun. ACM"}
+
+MACRO {ibmjrd} {"IBM J. Res. Dev."}
+
+MACRO {ibmsj} {"IBM Syst.~J."}
+
+MACRO {ieeese} {"IEEE Trans. Softw. Eng."}
+
+MACRO {ieeetc} {"IEEE Trans. Comput."}
+
+MACRO {ieeetcad}
+ {"IEEE Trans. Comput.-Aided Design Integrated Circuits"}
+
+MACRO {ipl} {"Inf. Process. Lett."}
+
+MACRO {jacm} {"J.~ACM"}
+
+MACRO {jcss} {"J.~Comput. Syst. Sci."}
+
+MACRO {scp} {"Sci. Comput. Programming"}
+
+MACRO {sicomp} {"SIAM J. Comput."}
+
+MACRO {tocs} {"ACM Trans. Comput. Syst."}
+
+MACRO {tods} {"ACM Trans. Database Syst."}
+
+MACRO {tog} {"ACM Trans. Gr."}
+
+MACRO {toms} {"ACM Trans. Math. Softw."}
+
+MACRO {toois} {"ACM Trans. Office Inf. Syst."}
+
+MACRO {toplas} {"ACM Trans. Prog. Lang. Syst."}
+
+MACRO {tcs} {"Theoretical Comput. Sci."}
+
+INTEGERS { nameptr namesleft numnames }
+
+FUNCTION {format.names}
+{ 's :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ "{vv~}{ll}{, jj}{, f.}" format.name$ 't :=
+ nameptr #1 >
+ {
+ namesleft #1 >
+ { ", " * t * }
+ {
+ numnames #2 >
+ { "," * }
+ 'skip$
+ if$
+ t "others" =
+ { " et~al." * }
+ { bbl.and space.word * t * }
+ if$
+ }
+ if$
+ }
+ 't
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+}
+
+FUNCTION {format.names.ed}
+{ 's :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ "{f.~}{vv~}{ll}{, jj}"
+ format.name$ 't :=
+ nameptr #1 >
+ {
+ namesleft #1 >
+ { ", " * t * }
+ {
+ numnames #2 >
+ { "," * }
+ 'skip$
+ if$
+ t "others" =
+ { " et~al." * }
+ { bbl.and space.word * t * }
+ if$
+ }
+ if$
+ }
+ 't
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+}
+
+FUNCTION {format.key}
+{ empty$
+ { key field.or.null }
+ { "" }
+ if$
+}
+
+FUNCTION {format.authors}
+{ author empty$
+ { "" }
+ {
+ author format.names
+ }
+ if$
+}
+
+FUNCTION {format.editors}
+{ editor empty$
+ { "" }
+ {
+ editor format.names
+ editor num.names$ #1 >
+ { ", " * bbl.editors * }
+ { ", " * bbl.editor * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.in.editors}
+{ editor empty$
+ { "" }
+ { editor format.names.ed
+ }
+ if$
+}
+
+FUNCTION {format.title}
+{ title empty$
+ { "" }
+ { title "t" change.case$
+ }
+ if$
+}
+
+FUNCTION {format.full.names}
+{'s :=
+ #1 'nameptr :=
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ "{vv~}{ll}" format.name$ 't :=
+ nameptr #1 >
+ {
+ namesleft #1 >
+ { ", " * t * }
+ {
+ numnames #2 >
+ { "," * }
+ 'skip$
+ if$
+ t "others" =
+ { " et~al." * }
+ { bbl.and space.word * t * }
+ if$
+ }
+ if$
+ }
+ 't
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+}
+
+FUNCTION {author.editor.key.full}
+{ author empty$
+ { editor empty$
+ { key empty$
+ { cite$ #1 #3 substring$ }
+ 'key
+ if$
+ }
+ { editor format.full.names }
+ if$
+ }
+ { author format.full.names }
+ if$
+}
+
+FUNCTION {author.key.full}
+{ author empty$
+ { key empty$
+ { cite$ #1 #3 substring$ }
+ 'key
+ if$
+ }
+ { author format.full.names }
+ if$
+}
+
+FUNCTION {editor.key.full}
+{ editor empty$
+ { key empty$
+ { cite$ #1 #3 substring$ }
+ 'key
+ if$
+ }
+ { editor format.full.names }
+ if$
+}
+
+FUNCTION {make.full.names}
+{ type$ "book" =
+ type$ "inbook" =
+ or
+ 'author.editor.key.full
+ { type$ "proceedings" =
+ 'editor.key.full
+ 'author.key.full
+ if$
+ }
+ if$
+}
+
+FUNCTION {output.bibitem}
+{ newline$
+ "\bibitem[" write$
+ label write$
+ ")" make.full.names duplicate$ short.list =
+ { pop$ }
+ { * }
+ if$
+ "]{" * write$
+ cite$ write$
+ "}" write$
+ newline$
+ ""
+ before.all 'output.state :=
+}
+
+FUNCTION {n.dashify}
+{ 't :=
+ ""
+ { t empty$ not }
+ { t #1 #1 substring$ "-" =
+ { t #1 #2 substring$ "--" = not
+ { "--" *
+ t #2 global.max$ substring$ 't :=
+ }
+ { { t #1 #1 substring$ "-" = }
+ { "-" *
+ t #2 global.max$ substring$ 't :=
+ }
+ while$
+ }
+ if$
+ }
+ { t #1 #1 substring$ *
+ t #2 global.max$ substring$ 't :=
+ }
+ if$
+ }
+ while$
+}
+
+FUNCTION {word.in}
+{ bbl.in
+ " " * }
+
+FUNCTION {format.date}
+{ year duplicate$ empty$
+ { "empty year in " cite$ * "; set to ????" * warning$
+ pop$ "????" }
+ 'skip$
+ if$
+}
+
+FUNCTION {format.btitle}
+{ title italics
+}
+
+FUNCTION {tie.or.space.connect}
+{ duplicate$ text.length$ #3 <
+ { "~" }
+ { " " }
+ if$
+ swap$ * *
+}
+
+FUNCTION {either.or.check}
+{ empty$
+ 'pop$
+ { "can't use both " swap$ * " fields in " * cite$ * warning$ }
+ if$
+}
+
+FUNCTION {format.bvolume}
+{ volume empty$
+ { "" }
+ { bbl.volume volume tie.or.space.connect
+ series empty$
+ 'skip$
+ { bbl.of space.word * series bold * }
+ if$
+ "volume and number" number either.or.check
+ }
+ if$
+}
+
+FUNCTION {format.number.series}
+{ volume empty$
+ { number empty$
+ { series field.or.null }
+ { output.state mid.sentence =
+ { bbl.number }
+ { bbl.number capitalize }
+ if$
+ number tie.or.space.connect
+ series empty$
+ { "there's a number but no series in " cite$ * warning$ }
+ { bbl.in space.word * series * }
+ if$
+ }
+ if$
+ }
+ { "" }
+ if$
+}
+
+FUNCTION {is.num}
+{ chr.to.int$
+ duplicate$ "0" chr.to.int$ < not
+ swap$ "9" chr.to.int$ > not and
+}
+
+FUNCTION {extract.num}
+{ duplicate$ 't :=
+ "" 's :=
+ { t empty$ not }
+ { t #1 #1 substring$
+ t #2 global.max$ substring$ 't :=
+ duplicate$ is.num
+ { s swap$ * 's := }
+ { pop$ "" 't := }
+ if$
+ }
+ while$
+ s empty$
+ 'skip$
+ { pop$ s }
+ if$
+}
+
+FUNCTION {convert.edition}
+{ edition extract.num "l" change.case$ 's :=
+ s "first" = s "1" = or
+ { bbl.first 't := }
+ { s "second" = s "2" = or
+ { bbl.second 't := }
+ { s "third" = s "3" = or
+ { bbl.third 't := }
+ { s "fourth" = s "4" = or
+ { bbl.fourth 't := }
+ { s "fifth" = s "5" = or
+ { bbl.fifth 't := }
+ { s #1 #1 substring$ is.num
+ { s eng.ord 't := }
+ { edition 't := }
+ if$
+ }
+ if$
+ }
+ if$
+ }
+ if$
+ }
+ if$
+ }
+ if$
+ t
+}
+
+FUNCTION {format.edition}
+{ edition empty$
+ { "" }
+ { output.state mid.sentence =
+ { convert.edition "l" change.case$ " " * bbl.edition * }
+ { convert.edition "t" change.case$ " " * bbl.edition * }
+ if$
+ }
+ if$
+}
+
+INTEGERS { multiresult }
+
+FUNCTION {multi.page.check}
+{ 't :=
+ #0 'multiresult :=
+ { multiresult not
+ t empty$ not
+ and
+ }
+ { t #1 #1 substring$
+ duplicate$ "-" =
+ swap$ duplicate$ "," =
+ swap$ "+" =
+ or or
+ { #1 'multiresult := }
+ { t #2 global.max$ substring$ 't := }
+ if$
+ }
+ while$
+ multiresult
+}
+
+FUNCTION {format.pages}
+{ pages empty$
+ { "" }
+ { pages multi.page.check
+ { bbl.pages pages n.dashify tie.or.space.connect }
+ { bbl.page pages tie.or.space.connect }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.vol.num.pages}
+{ volume field.or.null
+% emphasize
+ bold
+ number empty$
+ 'skip$
+ {
+ "(" number * ")" * *
+ volume empty$
+ { "there's a number but no volume in " cite$ * warning$ }
+ 'skip$
+ if$
+ }
+ if$
+ pages empty$
+ 'skip$
+ { duplicate$ empty$
+ { pop$ format.pages }
+ { ", " * pages n.dashify * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.chapter.pages}
+{ chapter empty$
+ 'format.pages
+ { type empty$
+ { bbl.chapter }
+ { type "l" change.case$ }
+ if$
+ chapter tie.or.space.connect
+ pages empty$
+ 'skip$
+ { ", " * format.pages * }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.in.ed.booktitle}
+{ booktitle empty$
+ { "" }
+ { editor empty$
+ { word.in booktitle emphasize * }
+ { word.in booktitle emphasize *
+ ", " *
+ bbl.edby
+ *
+ " " *
+ format.in.editors *
+ }
+ if$
+ }
+ if$
+}
+
+FUNCTION {format.thesis.type}
+{ type empty$
+ 'skip$
+ { pop$
+ type "t" change.case$
+ }
+ if$
+}
+
+FUNCTION {format.tr.number}
+{ type empty$
+ { bbl.techrep }
+ 'type
+ if$
+ number empty$
+ { "t" change.case$ }
+ { number tie.or.space.connect }
+ if$
+}
+
+FUNCTION {format.article.crossref}
+{
+ word.in
+ " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.book.crossref}
+{ volume empty$
+ { "empty volume in " cite$ * "'s crossref of " * crossref * warning$
+ word.in
+ }
+ { bbl.volume volume tie.or.space.connect
+ bbl.of space.word *
+ }
+ if$
+ " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.incoll.inproc.crossref}
+{
+ word.in
+ " \cite{" * crossref * "}" *
+}
+
+FUNCTION {format.publisher}
+{ publisher empty$
+ { "empty publisher in " cite$ * warning$ }
+ 'skip$
+ if$
+ ""
+ address empty$ publisher empty$ and
+ 'skip$
+ {
+ publisher empty$
+ { address empty$
+ 'skip$
+ { address * }
+ if$
+ }
+ { publisher *
+ address empty$
+ 'skip$
+ { ", " * address * }
+ if$
+ }
+ if$
+ }
+ if$
+ output
+}
+
+FUNCTION {article}
+{ output.bibitem
+ format.authors "author" output.check
+ author format.key output
+ format.date "year" output.check
+% fin.year
+ format.title "title" output.check
+ crossref missing$
+ { journal
+ italics
+ "journal" output.check
+ format.vol.num.pages output
+ }
+ { format.article.crossref output.nonnull
+ format.pages output
+ }
+ if$
+ note output
+ fin.entry
+}
+
+FUNCTION {book}
+{ output.bibitem
+ author empty$
+ { format.editors "author and editor" output.check
+ editor format.key output
+ }
+ { format.authors output.nonnull
+ crossref missing$
+ { "author and editor" editor either.or.check }
+ 'skip$
+ if$
+ }
+ if$
+ format.date "year" output.check
+% fin.year
+ format.btitle "title" output.check
+ crossref missing$
+ { format.bvolume output
+ format.number.series output
+ format.publisher
+ }
+ {
+ format.book.crossref output.nonnull
+ }
+ if$
+ format.edition output
+ note output
+ fin.entry
+}
+
+FUNCTION {booklet}
+{ output.bibitem
+ format.authors output
+ author format.key output
+ format.date "year" output.check
+ format.title "title" output.check
+ howpublished output
+ address output
+ note output
+ fin.entry
+}
+
+FUNCTION {inbook}
+{ output.bibitem
+ author empty$
+ { format.editors "author and editor" output.check
+ editor format.key output
+ }
+ { format.authors output.nonnull
+ crossref missing$
+ { "author and editor" editor either.or.check }
+ 'skip$
+ if$
+ }
+ if$
+ format.date "year" output.check
+ format.btitle "title" output.check
+ crossref missing$
+ {
+ format.bvolume output
+ format.chapter.pages "chapter and pages" output.check
+ format.number.series output
+ format.publisher
+ }
+ {
+ format.chapter.pages "chapter and pages" output.check
+ format.book.crossref output.nonnull
+ }
+ if$
+ format.edition output
+ note output
+ fin.entry
+}
+
+FUNCTION {incollection}
+{ output.bibitem
+ format.authors "author" output.check
+ author format.key output
+ format.date "year" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.in.ed.booktitle "booktitle" output.check
+ format.bvolume output
+ format.number.series output
+ format.chapter.pages output
+ format.publisher
+ format.edition output
+ }
+ { format.incoll.inproc.crossref output.nonnull
+ format.chapter.pages output
+ }
+ if$
+ note output
+ fin.entry
+}
+
+FUNCTION {inproceedings}
+{ output.bibitem
+ format.authors "author" output.check
+ author format.key output
+ format.date "year" output.check
+ format.title "title" output.check
+ crossref missing$
+ { format.in.ed.booktitle "booktitle" output.check
+ format.bvolume output
+ format.number.series output
+ format.pages output
+ publisher empty$
+ { organization output
+ address output
+ }
+ { organization output
+ format.publisher
+ }
+ if$
+ }
+ { format.incoll.inproc.crossref output.nonnull
+ format.pages output
+ }
+ if$
+ note output
+ fin.entry
+}
+
+FUNCTION {conference} { inproceedings }
+
+FUNCTION {manual}
+{ output.bibitem
+ format.authors output
+ author format.key output
+ format.date "year" output.check
+ format.btitle "title" output.check
+ organization output
+ address output
+ format.edition output
+ note output
+ fin.entry
+}
+
+FUNCTION {mastersthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ author format.key output
+ format.date "year" output.check
+ format.btitle "title" output.check
+ bbl.mthesis format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ note output
+ fin.entry
+}
+
+FUNCTION {misc}
+{ output.bibitem
+ format.authors output
+ author format.key output
+ format.date "year" output.check
+ format.title output
+ howpublished output
+ note output
+ fin.entry
+}
+
+FUNCTION {phdthesis}
+{ output.bibitem
+ format.authors "author" output.check
+ author format.key output
+ format.date "year" output.check
+ format.btitle "title" output.check
+ bbl.phdthesis format.thesis.type output.nonnull
+ school "school" output.check
+ address output
+ note output
+ fin.entry
+}
+
+FUNCTION {proceedings}
+{ output.bibitem
+ format.editors output
+ editor format.key output
+ format.date "year" output.check
+ format.btitle "title" output.check
+ format.bvolume output
+ format.number.series output
+ address output
+ organization output
+ publisher output
+ note output
+ fin.entry
+}
+
+FUNCTION {techreport}
+{ output.bibitem
+ format.authors "author" output.check
+ author format.key output
+ format.date "year" output.check
+ format.title "title" output.check
+ format.tr.number output.nonnull
+ institution "institution" output.check
+ address output
+ note output
+ fin.entry
+}
+
+FUNCTION {unpublished}
+{ output.bibitem
+ format.authors "author" output.check
+ author format.key output
+ format.date "year" output.check
+ format.title "title" output.check
+ note "note" output.check
+ fin.entry
+}
+
+FUNCTION {default.type} { misc }
+
+READ
+
+FUNCTION {sortify}
+{ purify$
+ "l" change.case$
+}
+
+INTEGERS { len }
+
+FUNCTION {chop.word}
+{ 's :=
+ 'len :=
+ s #1 len substring$ =
+ { s len #1 + global.max$ substring$ }
+ 's
+ if$
+}
+
+FUNCTION {format.lab.names}
+{ 's :=
+ s #1 "{vv~}{ll}" format.name$
+ s num.names$ duplicate$
+ #2 >
+ { pop$ " et~al." * }
+ { #2 <
+ 'skip$
+ { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
+ { " et~al." * }
+ { bbl.and
+ space.word * s #2 "{vv~}{ll}" format.name$ * }
+ if$
+ }
+ if$
+ }
+ if$
+}
+
+FUNCTION {author.key.label}
+{ author empty$
+ { key empty$
+ { cite$ #1 #3 substring$ }
+ 'key
+ if$
+ }
+ { author format.lab.names }
+ if$
+}
+
+FUNCTION {author.editor.key.label}
+{ author empty$
+ { editor empty$
+ { key empty$
+ { cite$ #1 #3 substring$ }
+ 'key
+ if$
+ }
+ { editor format.lab.names }
+ if$
+ }
+ { author format.lab.names }
+ if$
+}
+
+FUNCTION {editor.key.label}
+{ editor empty$
+ { key empty$
+ { cite$ #1 #3 substring$ }
+ 'key
+ if$
+ }
+ { editor format.lab.names }
+ if$
+}
+
+FUNCTION {calc.short.authors}
+{ type$ "book" =
+ type$ "inbook" =
+ or
+ 'author.editor.key.label
+ { type$ "proceedings" =
+ 'editor.key.label
+ 'author.key.label
+ if$
+ }
+ if$
+ 'short.list :=
+}
+
+FUNCTION {calc.label}
+{ calc.short.authors
+ short.list
+ "("
+ *
+ year duplicate$ empty$
+ { pop$ "????" }
+ 'skip$
+ if$
+ *
+ 'label :=
+}
+
+FUNCTION {sort.format.names}
+{ 's :=
+ #1 'nameptr :=
+ ""
+ s num.names$ 'numnames :=
+ numnames 'namesleft :=
+ { namesleft #0 > }
+ { s nameptr
+ "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}"
+ format.name$ 't :=
+ nameptr #1 >
+ {
+ " " *
+ namesleft #1 = t "others" = and
+ { "aaaaa" * }
+ { numnames #2 > nameptr #2 = and
+ { "zz" * year field.or.null * " " * }
+ 'skip$
+ if$
+ t sortify *
+ }
+ if$
+ }
+ { t sortify * }
+ if$
+ nameptr #1 + 'nameptr :=
+ namesleft #1 - 'namesleft :=
+ }
+ while$
+}
+
+FUNCTION {sort.format.title}
+{ 't :=
+ "A " #2
+ "An " #3
+ "The " #4 t chop.word
+ chop.word
+ chop.word
+ sortify
+ #1 global.max$ substring$
+}
+
+FUNCTION {author.sort}
+{ author empty$
+ { key empty$
+ { "to sort, need author or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { author sort.format.names }
+ if$
+}
+
+FUNCTION {author.editor.sort}
+{ author empty$
+ { editor empty$
+ { key empty$
+ { "to sort, need author, editor, or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { editor sort.format.names }
+ if$
+ }
+ { author sort.format.names }
+ if$
+}
+
+FUNCTION {editor.sort}
+{ editor empty$
+ { key empty$
+ { "to sort, need editor or key in " cite$ * warning$
+ ""
+ }
+ { key sortify }
+ if$
+ }
+ { editor sort.format.names }
+ if$
+}
+
+FUNCTION {presort}
+{ calc.label
+ label sortify
+ " "
+ *
+ type$ "book" =
+ type$ "inbook" =
+ or
+ 'author.editor.sort
+ { type$ "proceedings" =
+ 'editor.sort
+ 'author.sort
+ if$
+ }
+ if$
+ #1 entry.max$ substring$
+ 'sort.label :=
+ sort.label
+ *
+ " "
+ *
+ cite$
+ *
+ #1 entry.max$ substring$
+ 'sort.key$ :=
+}
+
+ITERATE {presort}
+
+SORT
+
+STRINGS { last.label next.extra }
+
+INTEGERS { last.extra.num number.label }
+
+FUNCTION {initialize.extra.label.stuff}
+{ #0 int.to.chr$ 'last.label :=
+ "" 'next.extra :=
+ #0 'last.extra.num :=
+ #0 'number.label :=
+}
+
+FUNCTION {forward.pass}
+{ last.label label =
+ { last.extra.num #1 + 'last.extra.num :=
+ last.extra.num int.to.chr$ 'extra.label :=
+ }
+ { "a" chr.to.int$ 'last.extra.num :=
+ "" 'extra.label :=
+ label 'last.label :=
+ }
+ if$
+ number.label #1 + 'number.label :=
+}
+
+FUNCTION {reverse.pass}
+{ next.extra "b" =
+ { "a" 'extra.label := }
+ 'skip$
+ if$
+ extra.label 'next.extra :=
+ extra.label
+ duplicate$ empty$
+ 'skip$
+ { "{\natexlab{" swap$ * "}}" * }
+ if$
+ 'extra.label :=
+ label extra.label * 'label :=
+}
+
+EXECUTE {initialize.extra.label.stuff}
+
+ITERATE {forward.pass}
+
+REVERSE {reverse.pass}
+
+FUNCTION {bib.sort.order}
+{ sort.label
+ " "
+ *
+ year field.or.null sortify
+ *
+ " "
+ *
+ cite$
+ *
+ #1 entry.max$ substring$
+ 'sort.key$ :=
+}
+
+ITERATE {bib.sort.order}
+
+SORT
+
+FUNCTION {begin.bib}
+{ preamble$ empty$
+ 'skip$
+ { preamble$ write$ newline$ }
+ if$
+ "\begin{thebibliography}{" number.label int.to.str$ * "}" *
+ write$ newline$
+ "\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi"
+ write$ newline$
+}
+
+EXECUTE {begin.bib}
+
+EXECUTE {init.state.consts}
+
+ITERATE {call.type$}
+
+FUNCTION {end.bib}
+{ newline$
+ "\end{thebibliography}" write$ newline$
+}
+
+EXECUTE {end.bib}
+%% End of customized bst file
+%%
+%% End of file `egs.bst'.
Added: seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji_extra.sty
===================================================================
--- seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji_extra.sty (rev 0)
+++ seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji_extra.sty 2012-08-07 23:03:13 UTC (rev 20558)
@@ -0,0 +1,627 @@
+% *******************************************************************
+% * TABLES AND FIGURES {extensions from AGU macros *
+% *******************************************************************
+
+% Additions and adjustments for tables and figures.
+
+% Footnotes for tables are to be identified with lower case alphabetics,
+% rather than numeric. \tablenotemark and \tablenotetext commands are
+% provided analogous to \footnotemark and \footnotetext, but with the
+% identifier *required*, like \altaffilmark and \altaffiltext. The
+% \tablenotetext must be specified before the \end{table}, since
+% \end{table} displays it.
+%
+% \tablenotemark{TAG LETTER(S)}
+% \tablenotetext{ALPHA TAG}{TEXT}
+%
+% Note that TAG LETTER == ALPHA TAG for corresponding text. It is the
+% responsibility of the author to get the correspondence correct.
+%
+% The table footnotes are coupled to the table in which they occur, rather
+% than being associated with a particular page, and they are printed with
+% the table (relatively close to the caption) instead of appearing at the
+% extreme bottom of the page. This is done to ensure that the notes wind
+% up on the same page as the table, since tables are floats and can migrate
+% from one page to another. There is the additional benefit that the notes
+% are unambiguously attached to the proper table, which is what is required
+% in the event that the editorial requirement of one table only per page
+% is ever changed to permit several tables per page.
+%
+% Footnotes are NOT supported for figures.
+
+\def\tablenotemark#1{\rlap{$^{\rm #1}$}}
+
+% The \tablenotetext command buffers the table note text and the "proper"
+% tablenote formatting information in a token buffer. The tablenotes are
+% dispensed into the vertical page list by \spew at tblnotes, which is
+% executed by \end{table}. Note that certain "global" tablenote formatting
+% details are handled by \spew at tblnotes, which also clears the tblnote list.
+% Praise and honor are due to Kresten Krab Thorup (krab at iesd.auc.dk) for
+% posting ftn.sty to the Usenet, from which I drew the technique.
+
+\newtoks\@temptokenb
+\def\tblnote at list{}
+
+\def\tablenotetext#1#2{
+ \@temptokena={\vspace{.5ex}{\noindent\llap{$^{#1}$}#2}\par}
+ \@temptokenb=\expandafter{\tblnote at list}
+ \xdef\tblnote at list{\the\@temptokenb\the\@temptokena}}
+
+\def\spew at tblnotes{
+ \ifx\tblnote at list\@empty\relax
+ \else
+ \vspace{4.5ex}
+ \footnoterule
+ \vspace{.5ex}
+ {\footnotesize\tblnote at list}
+ \gdef\tblnote at list{}
+ \fi}
+
+\def\endtable{\spew at tblnotes\end at float}
+\@namedef{endtable*}{\spew at tblnotes\end at dblfloat}
+
+% Add a \tableline command for use in tabular environments. This command
+% produces the horizontal rule(s) between the column headings and the body
+% of the table. Authors are discouraged from using any \hlines themselves,
+% and are typically forbidden from using vertical rules by editors.
+
+\let\tableline=\hline
+
+% \@makecaption determines formatting for figure and table captions.
+% For manuscripts, all captions should be set as flushleft paragraphs.
+
+\long\def\@makecaption#1#2{\vskip 2ex\noindent #1 #2\par}
+
+% The \tablenum command allows the author to override all automatic
+% table marking schemes.
+%
+% \tablenum{TEXT}
+
+\def\tablenum#1{\def\thetable{#1}\let\@currentlabel\thetable
+ \addtocounter{table}{\m at ne}}
+
+% The \figurenum command allows the author to override all automatic
+% figure marking schemes.
+%
+% \figurenum{TEXT}
+
+\def\figurenum#1{\def\thefigure{#1}\let\@currentlabel\thefigure
+ \addtocounter{figure}{\m at ne}}
+
+%
+% ********************************************************
+% * PLANO TABLES {from AGU Macros} *
+% ********************************************************
+
+% Plano tables are camera-ready pages that are included in a typeset
+% article the same way as line drawings, graphs, and other camera-ready
+% art, i.e., as "planographic" figures. There are desirable properties
+% for a formatter to have that are somewhat above and beyond LaTeX'x
+% tabular environment that would facilitate the creation of such tables.
+% Among these are breaking long tables across pages, using footnotes
+% in a table, specifying comments and references for tables, etc.
+%
+% What follows was inspired by supertab.sty by Theo Jurriens, 1988.
+
+% Commands for identifying table elements in a consistent way. Observe
+% that the formatting is embedded in the macro definitions so that the
+% author doesn't need to be concerned about stylistic nuances.
+%
+% \tablecaption{TEXT}
+% \tablehead{TEXT}
+% \colhead{HEADING}
+% \tabletail{TEXT}
+% \tablewidth{DIMEN}
+% \tableheadfrac{NUM}
+
+\newbox\pt at box
+\newdimen\pt at width
+\newcount\pt at line
+\newcount\pt at nlines
+\newcount\pt at ncol
+
+\def\colhead#1{\omit\hidewidth{#1}\hidewidth\global\advance\pt at ncol by\@ne}
+\def\tablecaption#1{\gdef\pt at caption{#1}} \def\pt at caption{\relax}
+\def\tablehead#1{\gdef\pt at head{\hline\hline\relax\\[-1.7ex]
+ #1\hskip\tabcolsep\\[.7ex]\hline\relax\\[-1.5ex]}} \def\pt at head{\relax}
+\def\tabletail#1{\gdef\pt at tail{#1}} \def\pt at tail{\relax}
+\def\tablewidth#1{\pt at width=#1} \pt at width\textwidth
+\def\tableheadfrac#1{\gdef\pt at headfrac{#1}} \def\pt at headfrac{.1}
+
+% Calculate the number of tabular rows that will fit in the body of the
+% table. The height of the table body and the number of lines are
+% calculated thus:
+%
+% bodyheight = \textheight * (1 - \pt at headfrac)
+% \pt at nlines = bodyheight / (\arraystretch * \baselineskip)
+%
+% The row height can be seen to be valid algebraically if one examines the
+% definitions for \strutbox, \@setstrut, and \@array. I could eliminate
+% this calculation, as well as its attendant parameters, if it were possible
+% to determine the accumulated height of the \halign box as TeX goes along.
+
+\def\pt at calcnlines{\@tempdima\pt at headfrac\textheight
+ \@tempdimb\textheight\advance\@tempdimb by-\@tempdima
+ \@tempdima\arraystretch\baselineskip
+ \divide\@tempdimb by\@tempdima
+ \global\pt at nlines\@tempdimb}
+
+% Define \pt at tabular, a ripoff of \@tabular but with \leavevmode removed
+% so tabular box can be set with \setbox. I do this so that table notes
+% can be set to natural width of table, if desired. Also, set \@acol
+% to \@ptabacol, which is called when building the preamble for the
+% \halign (assuming the first column format specification is "l", which
+% it should be for ApJ tables) so that \tabskip within the table is set
+% to \fill. This permits us to toggle between natural and fixed-width
+% tables without requiring the user to change markup. Note that by
+% forcing \tabskip always to be \fill, I pretty well nullify any
+% @{\hspace} commands the user puts in the template, but this environment
+% is for people who don't want to think about that sort of stuff anyway.
+
+\def\pt at tabular{\hbox \bgroup $\let\@acol\@ptabacol
+ \let\@classz\@tabclassz
+ \let\@classiv\@tabclassiv \let\\\@tabularcr\@tabarray}
+
+\def\@ptabacol{\edef\@preamble{\@preamble \hskip \tabcolsep\tabskip\fill}}
+
+% Permit different identifying strings, one for the first page of the
+% table and one for continuation pages. LaTeX's \fnum at table is set to
+% one or the other automatically in the environment. Note that caption
+% handling is not so graceful: you have to edit inside the big macros to
+% adjust this. Someday, I will be ambitious enough to fix this.
+
+\def\fnum at ptable{Table \thetable}
+\def\fnum at ptablecont{Table \thetable---{\rm Continued}}
+
+\def\set at mkcaption{\long\def\@makecaption##1##2{
+ \center\rm##1.\quad##2\endcenter\vskip 2.5ex}}
+\def\set at mkcaptioncont{\long\def\@makecaption##1##2{
+ \center\rm##1\endcenter\vskip 2.5ex}}
+
+\newenvironment{planotable}[1]{\def\pt at format{\string#1}%
+ \set at tblnotetext\pt at ncol=0}%
+ {\crcr\noalign{\vskip .7ex}\hline\endtabular%
+ \pt at width\wd\pt at box\box\pt at box\spew at ptblnotes%
+ \typeout{Table \thetable\space has been set to width \the\pt at width}%
+ \endcenter\end at float}
+
+\def\startdata{\pt at line=0\pt at calcnlines%
+ \ifdim\pt at width>\z@\def\@halignto{to \pt at width}\else\def\@halignto{}\fi%
+ \let\fnum at table=\fnum at ptable\set at mkcaption%
+ \@float{table}\center\caption{\pt at caption}\leavevmode%
+ \setbox\pt at box=\pt at tabular{\pt at format}\pt at head}
+
+% A kludgey kind of line delimiter is needed so that the line counter
+% can be checked prior to adding the line to the alignment box. This
+% is bad because this form does not permit the addition of vertical
+% space using the [.5ex] construct; this has to be done with an explicit
+% \vskip. And a disgusting \noalign is required, so I have to create
+% another silly piece of markup to accomplish this conveniently.
+%
+% What is desired, of course, is for this line count checking to take
+% place within the syntax of the regular LaTeX \\ command. I have been
+% giving myself apoplexy trying to figure this out for the last 36 hours,
+% and I have decided I will have to wait for the onset of my "lucid
+% period" for a solution. In the meantime...
+
+\def\pt at nl{\global\advance\pt at line by\@ne%
+ \ifnum\pt at line=\pt at nlines%
+ \endtabular\box\pt at box
+ \endcenter\end at float\clearpage%
+ \addtocounter{table}{\m at ne}%
+ \let\fnum at table=\fnum at ptablecont\set at mkcaptioncont%
+ \@float{table}\center\caption{\pt at caption}\leavevmode%
+ \global\pt at ncol=0%
+ \setbox\pt at box=\pt at tabular{\pt at format}\pt at head%
+ \global\pt at line=0%
+ \else\\
+ \fi}
+
+% Author markup commands for planotable environment line breaks.
+%
+% \nl == \nextline
+% \tablevspace{DIMEN}
+% \tablebreak
+
+\let\nl=\pt at nl
+\let\nextline=\pt at nl
+
+\def\tablevspace#1{\noalign{\vskip{#1}}}
+\def\tablebreak{\pt at line\pt at nlines\advance\pt at line by\m at ne\pt at nl}
+
+% We have some specialty heads that are sometimes wanted in tables.
+%
+% \cutinhead{TEXT}
+% \sidehead{TEXT}
+
+\def\cutinhead#1{\noalign{\vskip 1.5ex}
+ \hline\pt at nl\noalign{\vskip -4ex}
+ \multicolumn{\pt at ncol}{c}{#1}\pt at nl
+ \noalign{\vskip .8ex}
+ \hline\pt at nl\noalign{\vskip -2ex}}
+
+\def\sidehead#1{\noalign{\vskip 1.5ex}
+ \multicolumn{\pt at ncol}{@{\hskip\z@}l}{#1}\pt at nl
+ \noalign{\vskip .5ex}}
+
+\def\set at tblnotetext{\def\tablenotetext##1##2{{%
+ \@temptokena={\vspace{0ex}{%
+ \parbox{\pt at width}{\hskip1em$^{\rm ##1}$##2}\par}}%
+ \@temptokenb=\expandafter{\tblnote at list}
+ \xdef\tblnote at list{\the\@temptokenb\the\@temptokena}}}}
+
+\def\spew at ptblnotes{
+ \ifx\tblnote at list\@empty\relax
+ \else
+ \par
+ \vspace{2ex}
+ {\tblnote at list}
+ \gdef\tblnote at list{}
+ \fi}
+
+% Special kinds of table footnotes. Sometimes authors tabulate things
+% which have corresponding references, and it may be desirable to associate
+% these references with the table rather than (or in addition to) the
+% formal reference list. Occasionally, authors wish to append a short
+% paragraph of explanatory notes that pertain to the entire table, but
+% which are different than the caption.
+%
+% \tablerefs{REFERENCE LIST}
+% \tablecomments{TEXT}
+
+\def\tablerefs#1{\@temptokena={\vspace*{3ex}{%
+ \parbox{\pt at width}{\hskip1em\rm References. --- #1}\par}}%
+ \@temptokenb=\expandafter{\tblnote at list}
+ \xdef\tblnote at list{\the\@temptokenb\the\@temptokena}}
+
+\def\tablecomments#1{\@temptokena={\vspace*{3ex}{%
+ \parbox{\pt at width}{\hskip1em\rm Note. --- #1}\par}}%
+ \@temptokenb=\expandafter{\tblnote at list}
+ \xdef\tblnote at list{\the\@temptokenb\the\@temptokena}}
+
+\def\nodata{\multicolumn{1}{c}{$\cdots$}}
+
+%%% FROM EGS.CLS
+
+\def\ModuleVersion#1[#2]{}
+ \ModuleVersion{natbib}
+ [1998/07/14 6.8c (PWD)]
+%% Natbib coding copyright (C) 1994--1998 Patrick W. Daly
+\def\NAT at sort{0}
+\newcommand\NAT at open{(} \newcommand\NAT at close{)}
+\newcommand\NAT at sep{;} \newcommand\NAT at cmt{,}
+%%\newcommand\NAT at aysep{,} \newcommand\NAT at yrsep{,}
+\newcommand\NAT at aysep{} \newcommand\NAT at yrsep{,}
+
+\def\NAT at nmfmt#1{{#1}}
+\renewcommand\@cite%
+ [3]{\ifNAT at swa\NAT@@open\if\relax#2\relax\else#2\ \fi
+ #1\if\relax#3\relax\else\NAT at cmt\ #3\fi\NAT@@close\else#1\fi\endgroup}
+\providecommand\@firstofone[1]{#1}
+\def\@citex%
+ [#1][#2]#3{%
+ \NAT at sort@cites{#3}%
+ \let\@citea\@empty
+ \@cite{\let\NAT at nm\@empty\let\NAT at year\@empty
+ \@for\@citeb:=\NAT at cite@list\do
+ {\edef\@citeb{\expandafter\@firstofone\@citeb}%
+ \if at filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
+ \@ifundefined{b@\@citeb\@extra at b@citeb}{\@citea%
+ {\reset at font\bfseries ?}\NAT at citeundefined
+ \PackageWarning{natbib}%
+ {Citation `\@citeb' on page \thepage \space undefined}}%
+ {\let\NAT at last@nm=\NAT at nm\let\NAT at last@yr=\NAT at year
+ \NAT at parse{\@citeb}%
+ \ifNAT at full\let\NAT at nm\NAT at all@names\else
+ \let\NAT at nm\NAT at name\fi
+ \ifNAT at swa\ifcase\NAT at ctype
+ \ifx\NAT at last@nm\NAT at nm\NAT at yrsep
+ \ifx\NAT at last@yr\NAT at year
+ \hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at exlab
+ \hyper at natlinkend
+ \else\unskip\
+ \hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at date
+ \hyper at natlinkend
+ \fi
+ \else\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
+ \NAT at nmfmt{\NAT at nm}%
+ \hyper at natlinkbreak{\NAT at aysep\ }{\@citeb\@extra at b@citeb}%
+ \NAT at date\hyper at natlinkend
+ \fi
+ \or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
+ \NAT at nmfmt{\NAT at nm}\hyper at natlinkend
+ \or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
+ \NAT at date\hyper at natlinkend
+ \fi \def\@citea{\NAT at sep\ }%
+ \else\ifcase\NAT at ctype
+ \ifx\NAT at last@nm\NAT at nm\NAT at yrsep
+ \ifx\NAT at last@yr\NAT at year
+ \hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at exlab
+ \hyper at natlinkend
+ \else\unskip\
+ \hyper at natlinkstart{\@citeb\@extra at b@citeb}\NAT at date
+ \hyper at natlinkend
+ \fi
+ \else\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
+ \NAT at nmfmt{\NAT at nm}%
+ \hyper at natlinkbreak{\ \NAT@@open\if\relax#1\relax\else#1\ \fi}%
+ {\@citeb\@extra at b@citeb}%
+ \NAT at date\hyper at natlinkend\fi
+ \or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
+ \NAT at nmfmt{\NAT at nm}\hyper at natlinkend
+ \or\@citea\hyper at natlinkstart{\@citeb\@extra at b@citeb}%
+ \NAT at date\hyper at natlinkend\fi \def\@citea{\NAT@@close\NAT at sep\ }%
+ \fi
+ }}\ifNAT at swa\else\if\relax#2\relax\else\NAT at cmt\ #2\fi
+ \NAT@@close\fi}{#1}{#2}}
+\newif\ifNAT at par \NAT at partrue
+\newcommand\NAT@@open{\ifNAT at par\NAT at open\fi}
+\newcommand\NAT@@close{\ifNAT at par\NAT at close\fi}
+\renewcommand\@biblabel[1]{\hfill}
+\newlength{\bibhang}
+\setlength{\bibhang}{1em}
+\newlength{\bibsep}
+\setlength{\bibsep}{\z@}
+
+\newcommand\@bibsetup%
+ [1]{\setlength{\leftmargin}{\bibhang}\setlength{\itemindent}{-\leftmargin}%
+ \setlength{\itemsep}{\bibsep}\setlength{\parsep}{\z@}}
+\AtBeginDocument{\ifx\SK at def\@undefined\else
+\ifx\SK at cite\@empty\else
+ \SK at def\@citex[#1][#2]#3{\SK@\SK@@ref{#3}\SK@@citex[#1][#2]{#3}}\fi
+\ifx\SK at citeauthor\@undefined\def\HAR at checkdef{}\else
+ \let\citeauthor\SK at citeauthor
+ \let\citefullauthor\SK at citefullauthor
+ \let\citeyear\SK at citeyear\fi
+\fi}
+\newif\ifNAT at full\NAT at fullfalse
+\newif\ifNAT at swa
+\DeclareRobustCommand\citet
+ {\begingroup\NAT at swafalse\def\NAT at ctype{0}\NAT at partrue
+ \@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
+\newcommand\NAT at citetp{\@ifnextchar[{\NAT@@citetp}{\NAT@@citetp[]}}
+\newcommand\NAT@@citetp{}
+\def\NAT@@citetp[#1]{\@ifnextchar[{\@citex[#1]}{\@citex[][#1]}}
+\DeclareRobustCommand\citep
+ {\begingroup\NAT at swatrue\def\NAT at ctype{0}\NAT at partrue
+ \@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
+\DeclareRobustCommand\cite
+ {\begingroup\def\NAT at ctype{0}\NAT at partrue\NAT at swatrue
+ \@ifstar{\NAT at fulltrue\NAT at cites}{\NAT at fullfalse\NAT at cites}}
+\newcommand\NAT at cites{\@ifnextchar [{\NAT@@citetp}{%
+ \NAT at swafalse
+ \NAT@@citetp[]}}
+\DeclareRobustCommand\citeauthor
+ {\begingroup\NAT at swafalse\def\NAT at ctype{1}\NAT at parfalse
+ \@ifstar{\NAT at fulltrue\NAT at citetp}{\NAT at fullfalse\NAT at citetp}}
+\DeclareRobustCommand\citeyear
+ {\begingroup\NAT at swafalse\def\NAT at ctype{2}\NAT at parfalse\NAT at citetp}
+\DeclareRobustCommand\citeyearpar
+ {\begingroup\NAT at swatrue\def\NAT at ctype{2}\NAT at partrue\NAT at citetp}
+\newcommand\citetext[1]{\NAT at open#1\NAT at close}
+\DeclareRobustCommand\citefullauthor
+ {\citeauthor*}
+\renewcommand\nocite[1]{\@bsphack
+ \@for\@citeb:=#1\do{%
+ \edef\@citeb{\expandafter\@firstofone\@citeb}%
+ \if at filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
+ \if*\@citeb\else
+ \@ifundefined{b@\@citeb\@extra at b@citeb}{%
+ \NAT at citeundefined \PackageWarning{natbib}%
+ {Citation `\@citeb' undefined}}{}\fi}%
+ \@esphack}
+\newcommand\NAT at parse[1]{{%
+ \let\protect=\@unexpandable at protect\let~\relax
+ \let\active at prefix=\@gobble
+ \xdef\NAT at temp{\csname b@#1\@extra at b@citeb\endcsname}}%
+ \expandafter\NAT at split\NAT at temp
+ \expandafter\NAT at parse@date\NAT at date??????@@%
+}
+\newcommand\NAT at split[4]{%
+ \gdef\NAT at num{#1}\gdef\NAT at name{#3}\gdef\NAT at date{#2}%
+ \gdef\NAT at all@names{#4}%
+ \ifx\NAT at noname\NAT at all@names \gdef\NAT at all@names{#3}\fi}
+\newcommand\NAT at parse@date{}
+\def\NAT at parse@date#1#2#3#4#5#6@@{%
+ \ifnum\the\catcode`#1=11\def\NAT at year{}\def\NAT at exlab{#1}\else
+ \ifnum\the\catcode`#2=11\def\NAT at year{#1}\def\NAT at exlab{#2}\else
+ \ifnum\the\catcode`#3=11\def\NAT at year{#1#2}\def\NAT at exlab{#3}\else
+ \ifnum\the\catcode`#4=11\def\NAT at year{#1#2#3}\def\NAT at exlab{#4}\else
+ \def\NAT at year{#1#2#3#4}\def\NAT at exlab{{#5}}\fi\fi\fi\fi}
+\newcommand\NAT at ifcmd{\futurelet\NAT at temp\NAT at ifxcmd}
+\newcommand\NAT at ifxcmd{\ifx\NAT at temp\relax\else\expandafter\NAT at bare\fi}
+\def\NAT at bare#1(#2)#3()#4\@nil#5{%
+ \stepcounter{NAT at ctr}%
+ \NAT at wrout{\arabic {NAT at ctr}}{#2}{#1}{#3}{#5}
+}
+\newcommand\NAT at wrout[5]{%
+\if at filesw
+ {\let\protect\noexpand\let~\relax
+ \immediate
+ \write\@auxout{\string\bibcite{#5}{{#1}{#2}{{#3}}{{#4}}}}}\fi
+\ignorespaces}
+\def\NAT at noname{{}}
+\renewcommand\bibitem{%
+ \@ifnextchar[{\@lbibitem}{%
+ \stepcounter{NAT at ctr}\@lbibitem[\arabic{NAT at ctr}]}}
+\def\@lbibitem[#1]#2{%
+ \if\relax\@extra at b@citeb\relax\else
+ \@ifundefined{br@#2\@extra at b@citeb}{}{%
+ \@namedef{br@#2}{\@nameuse{br@#2\@extra at b@citeb}}}\fi
+ \@ifundefined{b@#2\@extra at b@citeb}{\def\NAT at num{}}{\NAT at parse{#2}}%
+ \item[\hfil\hyper at natanchorstart{#2\@extra at b@citeb}\@biblabel{\NAT at num}%
+ \hyper at natanchorend]%
+ \NAT at ifcmd#1()()\@nil{#2}}
+\ifx\SK at lbibitem\@undefined\else
+ \let\SK at lbibitem\@lbibitem
+ \def\@lbibitem[#1]#2{%
+ \SK at lbibitem[#1]{#2}\SK@\SK@@label{#2}\ignorespaces}\fi
+\providecommand\bibcite{}
+\renewcommand\bibcite[2]{\@ifundefined{b@#1\@extra at binfo}\relax
+ {\NAT at citemultiple
+ \PackageWarningNoLine{natbib}{Citation `#1' multiply defined}}%
+ \global\@namedef{b@#1\@extra at binfo}{#2}}
+\AtEndDocument{\NAT at swatrue\renewcommand\bibcite[2]%
+ {\NAT at testdef{#1}{#2}}}
+\newcommand\NAT at testdef[2]{%
+ \def\NAT at temp{#2}\expandafter \ifx \csname b@#1\@extra at binfo\endcsname
+ \NAT at temp \else \ifNAT at swa \NAT at swafalse
+ \PackageWarningNoLine{natbib}{Citation(s) may have
+ changed.\MessageBreak
+ Rerun to get citations correct}\fi\fi}
+%%\def\bibsection{\if at draft\newpage\fi
+%% \noappendix\section*{\refname}}
+\def\bibsection{\section*{\refname}}
+\newcounter{NAT at ctr}
+\renewenvironment{thebibliography}[1]{%
+ \bibfont\bibsection\parindent \z@\list
+ {\@biblabel{\arabic{NAT at ctr}}}{\@bibsetup{#1}%
+ \setcounter{NAT at ctr}{0}}%
+ \def\newblock{\hskip .11em plus.33em minus.07em}%
+ \sloppy\clubpenalty4000\widowpenalty4000
+ \sfcode`\.=1000\relax
+ }{\def\@noitemerr{%
+ \PackageWarning{natbib}
+ {Empty `thebibliography' environment}}%
+ \endlist\vskip-\lastskip}
+\let\bibfont=\small
+\providecommand\reset at font{\relax}
+\providecommand\bibname{Bibliography}
+\providecommand\refname{References}
+\newcommand\NAT at citeundefined{\gdef \NAT at undefined {%
+ \PackageWarningNoLine{natbib}{There were undefined citations}}}
+\let \NAT at undefined \relax
+\newcommand\NAT at citemultiple{\gdef \NAT at multiple {%
+ \PackageWarningNoLine{natbib}{There were multiply defined citations}}}
+\let \NAT at multiple \relax
+\AtEndDocument{\NAT at undefined\NAT at multiple}
+\providecommand\@mkboth[2]{}
+\providecommand\MakeUppercase{\uppercase}
+\providecommand{\@extra at b@citeb}{}
+\gdef\@extra at binfo{}
+\providecommand\hyper at natanchorstart[1]{}
+\providecommand\hyper at natanchorend{}
+\providecommand\hyper at natlinkstart[1]{}
+\providecommand\hyper at natlinkend{}
+\providecommand\hyper at natlinkbreak[2]{#1}
+\ifnum\NAT at sort>0
+\newcommand\NAT at sort@cites[1]{%
+\@tempcntb\m at ne
+\let\@celt\delimiter
+\def\NAT at num@list{}%
+\def\NAT at cite@list{}%
+\def\NAT at nonsort@list{}%
+\@for \@citeb:=#1\do{\NAT at make@cite at list}%
+\edef\NAT at cite@list{\NAT at cite@list\NAT at nonsort@list}%
+\edef\NAT at cite@list{\expandafter\NAT at xcom\NAT at cite@list @@}}
+\begingroup \catcode`\_=8
+\gdef\NAT at make@cite at list{%
+ \edef\@citeb{\expandafter\@firstofone\@citeb}%
+ \@ifundefined{b@\@citeb\@extra at b@citeb}{\def\NAT at num{A}}%
+ {\NAT at parse{\@citeb}}%
+ \ifcat _\ifnum\z@<0\NAT at num _\else A\fi
+ \@tempcnta\NAT at num \relax
+ \ifnum \@tempcnta>\@tempcntb
+ \edef\NAT at num@list{\NAT at num@list \@celt{\NAT at num}}%
+ \edef\NAT at cite@list{\NAT at cite@list\@citeb,}%
+ \@tempcntb\@tempcnta
+ \else
+ \let\NAT@@cite at list=\NAT at cite@list \def\NAT at cite@list{}%
+ \edef\NAT at num@list{\expandafter\NAT at num@celt \NAT at num@list \@gobble @}%
+ {\let\@celt=\NAT at celt\NAT at num@list}%
+ \fi
+ \else
+ \edef\NAT at nonsort@list{\NAT at nonsort@list\@citeb,}%
+ \fi}
+\endgroup
+\def\NAT at celt#1{\ifnum #1<\@tempcnta
+ \xdef\NAT at cite@list{\NAT at cite@list\expandafter\NAT at nextc\NAT@@cite at list @@}%
+ \xdef\NAT@@cite at list{\expandafter\NAT at restc\NAT@@cite at list}%
+ \else
+ \xdef\NAT at cite@list{\NAT at cite@list\@citeb,\NAT@@cite at list}\let\@celt\@gobble%
+ \fi}
+\def\NAT at num@celt#1#2{\ifx \@celt #1%
+ \ifnum #2<\@tempcnta
+ \@celt{#2}%
+ \expandafter\expandafter\expandafter\NAT at num@celt
+ \else
+ \@celt{\number\@tempcnta}\@celt{#2}%
+ \fi\fi}
+\def\NAT at nextc#1,#2@@{#1,}
+\def\NAT at restc#1,#2{#2}
+\def\NAT at xcom#1,@@{#1}
+\else
+ \newcommand\NAT at sort@cites[1]{\edef\NAT at cite@list{#1}}\fi
+
+
+\def\ModuleVersion#1[#2]{}
+ \ModuleVersion{balance}
+ [1997/04/29 4.2b (PWD)]
+%% Balance coding copyright (C) 1994--1997 Patrick W. Daly
+\newcommand{\@BAlancecol}{\if at twocolumn
+ \setbox0=\vbox{\unvbox\@outputbox} \@tempdima=\ht0
+ \advance\@tempdima by \topskip \advance\@tempdima
+ by -\baselineskip \divide\@tempdima by 2
+ \splittopskip=\topskip
+ {\vbadness=\@M \loop \global\setbox3=\copy0
+ \global\setbox1=\vsplit3 to \@tempdima
+ \ifdim\ht3>\@tempdima \global\advance\@tempdima by 1pt \repeat}
+ \setbox\@leftcolumn=\vbox to \@tempdima{\unvbox1\vfil}
+ \setbox\@outputbox=\vbox to \@tempdima
+ {\dimen2=\dp3\unvbox3\kern-\dimen2
+ \vfil}
+ \fi}
+\newif\if at BAlanceone
+\global\@BAlanceonefalse
+\newdimen\oldvsize
+\newcommand{\@BAdblcol}{\if at firstcolumn
+ \unvbox\@outputbox \penalty\outputpenalty
+ \global\oldvsize=\@colht \global\multiply \@colht by 2
+ \global\@BAlanceonetrue
+ \global\@firstcolumnfalse
+ \else \global\@firstcolumntrue
+ \if at BAlanceone
+ \global\@BAlanceonefalse\@BAlancecol
+ \global\@colht=\oldvsize \else
+ \PackageWarningNoLine{balance}
+ {You have called \protect\balance\space
+ in second column\MessageBreak
+ Columns might not be balanced}\fi
+ \setbox\@outputbox\vbox to \@colht{\hbox to\textwidth
+ {\hbox to\columnwidth {\box\@leftcolumn \hss}\hfil
+ \vrule width\columnseprule\hfil \hbox to\columnwidth
+ {\box\@outputbox \hss}}\vfil}\@combinedblfloats
+ \@outputpage \begingroup \@dblfloatplacement
+ \@startdblcolumn \@whilesw\if at fcolmade \fi
+ {\@outputpage\@startdblcolumn}\endgroup
+ \fi}
+\newcommand{\@BAcleardblpage}{\clearpage\if at twoside \ifodd\c at page\else
+ \hbox{}\newpage\fi\fi}
+\newcommand{\@@cleardblpage}{}
+\let\@@cleardblpage=\cleardoublepage
+
+\newcommand{\@@utputdblcol}{}
+\let\@@utputdblcol=\@outputdblcol
+\newcommand{\balance}{\global\let\@outputdblcol=\@BAdblcol
+ \global\let\cleardoublepage=\@BAcleardblpage}
+\newcommand{\nobalance}{\global\let\@outputdblcol=\@@utputdblcol
+ \global\let\cleardoublepage=\@@cleardblpage}
+%%
+%% FIGBOX
+\long\def\@makenarrowcap#1#2{\hfill\vbox to \z@{\hsize=5cm \vss
+ \reset at font\small{\bf #1.} #2\par\null}}
+\def\figbox{\@ifstar{\let\egsbox\makebox\@figbox}
+ {\let\egsbox\framebox\@figbox}}
+\def\@figbox#1#2#3{\setbox\@tempboxa=\hbox{%
+ \if!#1!\egsbox{#3}\else
+ \egsbox[#1][c]{\if!#2!#3\else\@tempdima#2\relax
+ \divide\@tempdima by2\relax
+ \advance\@tempdima by-\fboxsep \advance\@tempdima by-\fboxrule
+ \vrule\@height\@tempdima\@depth\@tempdima\@width\z@
+ \vbox to \z@{\vss\hbox{#3}\vss}\fi}\fi}%
+ \@tempdima=\hsize \advance\@tempdima by-\wd\@tempboxa
+ \box\@tempboxa
+ \vspace{0pt}}
+%%
+%% IFTWOCOL
+\def\iftwocol#1#2{\if at twocolumn#1\else #2\fi}
\ No newline at end of file
Added: seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji_modified_cours_UPPA.cls
===================================================================
--- seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji_modified_cours_UPPA.cls (rev 0)
+++ seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/gji_modified_cours_UPPA.cls 2012-08-07 23:03:13 UTC (rev 20558)
@@ -0,0 +1,1532 @@
+% Documentclass gji.cls
+% for Geophysical Journal International
+% Based on the MN journal document style
+%
+
+% Version 2.0 for Latex 2e extensively rewritten by
+% Brian Kennett, Pacific Region Office, GJI
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesClass{gji_modified_cours_UPPA}[1995/11/30 v2.0 LaTeX2e document class]
+
+\def\f at s@s{}%
+%
+
+
+%
+\typeout{Document Class `GJI' \f at s@s V2.0, released 1998 Nov}
+
+\def\f at ce{cm}
+
+% Journals use two-sided printing.
+%
+\@twosidetrue
+\@twocolumntrue
+\@mparswitchtrue
+\def\ds at draft{\overfullrule 5pt}
+\def\ds at twocolumn{\@twocolumntrue}
+\def\ds at onecolumn{\@twocolumnfalse}
+
+% fasttrack option
+%
+\newif\if at fasttrack
+\def\ds at fasttrack{\@fasttracktrue}
+
+% landscape option
+%
+\newif\ifGJ at landscape
+\def\ds at landscape{\GJ at landscapetrue}
+
+% galley option
+%
+\newif\ifGJ at galley
+\def\ds at galley{\GJ at galleytrue}
+
+% referee option
+%
+\newif\ifGJ at referee
+\def\ds at referee{%
+ \GJ at refereetrue
+ \@twocolumnfalse
+}
+\newif\ifGJ at mreferee
+\def\ds at mreferee{%
+ \GJ at mrefereetrue
+ \@twocolumnfalse
+}
+\newif\ifGJ at camera
+\def\ds at camera{%
+ \GJ at cameratrue
+}
+\newif\ifGJ at extra
+\def\ds at extra{%
+ \GJ at extratrue
+}
+\newif\ifdoublesp at cing
+\def\ds at doublespacing{%
+ \doublesp at cingtrue
+}%
+\ExecuteOptions{a4paper,twoside,final}
+\ProcessOptions
+%
+% ****************************************
+% * FONTS *
+% ****************************************
+%
+\lineskip 1pt
+\normallineskip 1pt
+\ifGJ at referee
+ \renewcommand\baselinestretch{1.75}
+\else
+ \ifdoublesp at cing
+ \renewcommand\baselinestretch{2}
+ \else
+ \renewcommand\baselinestretch{1}
+\fi\fi
+\ifGJ at mreferee
+ \renewcommand\baselinestretch{1.75}
+\fi
+
+\renewcommand\normalsize{\@setfontsize\normalsize\@ixpt{12}%
+ \abovedisplayskip 4pt plus 1pt minus 1pt
+ \belowdisplayskip \abovedisplayskip
+ \abovedisplayshortskip 4pt plus 1pt
+ \belowdisplayshortskip \abovedisplayshortskip
+ \let\@listi\@listI}
+\newcommand\small{\@setfontsize\small\@viiipt{10}%
+ \abovedisplayskip 4pt plus 1pt minus 1pt
+ \belowdisplayskip \abovedisplayskip
+ \abovedisplayshortskip 4pt plus 1pt
+ \belowdisplayshortskip \abovedisplayshortskip
+ \def\@listi{\leftmargin\leftmargini
+ \topsep 2pt plus 1pt minus 1pt
+ \parsep \z@
+ \itemsep 2pt}}
+\newcommand\footnotesize{\@setfontsize\footnotesize\@viiipt{10}%
+ \abovedisplayskip 4pt plus 1pt minus 1pt
+ \belowdisplayskip \abovedisplayskip
+ \abovedisplayshortskip 4pt plus 1pt
+ \belowdisplayshortskip \abovedisplayshortskip
+ \renewcommand\@listi{\leftmargin\leftmargini
+ \topsep 2pt plus 1pt minus 1pt
+ \parsep \z@
+ \itemsep 2pt}}
+\newcommand\scriptsize{\@setfontsize\scriptsize\@vipt{8}}
+\newcommand\tiny{\@setfontsize\tiny\@vpt{6}}
+
+\newcommand\large{\@setfontsize\large\@xpt{12}}
+\newcommand\Large{\@setfontsize\Large\@xiipt{14}}
+\newcommand\LARGE{\@setfontsize\LARGE\@xivpt{17}}
+\newcommand\huge{\@setfontsize\huge\@xviipt{20}}
+\newcommand\Huge{\@setfontsize\Huge\@xxpt{25}}
+
+\if at twocolumn
+ \renewcommand\normalsize{\@setfontsize\normalsize\@ixpt{11}%
+ \abovedisplayskip 6pt plus 2pt minus 2pt
+ \belowdisplayskip \abovedisplayskip
+ \abovedisplayshortskip 6pt plus 2pt
+ \belowdisplayshortskip \abovedisplayshortskip
+ \let\@listi\@listI}
+ \renewcommand\large{\@setfontsize\large\@xpt{11}}
+\fi
+
+\ifGJ at referee
+ \renewcommand\normalsize{\@setfontsize\normalsize\@xiipt{14}%
+ \abovedisplayskip 8pt plus 1pt minus 1pt
+ \belowdisplayskip \abovedisplayskip
+ \abovedisplayshortskip 4pt plus 1pt
+ \belowdisplayshortskip \abovedisplayshortskip
+ \let\@listi\@listI}
+ \renewcommand\small{\@setfontsize\small\@xipt{11}%
+ \abovedisplayskip 5pt plus 1pt minus 1pt
+ \belowdisplayskip \abovedisplayskip
+ \abovedisplayshortskip 4pt plus 1pt
+ \belowdisplayshortskip \abovedisplayshortskip
+ \def\@listi{\leftmargin\leftmargini
+ \topsep 2pt plus 1pt minus 1pt
+ \parsep \z@
+ \itemsep 2pt}}
+ \renewcommand\large{\@setfontsize\large\@xiipt{13}}
+ \renewcommand\Large{\@setfontsize\Large\@xiipt{15}}
+ \renewcommand\LARGE{\@setfontsize\LARGE\@xivpt{18}}
+\fi
+
+\ifGJ at mreferee
+ \renewcommand\normalsize{\@setfontsize\normalsize\@xipt{11}%
+ \abovedisplayskip 8pt plus 1pt minus 1pt
+ \belowdisplayskip \abovedisplayskip
+ \abovedisplayshortskip 4pt plus 1pt
+ \belowdisplayshortskip \abovedisplayshortskip
+ \let\@listi\@listI}
+ \renewcommand\small{\@setfontsize\small\@xpt{10}%
+ \abovedisplayskip 5pt plus 1pt minus 1pt
+ \belowdisplayskip \abovedisplayskip
+ \abovedisplayshortskip 4pt plus 1pt
+ \belowdisplayshortskip \abovedisplayshortskip
+ \def\@listi{\leftmargin\leftmargini
+ \topsep 2pt plus 1pt minus 1pt
+ \parsep \z@
+ \itemsep 2pt}}
+ \renewcommand\large{\@setfontsize\large\@xiipt{13}}
+ \renewcommand\Large{\@setfontsize\Large\@xiipt{15}}
+ \renewcommand\LARGE{\@setfontsize\LARGE\@xivpt{18}}
+\fi
+
+\ifGJ at camera
+ \renewcommand\normalsize{\@setfontsize\normalsize\@xpt{11}%
+ \abovedisplayskip 6pt plus 2pt minus 2pt
+ \belowdisplayskip \abovedisplayskip
+ \abovedisplayshortskip 6pt plus 2pt
+ \belowdisplayshortskip \abovedisplayshortskip
+ \let\@listi\@listI}
+ \renewcommand\large{\@setfontsize\large\@xipt{12}}
+\fi
+
+\normalsize
+
+\newcommand{\mitbf}[1]{
+ \hbox{\mathversion{bold}$#1$}}
+ \newcommand{\rmn}[1] {{\mathrm #1}}
+ \newcommand{\itl}[1] {{\mathit #1}}
+ \newcommand{\bld}[1] {{\mathbf #1}}
+
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
+\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
+\DeclareRobustCommand\cal{\@fontswitch{\relax}{\mathcal}}
+\DeclareRobustCommand\mit{\@fontswitch{\relax}{\mathchoice}}
+%\DeclareRobustCommand*\cal{\@fontswitch{\relax}{\mathcal}}
+%\DeclareRobustCommand*\mit{\@fontswitch{\relax}{\mathchoice}}
+%
+
+
+% Astronomy and Astrophysics symbol macros
+
+\newcommand\la{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr<\cr\sim\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr
+<\cr\sim\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr
+<\cr\sim\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+<\cr\sim\cr}}}}}
+
+\newcommand\ga{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr>\cr\sim\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr
+>\cr\sim\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr
+>\cr\sim\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+>\cr\sim\cr}}}}}
+
+\newcommand\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip
+\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr\gets\cr\to\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr\gets
+\cr\to\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr\gets
+\cr\to\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+\gets\cr\to\cr}}}}}
+
+\newcommand\cor{\mathrel{\mathchoice {\hbox{$\widehat=$}}{\hbox{$\widehat=$}}
+{\hbox{$\reset at font\scriptstyle\hat=$}}
+{\hbox{$\reset at font\scriptscriptstyle\hat=$}}}}
+
+\newcommand\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr<\cr
+\noalign{\vskip1.2pt}=\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr<\cr
+\noalign{\vskip1pt}=\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+<\cr
+\noalign{\vskip0.9pt}=\cr}}}}}
+
+\newcommand\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr>\cr
+\noalign{\vskip1.2pt}=\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr>\cr
+\noalign{\vskip1pt}=\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+>\cr
+\noalign{\vskip0.9pt}=\cr}}}}}
+
+\newcommand\sol{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr\sim\cr<\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr\sim\cr
+<\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr\sim\cr
+<\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+\sim\cr<\cr}}}}}
+
+\newcommand\sog{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr\sim\cr>\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr\sim\cr
+>\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr
+\sim\cr>\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+\sim\cr>\cr}}}}}
+
+\newcommand\lse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr<\cr\simeq\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr
+<\cr\simeq\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr
+<\cr\simeq\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+<\cr\simeq\cr}}}}}
+
+\newcommand\gse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr>\cr\simeq\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr
+>\cr\simeq\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr
+>\cr\simeq\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+>\cr\simeq\cr}}}}}
+
+\newcommand\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1.5pt}<\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr
+>\cr\noalign{\vskip-1.5pt}<\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr
+>\cr\noalign{\vskip-1pt}<\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+>\cr\noalign{\vskip-0.5pt}<\cr}}}}}
+
+\newcommand\leogr{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr<\cr\noalign{\vskip-1.5pt}>\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr
+<\cr\noalign{\vskip-1.5pt}>\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr
+<\cr\noalign{\vskip-1pt}>\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+<\cr\noalign{\vskip-0.5pt}>\cr}}}}}
+
+\newcommand\loa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr<\cr\approx\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr
+<\cr\approx\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr
+<\cr\approx\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+<\cr\approx\cr}}}}}
+
+\newcommand\goa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
+$\reset at font\displaystyle##$\hfil\cr>\cr\approx\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\textstyle##$\hfil\cr
+>\cr\approx\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptstyle##$\hfil\cr
+>\cr\approx\cr}}}
+{\vcenter{\offinterlineskip\halign{\hfil$\reset at font\scriptscriptstyle##$\hfil\cr
+>\cr\approx\cr}}}}}
+
+\newcommand\sun{\hbox{$\odot$}}
+\newcommand\earth{\hbox{$\oplus$}}
+\newcommand\degr{\hbox{$^\circ$}}
+\newcommand\diameter{{\ifmmode\mathchoice
+{\ooalign{\hfil\hbox{$\reset at font\displaystyle/$}\hfil\crcr
+{\hbox{$\reset at font\displaystyle\mathchar"20D$}}}}
+{\ooalign{\hfil\hbox{$\reset at font\textstyle/$}\hfil\crcr
+{\hbox{$\reset at font\textstyle\mathchar"20D$}}}}
+{\ooalign{\hfil\hbox{$\reset at font\scriptstyle/$}\hfil\crcr
+{\hbox{$\reset at font\scriptstyle\mathchar"20D$}}}}
+{\ooalign{\hfil\hbox{$\reset at font\scriptscriptstyle/$}\hfil\crcr
+{\hbox{$\reset at font\scriptscriptstyle\mathchar"20D$}}}}
+\else{\ooalign{\hfil/\hfil\crcr\mathhexbox20D}}%
+\fi}}
+
+\newcommand\sq{\ifmmode\squareforqed\else{\unskip\nobreak\hfil
+\penalty50\hskip1em\null\nobreak\hfil\squareforqed
+\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}
+\newcommand\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}
+
+\newcommand{\romn}[1] {{\mathrm #1}}
+
+\newcommand\fd{\hbox{$.\!\!^{\reset at font\romn d}$}}
+\newcommand\fh{\hbox{$.\!\!^{\reset at font\romn h}$}}
+\newcommand\fm{\hbox{$.\!\!^{\reset at font\romn m}$}}
+\newcommand\fs{\hbox{$.\!\!^{\reset at font\romn s}$}}
+\newcommand\fdg{\hbox{$.\!\!^\circ$}}
+\newcommand\farcm{\hbox{$.\mkern-4mu^\prime$}}
+\newcommand\farcs{\hbox{$.\!\!^{\prime\prime}$}}
+\newcommand\fp{\hbox{$.\!\!^{\reset at font\reset at font\scriptscriptstyle\romn p}$}}
+\newcommand\arcmin{\hbox{$^\prime$}}
+\newcommand\arcsec{\hbox{$^{\prime\prime}$}}
+
+\def\micron{\hbox{$\mu$m}}
+
+\newcommand\case[2]{\hbox{$\frac{#1}{#2}$}}
+\newcommand\slantfrac[2]{\hbox{$\,^#1\!/_#2$}}
+\newcommand\onehalf{\slantfrac{1}{2}}
+\newcommand\onethird{\slantfrac{1}{3}}
+\newcommand\twothirds{\slantfrac{2}{3}}
+\newcommand\onequarter{\slantfrac{1}{4}}
+\newcommand\threequarters{\slantfrac{3}{4}}
+\newcommand\fhf{\case{1}{2}}
+\newcommand\fqr{\case{1}{4}}
+%
+%\chemical from Kopka & Daly
+\newlength\fntxvi
+\newlength\fntxvii
+\newcommand{\chemical}[1]
+{{\fontencoding{OMS}\fontfamily{cmsy}\selectfont
+ \fntxvi\the\fontdimen16\font
+ \fntxvii\the\fontdimen17\font
+ \fontdimen16\font=2pt\fontdimen17\font=2pt
+ $\mathrm{#1}$
+ \fontencoding{OMS}\fontfamily{cmsy}\selectfont
+ \fontdimen16\font=\fntxvi \fontdimen17\font=\fntxvii}}
+
+% ****************************************
+% * PAGE LAYOUT *
+% ****************************************
+%
+% SIDE MARGINS:
+\if at twocolumn
+ \setlength\oddsidemargin{-2.5pc}
+ \setlength\evensidemargin{-2.5pc}
+\else
+ \ifGJ at referee
+ \setlength\oddsidemargin{\z@}
+ \setlength\evensidemargin{\z@}
+ \else
+ \setlength\oddsidemargin{-2pc}
+ \setlength\evensidemargin{-2pc}
+ \fi
+\fi
+\setlength\marginparwidth{4pc}
+\setlength\marginparsep{0.5pc}
+
+% VERTICAL SPACING:
+%\if at twocolumn
+ \setlength\topmargin{-2pc}
+%\else
+ \setlength\topmargin{\z@}
+%\fi
+\setlength{\headheight}{14pt}
+\setlength{\headsep} {15pt}
+\setlength{\topskip} {9pt}
+%\setlength{\footheight}{11pt}
+\setlength{\footskip} {26pt}
+%
+% DIMENSION OF TEXT:
+%
+\newdimen\GJ at measure
+\GJ at measure 42pc
+%
+\setlength\textheight{682pt}
+\setlength\textwidth{\GJ at measure}
+%
+\ifGJ at landscape
+ \setlength\textwidth{\textheight}
+ \setlength\textheight{\GJ at measure}
+\fi
+\ifGJ at referee
+ \setlength\textwidth{39pc}
+\fi
+\setlength\columnsep{2pc}
+\setlength\columnseprule{0pt}
+
+\ifGJ at mreferee
+\setlength {\textwidth} {156.0mm}
+\setlength {\textheight} {230.0mm}
+\setlength {\evensidemargin}{0mm}
+\setlength {\oddsidemargin} {0mm}
+\setlength {\topmargin} {0mm}
+\setlength {\baselineskip} {17pt}
+\setlength {\parindent} {5mm}
+\fi
+
+% FOOTNOTES:
+\setlength\footnotesep{6pt}
+\setlength\skip{\footins 19.5pt plus 12pt minus 1pt}
+
+% FLOATS:
+\setlength\floatsep{ 12pt plus 5.5pt minus 1pt}
+\setlength\textfloatsep{ 12pt plus 7.5pt}
+\setlength\intextsep{ 12pt plus 5.5pt minus 2pt}
+%%\setlength\@maxsep{ 15pt }
+\setlength\dblfloatsep{ 12pt plus 5.5pt minus 2pt }
+\setlength\dbltextfloatsep{ 15pt plus 4.5pt minus 3pt}
+%%\setlength\@dblmaxsep{ 15pt }
+\setlength\@fptop{ 0pt plus 0fil}
+\setlength\@fpsep{ 12pt plus 0fil }
+\setlength\@fpbot{ 0pt plus 3fil }
+\setlength\@dblfptop{ 0pt plus 0fil}
+\setlength\@dblfpsep{ 12pt plus 0fil}
+\setlength\@dblfpbot{ 0pt plus 3fil}
+\setlength\marginparpush{ 5pt }
+
+% ****************************************
+% * PARAGRAPHING *
+% ****************************************
+%
+\setlength\parskip{ \z@ plus .1pt }
+\setlength\parindent{ 18pt }
+\setlength\partopsep{ 0pt plus 1pt }
+\@lowpenalty 51
+\@medpenalty 151
+\@highpenalty 301
+\@beginparpenalty -\@lowpenalty
+\@endparpenalty -\@lowpenalty
+\@itempenalty -\@lowpenalty
+\clubpenalty=0
+\widowpenalty=10000
+
+% ****************************************
+% * PARTS & SECTIONS NUMBERS *
+% ****************************************
+%
+\newcounter {part}
+\newcounter {section}
+\newcounter {subsection}[section]
+\newcounter {subsubsection}[subsection]
+\newcounter {paragraph}[subsubsection]
+\newcounter {subparagraph}[paragraph]
+\renewcommand\thepart {\arabic{part}}
+\renewcommand\thesection {\arabic{section}}
+\renewcommand\thesubsection {\thesection.\arabic{subsection}}
+\renewcommand\thesubsubsection {\thesubsection.\arabic{subsubsection}}
+\renewcommand\theparagraph {\thesubsubsection.\arabic{paragraph}}
+\renewcommand\thesubparagraph {\theparagraph.\arabic{subparagraph}}
+
+% Sometimes people want to number equations by section, rather than
+% sequentially through the whole paper.
+
+\newcommand\eqsecnum{
+ \@newctr{equation}[section]
+ \def\theequation{\normalsize\mbox{\arabic{section}.\arabic{equation}}}}
+% \def\theequation{\mbox{\arabic{section}.\arabic{equation}}}}
+
+\newcommand\eqsubsecnum{
+ \@newctr{equation}[subsection]
+ \def\theequation{\normalsize%
+ \mbox{\arabic{section}.\arabic{subsection}.\arabic{equation}}}}
+% \def\theequation
+% {\mbox{\arabic{section}.\arabic{subsection}.\arabic{equation}}}}
+
+
+% ****************************************
+% * PARTS *
+% ****************************************
+%
+\def\part{\par \addvspace{4ex}\@afterindentfalse
+ \secdef\@part\@spart}
+\def\@part[#1]#2{\ifnum \c at secnumdepth >\m at ne
+ \refstepcounter{part}
+ \addcontentsline{toc}{part}{Part \thepart: #1}
+ \else \addcontentsline{toc}{part}{#1}
+ \fi
+ {\parindent 0pt \raggedright
+ \ifnum \c at secnumdepth >\m at ne
+ \reset at font\large\rm PART
+ \ifcase\thepart \or ONE \or TWO \or THREE \or FOUR \or FIVE
+ \or SIX \or SEVEN \or EIGHT \or NINE \or TEN \else \fi
+ \par \nobreak
+ \fi
+ \reset at font\LARGE \rm #2 \markboth{}{}\par }
+ \nobreak \vskip 3ex \@afterheading}
+\def\@spart#1{{\parindent 0pt \raggedright
+ \reset at font\LARGE \rm #1\par}
+ \nobreak \vskip 3ex \@afterheading}
+
+% ****************************************
+% * SECTIONS *
+% ****************************************
+%
+% \@startsection modified to leave less space before \subsection
+% if it immediately follows \section
+
+% \@startsection {NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}
+
+\def\@startsection#1#2#3#4#5#6{\if at noskipsec \leavevmode \fi
+ \par \@tempskipa #4\relax
+ \@afterindenttrue
+ \ifdim \@tempskipa <\z@ \@tempskipa -\@tempskipa \@afterindentfalse\fi
+ \if at nobreak
+ \everypar{} \ifnum#2=2 \vskip 0pt plus1pt\fi % was 6pt
+ \else
+ \addpenalty{\@secpenalty}\addvspace{\@tempskipa}
+ \fi \@ifstar
+ {\@ssect{#3}{#4}{#5}{#6}}{\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}}
+
+%\def\GJ at hangraggedright{\rightskip\@flushglue \let\\=\newline}
+%\def\GJ at raggedright{\rightskip\@flushglue \let\\=\@centercr
+% \parindent=\GJ at indent}
+
+\def\GJ at hangraggedright{\rightskip=\@flushglue \let\\=\@centercr \parindent=0pt}
+
+\def\section{\@startsection{section}{1}{\z@}
+ {-24pt plus -12pt minus -1pt}{6pt}
+ {\GJ at hangraggedright\reset at font\normalsize\bf}}
+\def\subsection{\@startsection{subsection}{2}{\z@}
+ {-18pt plus -9pt minus -1pt}{6pt}
+ {\GJ at hangraggedright\reset at font\normalsize\bf}}
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}
+ {-18pt plus -9pt minus -1pt}{6pt}
+ {\GJ at hangraggedright\reset at font\normalsize\it}}
+\def\paragraph{\@startsection{paragraph}{4}{\z@}
+ {12pt plus 2.25pt minus 1pt}{-0.5em}{\reset at font\normalsize\bf}}
+\def\subparagraph{\@startsection{subparagraph}{5}{\parindent}
+ {12pt plus 2.25pt minus 1pt}{-0.5em}{\reset at font\normalsize\it}}
+\setcounter{secnumdepth}{4}
+%
+\newif\if at levelone
+%
+% \@sect{NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}[ARG1]{ARG2}
+\def\@sect#1#2#3#4#5#6[#7]#8{%
+ \ifnum #2>\c at secnumdepth
+ \def\@svsec{}%
+ \else
+ \refstepcounter{#1}
+ \ifnum #2=\@ne \global\@levelonetrue % if level=1 ie. section
+ \ifGJ at appendix \edef\@svsec{}%
+ \else \edef\@svsec{\csname the#1\endcsname\hskip 1em}%
+ \fi
+ \else \edef\@svsec{\csname the#1\endcsname\hskip 1em}%
+ \fi
+ \fi
+ \@tempskipa #5\relax
+ \ifdim \@tempskipa>\z@
+ \begingroup #6\relax
+ \ifnum #2=\@ne
+ \ifGJ at appendix
+ \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M
+ APPENDIX \csname the#1\endcsname:\hskip 0.5em\uppercase{#8}\par}%
+ \else
+ \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M
+ \uppercase{#8}\par}%
+ \fi
+ \else
+ \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%
+ \fi
+ \endgroup
+ \csname #1mark\endcsname{#7}%
+ \addcontentsline{toc}{#1}{\ifnum #2>\c at secnumdepth \else %ajw
+ \protect\numberline{\csname the#1\endcsname}\fi #7}%ajw
+ \else
+ \def\@svsechd{#6\hskip #3\@svsec \ifnum #2=\@ne\uppercase{#8}\else #8\fi
+ \csname #1mark\endcsname{#7}
+ \addcontentsline{toc}{#1}{\ifnum #2>\c at secnumdepth \else %ajw
+ \protect\numberline{\csname the#1\endcsname}\fi#7}%ajw
+ }\fi
+ \@xsect{#5}}
+
+% from latex.tex
+% \@ssect{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}{ARG}
+\def\@ssect#1#2#3#4#5{%
+ \@tempskipa #3\relax
+ \ifdim \@tempskipa>\z@
+ \begingroup #4\@hangfrom{\hskip #1}{%
+ \interlinepenalty \@M
+ \if at levelone
+ \uppercase{#5}\global\@levelonefalse
+ \else{#5}
+ \fi\par}%
+ \endgroup
+ \else
+ \def\@svsechd{#4\hskip #1\relax
+ \if at levelone
+ \uppercase{#5}\global\@levelonefalse
+ \else{#5}
+ \fi}
+ \fi
+ \@xsect{#3}%
+}
+
+\newif\ifGJ at appendix
+\def\appendix{\par
+ \GJ at appendixtrue
+ \setcounter{section}{0}
+% \def\thesection{A\arabic{section}}
+ \renewcommand\thesection{\Alph{section}}
+ \renewcommand\thesubsection{\thesection\arabic{subsection}}
+ \setcounter{equation}{0}
+% \def\theequation{A\arabic{equation}}
+ \@newctr{equation}[section]
+\renewcommand\theequation{\hbox{\normalsize\Alph{section}.\arabic{equation}}}
+%\renewcommand\theequation{\hbox{\Alph{section}.\arabic{equation}}}
+\setcounter{figure}{0}
+ \renewcommand\thefigure{A\@arabic\c at figure}
+ \setcounter{table}{0}
+ \renewcommand\thetable{A\@arabic\c at table}
+}
+
+\newcommand\resetfigno{
+ \setcounter{figure}{0}
+ \renewcommand\thefigure{\@arabic\c at figure}
+}
+% ****************************************
+% * SKIPS *
+% ****************************************
+%
+\newskip\@indentskip
+\newskip\smallindent
+\newskip\@footindent
+\newskip\@leftskip
+\@indentskip=18pt
+\smallindent=1.5em
+\@footindent=\smallindent
+\@leftskip=\z@
+
+% ****************************************
+% * LISTS *
+% ****************************************
+%
+\setlength\leftmargini{ \z@ }
+\setlength\leftmarginii{ 1.25pc }
+\setlength\leftmarginiii{ 1.25pc }
+\setlength\leftmarginiv{ 1.25pc }
+\setlength\leftmarginv{ 1pc }
+\setlength\leftmarginvi{ 1pc }
+\setlength\leftmargin{\leftmargini}
+\setlength\labelsep{ 0.5em}
+\labelwidth\leftmargini\advance\labelwidth-\labelsep
+%
+% label macros for Range-Left and Range-Right labels
+\def\makeRLlabel#1{\rlap{#1}\hss}
+\def\makeRRlabel#1{\hss\llap{#1}}
+\def\makenewlabel#1{#1}
+%
+\def\@listI{\leftmargin\leftmargini
+ \parsep \z@
+ \topsep 6pt plus 1pt minus 1pt
+ \itemsep \z@ plus .1pt
+}
+\let\@listi\@listI
+\@listi
+\def\@listii{\leftmargin\leftmarginii
+ \labelwidth\leftmarginii\advance\labelwidth-\labelsep
+ \topsep 6pt plus 1pt minus 1pt
+ \parsep \z@
+ \itemsep \z@ plus .1pt
+}
+\def\@listiii{\leftmargin\leftmarginiii
+ \labelwidth\leftmarginiii\advance\labelwidth-\labelsep
+ \topsep 6pt plus 1pt minus 1pt
+ \parsep \z@
+ \partopsep \z@
+ \itemsep \topsep
+}
+\def\@listiv{\leftmargin\leftmarginiv
+ \labelwidth\leftmarginiv\advance\labelwidth-\labelsep
+}
+\def\@listv{\leftmargin\leftmarginv
+ \labelwidth\leftmarginv\advance\labelwidth-\labelsep
+}
+\def\@listvi{\leftmargin\leftmarginvi
+ \labelwidth\leftmarginvi\advance\labelwidth-\labelsep
+}
+%
+% ITEMIZE
+\def\itemize{%
+ \ifnum \@itemdepth >3 \@toodeep
+ \else \advance\@itemdepth \@ne
+ \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
+ \list{\csname\@itemitem\endcsname}%
+ {\let\makelabel\makeRRlabel}%
+ \leftmargin 3.5em\labelsep 0.5em\itemindent 2.0em\labelwidth 0.5em%
+ \fi}
+\def\labelitemi{$\bullet$}
+\def\labelitemii{--}
+\def\labelitemiii{$\cdot$}
+\def\labelitemiv{*}
+%
+% ENUMERATE
+% -- enumerate with optional argument to set left margin...
+\def\enumerate{\ifnum \@enumdepth >3 \@toodeep \else
+ \advance\@enumdepth \@ne
+ \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
+ \fi
+ \@ifnextchar [{\@enumeratetwo}{\@enumerateone}%
+}
+\def\@enumeratetwo[#1]{%
+ \list{\csname label\@enumctr\endcsname}%
+ {\settowidth\labelwidth{[#1]}
+ \leftmargin\z@
+ \usecounter{\@enumctr}
+ \let\makelabel\makenewlabel}
+}
+\def\@enumerateone{%
+ \list{\csname label\@enumctr\endcsname}%
+ {\usecounter{\@enumctr}\itemindent=1em
+ \let\makelabel\makenewlabel}}
+%
+\renewcommand\theenumi{{\rm (\roman{enumi})}}
+\renewcommand\theenumii{{\rm (\alph{enumii})}}
+\renewcommand\theenumiii{{\rm \arabic{enumiii}.}}
+\renewcommand\theenumiv{{\rm \Alph{enumiv}.}}
+
+\newcommand\labelenumi{\theenumi}
+\newcommand\labelenumii{\theenumii}
+\newcommand\labelenumiii{\theenumiii}
+\newcommand\labelenumiv{\theenumiv}
+
+\renewcommand\p at enumii{\theenumi}
+\renewcommand\p at enumiii{\theenumi(\theenumii)}
+\renewcommand\p at enumiv{\p at enumiii\theenumiii}
+%
+% DESCRIPTION
+%\def\descriptionlabel[1]{\hspace\labelsep\bfseries #1}
+%\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
+% \leftmargin 1em
+% \itemindent-1em
+%}}
+\newcommand\descriptionlabel[1]{\bfseries #1}
+\def\description{\list{}{\labelwidth\z@
+ \leftmargin \z@
+ \itemindent 1em
+}}
+\let\enddescription\endlist
+
+% ****************************************
+% * DISPLAYED TEXT *
+% ****************************************
+%
+% VERSE
+\def\verse{\let\\=\@centercr
+ \list{}{\itemsep\z@
+ \itemindent -\@indentskip
+ \listparindent \itemindent
+ \rightmargin\leftmargin
+ \advance\leftmargin \@indentskip}\item[]}
+\let\endverse\endlist
+%
+% QUOTATION
+\def\quotation{\list{}{\listparindent \smallindent
+% \itemindent\listparindent
+ \leftmargin\z@\rightmargin\leftmargin
+ \parsep 0pt plus 1pt}\item[]\reset at font\small}
+\let\endquotation=\endlist
+%
+% QUOTE
+\def\quote{\list{}{\leftmargin\z@\rightmargin\leftmargin}\item[]\reset at font\small}
+\let\endquote=\endlist
+
+% ****************************************
+% * OTHER ENVIRONMENTS *
+% ****************************************
+%
+% THEOREM
+\def\@begintheorem#1#2{\reset at font\rm \trivlist \item[\hskip \labelsep{\reset at font\bf #1\ #2.}]}
+\def\@opargbegintheorem#1#2#3{\reset at font\rm \trivlist
+ \item[\hskip \labelsep{\reset at font\bf #1\ #2.\ (#3)}]}
+\def\@endtheorem{\endtrivlist}
+%
+% PROOF
+\def\proof{\reset at font\rm \trivlist \item[\hskip \labelsep{\reset at font\it Proof.}]}
+\def\endproof{\hspace*{1em}{\begin{picture}(6.5,6.5)%
+ \put(0,0){\framebox(6.5,6.5){}}\end{picture}}\endtrivlist}
+\@namedef{proof*}{\reset at font\rm \trivlist \item[\hskip \labelsep{\reset at font\it Proof.}]}
+\@namedef{endproof*}{\endtrivlist}
+\def\proofbox{\begin{picture}(6.5,6.5)%
+ \put(0,0){\framebox(6.5,6.5){}}\end{picture}}
+%
+% TITLEPAGE
+\def\titlepage{\@restonecolfalse\if at twocolumn\@restonecoltrue\onecolumn
+ \else \newpage \fi \thispagestyle{empty}\c at page\z@}
+\def\endtitlepage{\if at restonecol\twocolumn \else \newpage \fi}
+
+% ARRAY AND TABULAR
+%
+\setlength\arraycolsep{ 5pt }
+\setlength\tabcolsep{ 6pt }
+\setlength\arrayrulewidth{ .5pt }
+\setlength\doublerulesep{ 1.5pt }
+
+\def\tabular{\def\@halignto{}
+ \def\hline{\noalign{\ifnum0=`}\fi
+ \vskip 3pt
+ \hrule \@height \arrayrulewidth
+% {\hbox to 0.667\textwidth{\hrulefill}}
+ \vskip 3pt
+ \futurelet \@tempa\@xhline}
+ \def\fullhline{\noalign{\ifnum0=`}\fi
+ \vskip 3pt
+ \hrule \@height \arrayrulewidth
+% {\hbox to \textwidth{\hrulefill}}
+ \vskip 3pt
+ \futurelet \@tempa\@xhline}
+ \def\@xhline{\ifx\@tempa\hline
+ \vskip -6pt
+ \vskip \doublerulesep
+ \fi
+ \ifnum0=`{\fi}}
+ \def\@arrayrule{\@addtopreamble{\hskip -.5\arrayrulewidth
+% \vrule \@width \arrayrulewidth
+ \hskip .5\arrayrulewidth}}
+\@tabular
+}
+% TABBING
+%
+\tabbingsep \labelsep
+
+% MINIPAGE
+%
+\skip\@mpfootins = \skip\footins
+
+% FRAMEBOX
+%
+% Space left between box and text by \fbox and \framebox.
+\setlength\fboxsep{3pt}
+% Width of rules in box made by \fbox and \framebox.
+\setlength\fboxrule{\arrayrulewidth}
+
+% ****************************************
+% * TITLE AND ABSTRACT *
+% ****************************************
+%
+\def\maketitle{\par
+ \begingroup
+% \def\thefootnote{\fnsymbol{footnote}}
+% \def\@makefnmark{\hbox to 0pt{$^{\@thefnmark}$\hss}}
+ \if at twocolumn
+ \twocolumn[\vspace*{17pt}\@maketitle]
+ \else
+ \newpage
+ \global\@topnum\z@
+ \@maketitle
+ \fi
+ \thispagestyle{titlepage}
+% \@thanks
+ \endgroup
+% \setcounter{footnote}{0}
+ \let\maketitle\relax
+ \let\@maketitle\relax
+ \gdef\@author{}
+ \gdef\@title{}
+% \gdef\@thanks{}
+ \let\thanks\relax
+}
+\def\and{\end{author at tabular}\vskip 3pt\par
+ \begin{author at tabular}[t]{@{}l@{}}}
+\def\@maketitle{\newpage
+ \vspace*{7pt}
+ {\raggedright \sloppy
+ {\reset at font\huge \bf \@title \par}
+ \vskip 23pt
+ {\reset at font\LARGE
+ \begin{author at tabular}[t]{@{}l@{}}\@author
+ \end{author at tabular}\par}
+ \vskip 22pt
+ }
+ \par\noindent
+ \ifGJ at mreferee
+ \else
+ {\reset at font\small \@date \par}
+ \vskip 22pt
+ \fi
+}
+% abstract/summary
+\def\summary{\if at twocolumn
+ \start at GJbox\@summary
+ \else
+ \@summary
+ \fi}
+\def\endsummary{\if at twocolumn
+ \endlist\finish at GJbox
+ \else
+ \endlist
+ \fi}
+\def\abstract{\if at twocolumn
+ \start at GJbox\@summary
+ \else
+ \@summary
+ \fi}
+\def\endabstract{\if at twocolumn
+ \endlist\finish at GJbox
+ \else
+ \endlist
+ \fi}
+\def\left at zm{10.5pc}
+\ifGJ at mreferee
+ \def\left at zm{1.5pc}
+\fi
+\ifGJ at referee
+ \def\left at zm{1.5pc}
+\fi
+\def\@summary{\list{}{%
+ \labelwidth\z@ \labelsep\z@
+ \leftmargin\left at zm \rightmargin\z@
+ \parsep 0pt plus 1pt}\item[]\reset at font
+ \normalsize{\bf SUMMARY}\\\reset at font\large} % BK GJI 1.1
+
+%
+\newif\ifGJ at keywords
+\def\keywords{\if at twocolumn
+ \start at GJbox\@keywords
+ \else
+ \@keywords
+ \fi
+}
+\def\@keywords{\list{}{%
+ \labelwidth\z@ \labelsep\z@
+ \leftmargin\left at zm \rightmargin\z@
+ \parsep 0pt plus 1pt}\item[]\reset at font\large{\bf Key words: }}
+\def\endkeywords{\if at twocolumn
+ \endlist\addvspace{37pt plus 0.5\baselineskip}\finish at GJbox
+ \else
+ \endlist
+ \fi
+ \@thanks
+ \gdef\@thanks{}
+ \GJ at keywordstrue
+}
+\def\nokeywords{\ifGJ at keywords\else
+ \if at twocolumn \start at GJbox\addvspace{37pt}\finish at GJbox \fi
+ \@thanks
+ \gdef\@thanks{}\fi
+}
+
+\def\author at tabular{\def\@halignto{}\@authortable}
+\let\endauthor at tabular=\endtabular
+%
+\def\author at tabcrone{\vspace{2pt}{\ifnum0=`}\fi%
+ \@xtabularcr[-7pt]\reset at font\small\it
+ \let\\=\author at tabcrtwo\ignorespaces}
+%
+\def\author at tabcrtwo{{\ifnum0=`}\fi\@xtabularcr[-7pt]\reset at font\small\it
+ \let\\=\author at tabcrtwo\ignorespaces}
+%
+\def\@authortable{\leavevmode \hbox \bgroup $\let\@acol\@tabacol
+ \let\@classz\@tabclassz \let\@classiv\@tabclassiv
+ \let\\=\author at tabcrone\ignorespaces \@tabarray}
+
+\def\start at GJbox{\@next\@currbox\@freelist{}{}%
+ \global\setbox\@currbox
+ \vbox\bgroup
+ \hsize \textwidth
+ \@parboxrestore
+}
+\def\finish at GJbox{\par\vskip -\dbltextfloatsep
+ \egroup
+ \global\count\@currbox\tw@
+ \global\@dbltopnum\@ne
+ \global\@dbltoproom\maxdimen\@addtodblcol
+ \global\vsize\@colht
+ \global\@colroom\@colht
+}
+
+% ****************************************
+% * PAGE STYLES *
+% ****************************************
+%
+\mark{{}{}}
+\gdef\@author{\mbox{}}
+\def\author{\@ifnextchar [{\@authortwo}{\@authorone}}
+\def\@authortwo[#1]#2{\gdef\@author{#2}\gdef\@shortauthor{#1}}
+\def\@authorone#1{\gdef\@author{#1}\gdef\@shortauthor{#1}}
+%\def\shortauthor#1{\gdef\@shortauthor{#1}}
+\gdef\@shortauthor{}
+\gdef\@title{\mbox{}}
+\def\title{\@ifnextchar [{\@titletwo}{\@titleone}}
+\def\@titletwo[#1]#2{\gdef\@title{#2}\gdef\@shorttitle{#1}}
+\def\@titleone#1{\gdef\@title{#1}\gdef\@shorttitle{#1}}
+%\def\shorttitle#1{\gdef\@shorttitle{#1}}
+\gdef\@shorttitle{}
+\def\volume#1{\gdef\@volume{#1}}
+\gdef\@volume{000}
+\def\tod at y{\today}
+\def\microfiche#1{\gdef\@microfiche{#1}}
+\gdef\@microfiche{}
+\def\pubyear#1{\gdef\@pubyear{#1}}
+\gdef\@pubyear{0000}
+\def\pagerange#1{\gdef\@pagerange{#1}}
+\gdef\@pagerange{000--000}
+\def\journal#1{\gdef\@journal{#1}}
+\def\plate#1{\gdef\pl at te{#1}}
+\ifx\CUP at mtlplain@loaded\undefined
+ \def\@printed{\qquad Printed \tod at y}
+\else
+ \def\@printed{}
+\fi
+
+\gdef\@journal{ }
+\ifGJ at referee
+ \def\@journal{submitted to {\it Geophys. J. Int.} }
+\fi
+\ifGJ at mreferee
+ \def\@journal{submitted to {\it Geophys. J. Int.}}
+\fi
+%
+% \ps at empty and \ps at plain defined in LATEX.TEX
+%
+\def\@ddell{}
+\if at fasttrack
+ \def\@ddell{F}
+\fi
+\def\ps at headings{\let\@mkboth\markboth
+\ifGJ at mreferee
+ \def\@oddhead{\normalsize\hfill{\it\@shorttitle}\hspace{1.5em}\rm\@ddell\thepage}
+ \def\@oddfoot{}
+ \def\@evenhead{\normalsize\@ddell\thepage\hspace{1.5em}\it\@shortauthor\hfill}
+ \def\@evenfoot{}
+\else
+ \def\@oddhead{\Large\hfill{\it\@shorttitle}\hspace{1.5em}\rm\@ddell\thepage}
+ \def\@oddfoot{}
+ \def\@evenhead{\Large\@ddell\thepage\hspace{1.5em}\it\@shortauthor\hfill}
+ \def\@evenfoot{}
+\fi
+ \def\sectionmark##1{\markboth{##1}{}}
+ \def\subsectionmark##1{\markright{##1}}}
+\def\ps at myheadings{\let\@mkboth\@gobbletwo
+\ifGJ at mreferee
+ \def\@oddhead{\normalsize\hfill\it\rightmark\hspace{1.5em}\rm\@ddell\thepage}
+ \def\@oddfoot{}
+ \def\@evenhead{\normalsize\@ddell\thepage\hspace{1.5em}\it\leftmark\hfill}
+ \def\@evenfoot{}
+\else
+ \def\@oddhead{\Large\hfill\it\rightmark\hspace{1.5em}\rm\@ddell\thepage}
+ \def\@oddfoot{}
+ \def\@evenhead{\Large\@ddell\thepage\hspace{1.5em}\it\leftmark\hfill}
+ \def\@evenfoot{}
+\fi
+ \def\sectionmark##1{}
+ \def\subsectionmark##1{}}
+\def\ps at titlepage{\let\@mkboth\@gobbletwo
+ \def\@oddhead{\footnotesize\@journal\hfill}
+% \raisebox{0pt}[8pt][1pt]{\parbox{0.7\textwidth}{\@journal\\
+% \copyright\ \number\year\ BCS}} \hfill}
+ \def\@oddfoot{}
+ \def\@evenhead{\footnotesize\@journal\hfill}
+% \raisebox{0pt}[8pt][1pt]{\parbox{0.7\textwidth}{\@journal\\
+% \copyright\ \number\year\ BCS}} \hfill}
+ \def\@evenfoot{}
+ \def\sectionmark##1{}
+ \def\subsectionmark##1{}}
+\def\ps at plate{\let\@mkboth\@gobbletwo
+ \def\@oddhead{\footnotesize\pl at te\hfill}\def\@oddfoot{}
+ \def\@evenhead{\footnotesize\pl at te\hfill}\def\@evenfoot{}
+}
+
+% ****************************************
+% * TABLE OF CONTENTS, ETC. *
+% ****************************************
+%
+\def\@pnumwidth{1.55em}
+\def\@tocrmarg {2.55em}
+\def\@dotsep{4.5}
+\setcounter{tocdepth}{2}
+\def\@undottedtocline#1#2#3#4#5{\ifnum #1>\c at tocdepth
+ \else
+ \vskip \z@ plus .2pt
+ {\hangindent #2\relax
+ \rightskip \@tocrmarg \parfillskip -\rightskip
+ \parindent #2\relax \@afterindenttrue
+ \interlinepenalty\@M \leavevmode
+ \@tempdima #3\relax #4\nobreak \hfill \nobreak
+ \hbox to\@pnumwidth{\hfil\reset at font\rm \ }\par}\fi}
+\def\tableofcontents{\@restonecolfalse
+ \if at twocolumn\@restonecoltrue\onecolumn\fi
+ \section*{CONTENTS} \@starttoc{toc}
+ \if at restonecol\twocolumn\fi \par\vspace{12pt}}
+\def\l at part#1#2{\addpenalty{-\@highpenalty}
+ \addvspace{2.25em plus 1pt}
+ \begingroup
+ \parindent \z@ \rightskip \@pnumwidth
+ \parfillskip -\@pnumwidth
+ {\reset at font\normalsize\rm
+ \leavevmode \hspace*{3pc}
+ #1\hfil \hbox to\@pnumwidth{\hss \ }}\par
+ \nobreak \global\@nobreaktrue
+ \everypar{\global\@nobreakfalse\everypar{}}\endgroup}
+\def\l at section#1#2{\addpenalty{\@secpenalty}
+ \@tempdima 1.5em
+ \begingroup
+ \parindent \z@ \rightskip \@pnumwidth
+ \parfillskip -\@pnumwidth \reset at font\rm \leavevmode
+ \advance\leftskip\@tempdima \hskip -\leftskip
+ #1\nobreak\hfil \nobreak\hbox to\@pnumwidth{\hss \ }\par
+ \endgroup}
+\def\l at subsection{\@undottedtocline{2}{1.5em}{2.3em}}
+\def\l at subsubsection{\@undottedtocline{3}{3.8em}{3.2em}}
+\def\l at paragraph{\@undottedtocline{4}{7.0em}{4.1em}}
+\def\l at subparagraph{\@undottedtocline{5}{10em}{5em}}
+\def\listoffigures{\@restonecolfalse
+ \if at twocolumn\@restonecoltrue\onecolumn\fi
+ \section*{LIST OF FIGURES\@mkboth{LIST OF FIGURES}{LIST OF FIGURES}}
+ \@starttoc{lof} \if at restonecol\twocolumn\fi}
+\def\l at figure{\@undottedtocline{1}{1.5em}{2.3em}}
+\def\listoftables{\@restonecolfalse
+ \if at twocolumn\@restonecoltrue\onecolumn\fi
+ \section*{LIST OF TABLES\@mkboth{LIST OF TABLES}{LIST OF TABLES}}
+ \@starttoc{lot} \if at restonecol\twocolumn\fi}
+\let\l at table\l at figure
+
+% ****************************************
+% * BIBLIOGRAPHY *
+% ****************************************
+%
+
+\newcounter{dummy}
+\def\thebibliography#1{\section*{REFERENCES}
+ \addcontentsline{toc}{section}{REFERENCES}
+ \list{}{\usecounter{dummy}%
+ \labelwidth\z@
+ \leftmargin 1.5em
+ \itemsep \z@
+ \itemindent-\leftmargin}
+ \reset at font\small
+ \parindent\z@
+ \parskip\z@ plus .1pt\relax
+ \def\newblock{\hskip .11em plus .33em minus .07em}
+ \sloppy\clubpenalty4000\widowpenalty4000
+ \sfcode`\.=1000\relax
+}
+\let\endthebibliography=\endlist
+\def\@biblabel#1{\hspace*{\labelsep}[#1]}
+
+% For AGU compatability use a {references} environment
+% It is not necessary to use the thebibliography environment. This style
+% defines a references environment that simply sets off the list of references
+% and adjusts spacing parameters. It is not possible to use \bibitems
+% within the references environment. (The \reference command cannot be
+% shortened to \ref; \ref is used in vanilla LaTeX for cross-referencing.)
+%
+% \begin{references}
+% \reference <bibliographic data>
+% \end{references}
+%
+% \markcite{TEXT}
+%
+% Observe that the bibliographic data supplied by the author must also
+% conform to the standards of the journal. I have elected not to burden
+% authors with tedious LaTeX commands which would require many curly braces
+% to delimit the bibliographic fields because many of the journals I have
+% targeted in this project have agreed to reduce typographic overhead (bolding,
+% italicizing, etc.) in reference lists. (See Abt's editorial in ApJ 357.)
+% It is the responsibility of the author to get these fields in the proper
+% order with the correct punctuation; the information will be typeset as is,
+% i.e., in roman with no size or style changes.
+%
+% Macros are provided for many of the oft-referenced journals so that authors
+% may use the LaTeX names rather than having to look up a particular journal's
+% specific abbreviation. In principle, all the journals should be using the
+% same abbreviations, too, but I anticipate some changes in the specific
+% abbreviations before a set is finally settled on. As long as these macros
+% are kept up to date, authors need not be concerned about such editorial
+% changes.
+%
+% Corresponding with the non-BibTeX references environment and \reference
+% command for the reference list is the \markcite command. This can be
+% used to identify in-text citations; in this case, the author provides
+% the actual citation text as opposed to the symbolic tag. The use of
+% this is encouraged, even for journals where no special formatting of
+% citation call-outs is required; it is crucial for the future use of
+% on-line browsers.
+
+\def\references{\section*{REFERENCES}
+ \bgroup\parindent=\z@\parskip=\z@\reset at font\small
+ \def\refpar{\par\hangindent=1em\hangafter=1}}
+\def\endreferences{\refpar\egroup}
+%%\let\endreferences=\endlist
+
+%% \small should probably be \scriptsize to match print version
+
+
+\def\reference{\relax\refpar} % Generic: might be better...
+\def\markcite#1{#1\relax}
+
+
+
+% ****************************************
+% * THE INDEX *
+% ****************************************
+%
+\newif\if at restonecol
+\def\theindex{\section*{INDEX}
+ \addcontentsline{toc}{section}{INDEX}
+ \reset at font\footnotesize \parindent\z@ \parskip\z@ plus .1pt\relax
+ \let\item\@idxitem}
+\def\@idxitem{\par\hangindent 1em}
+\def\subitem {\par\hangindent 1em \hspace*{1em}}
+\def\subsubitem{\par\hangindent 1em\hspace*{1em}}
+\def\endtheindex{\if at restonecol\onecolumn\else\clearpage\fi}
+\def\indexspace{\par\vskip\baselineskip \relax}
+
+% ****************************************
+% * FOOTNOTES *
+% ****************************************
+%
+\def\footnoterule{\kern-3\p@ \hrule width 12pc height \z@ \kern 3\p@}
+
+\renewcommand{\thefootnote}{\mbox{{$\fnsymbol{footnote}$}}}
+
+\def\@fnsymbol#1{\ifcase#1\or \mbox{$\star$}\or \dagger\or \ddagger\or
+ \S \or \P \or \|\or **\or \dagger\dagger
+ \or \ddagger\ddagger\or \S\S\or \P\P\or \|\|\else ***
+ \fi\relax}
+
+\long\def\@makefntext#1{\parindent 1em\noindent
+ $^{\@thefnmark}$\hspace{4pt}#1}
+
+%\long\def\@makefntext#1{\@setpar{\@@par\@tempdima \hsize
+% \advance\@tempdima-18pt\parshape \@ne 18pt\@tempdima}\par
+% \noindent \hbox to \z@{\hss$^{\@thefnmark}$\hspace{0.5em}}#1}
+
+% ****************************************
+% * FIGURES AND TABLES *
+% ****************************************
+%
+\setcounter{topnumber}{2}
+\renewcommand\topfraction{.9}
+\setcounter{bottomnumber}{1}
+\renewcommand\bottomfraction{.9}
+\setcounter{totalnumber}{3}
+\renewcommand\textfraction{.1}
+\renewcommand\floatpagefraction{.9}
+\setcounter{dbltopnumber}{2}
+\renewcommand\dbltopfraction{.9}
+\renewcommand\dblfloatpagefraction{.9}
+
+\newif\ifst at rredfloat
+\newcounter{table}
+\def\thetable{\@arabic\c at table}
+\def\fps at table{tbp}
+\def\ftype at table{1}
+\def\fstyle at table{\reset at font\small\rm}
+\def\ext at table{lot}
+\def\fnum at table{Table \thetable}
+\def\table{\let\@makecaption=\GJ at maketablecaption%
+ \@float{table}\fstyle at table}
+\let\endtable\end at float
+\@namedef{table*}{\st at rredfloattrue\let\@makecaption=\GJ at maketablecaption%
+ \@dblfloat{table}\centering\fstyle at table}
+\@namedef{endtable*}{\end at dblfloat\st at rredfloatfalse}
+
+\newcounter{figure}
+\def\thefigure{\@arabic\c at figure}
+\def\fps at figure{tbp}
+\def\ftype at figure{2}
+\def\fstyle at figure{\reset at font\small\rm}
+\def\ext at figure{lof}
+\def\fnum at figure{Figure \thefigure}
+\def\figure{\let\@makecaption=\GJ at makefigurecaption%
+ \@float{figure}\fstyle at figure}
+\let\endfigure\end at float
+\@namedef{figure*}{\st at rredfloattrue\let\@makecaption=\GJ at makefigurecaption%
+ \@dblfloat{figure}\centering\fstyle at figure}
+\@namedef{endfigure*}{\end at dblfloat\st at rredfloatfalse}
+
+\long\def\GJ at makefigurecaption#1#2{\vskip 6pt
+ \setbox\@tempboxa\hbox{\reset at font\small{\bf #1.} #2}
+ \ifdim \wd\@tempboxa >\hsize
+ \reset at font\small{\bf #1.} #2\par
+ \else
+ \ifst at rredfloat
+ \hbox to\hsize{\hfill\box\@tempboxa\hfill}
+ \else
+ \hbox to\hsize{\box\@tempboxa\hfill}
+ \fi
+ \fi
+ \vskip 6pt
+}
+
+\long\def\GJ at maketablecaption#1#2{\vskip 6pt
+ \setbox\@tempboxa\hbox{\reset at font\small{\bf #1.} #2}
+ \ifdim \wd\@tempboxa >\hsize
+ \reset at font\small{\bf #1.} #2\par
+ \else
+ \hbox to\hsize{\box\@tempboxa\hfill}
+ \fi
+ \vskip 6pt
+}
+
+%\def\caption{\refstepcounter\@captype \@dblarg{\@caption\@captype}}
+\def\caption{\@ifstar{\GJ at caption\@captype}%
+ {\refstepcounter\@captype \@dblarg{\@caption\@captype}}%
+}
+\long\def\GJ at caption#1#2{%\par
+ \begingroup
+ \@parboxrestore
+ \reset at font\normalsize
+ \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #2}\par
+ \endgroup}
+
+% ****************************************
+% * Specials *
+% ****************************************
+%
+%
+% The following code is taken from authordate.sty, by David Rhead, of
+% the Cripps Computing Centre (February 1990), with some modifications
+% by ggw. It is intended for documents
+% that use the author-date citation system. When used in conjunction with
+% authordate1.bst, ... , authordate4.bst, it allows citations of the
+% form \shortcite{bloggs-60} as well as the usual
+% \cite{bloggs-60}.
+% When
+% ... \cite{bloggs-60} ... \shortcite{bloggs-60} ...
+% appears in the input file,
+% ... (Bloggs, 1960) ... (1960) ...
+% appears in the final document.
+%
+% Code taken from apalike.sty.
+%
+\ifGJ at extra
+\else
+\def\@cite#1#2{(#1\if at tempswa , #2\fi)}
+\def\@cited#1#2{#1\if at tempswa (#2)\fi}
+\def\@biblabel#1{}
+
+% Set length of hanging indentation for bibliography entries
+%
+\newlength{\bibhang}
+\setlength{\bibhang}{1em}
+\fi
+% Define default title and page-head text.
+%
+\def\bibtitle{References}
+\def\bibheadtitle{REFERENCES}
+
+% Code taken from aaai.sty.
+%
+% don't box citations, add space between multiple citations, separate with ;
+\def\@citex[#1]#2{\if at filesw\immediate\write\@auxout{\string\citation{#2}}\fi
+ \def\@citea{}\@cite{\@for\@citeb:=#2\do
+ {\@citea\def\@citea{; }\@ifundefined
+ {b@\@citeb}{@warning
+ {Citation `\@citeb' on page \thepage \space undefined}}%
+{\csname b@\@citeb\endcsname}}}{#1}}
+% Allow short (name-less) citations, when used in
+% conjunction with a bibliography style that creates labels like
+% \citename{<names> }<year>
+\let\@internalcite\cite
+\def\cite{\def\citename##1{##1}\@internalcite}
+\def\shortcite{\def\citename##1{}\@internalcite}
+
+
+\def\bsp{\medskip\reset at font\small\noindent This paper has been produced
+ using the Blackwell Scientific Publications GJI \LaTeX2e\ class file.}
+
+
+% ****************************************
+% * FLEQN *
+% ****************************************
+%
+%%
+% FLEQN DOCUMENT-STYLE OPTION - released 9 March 1987
+% for LaTeX version 2.09
+% Copyright (C) 1987 by Leslie Lamport
+%
+% The following commands make the displayed math environments flush left,
+% with an indentation of \mathindent from the prevailing left margin.
+
+\def\[{\relax\ifmmode\@badmath\else\begin{trivlist}\item[]\leavevmode
+ \hbox to\linewidth\bgroup$
+ \displaystyle
+ \hskip\mathindent\bgroup\fi}
+
+\def\]{\relax\ifmmode \egroup $\hfil
+ \egroup \end{trivlist}\else \@badmath \fi}
+
+\def\equation{\refstepcounter{equation}\trivlist \item[]\leavevmode
+ \hbox to\linewidth\bgroup $
+ \displaystyle
+\hskip\mathindent}
+
+
+\def\endequation{$\hfil
+ \displaywidth\linewidth\@eqnnum\egroup \endtrivlist}
+
+\def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
+\global\@eqnswtrue
+\global\@eqcnt\z@\tabskip\mathindent\let\\=\@eqncr
+\abovedisplayskip\topsep\ifvmode\advance\abovedisplayskip\partopsep\fi
+\belowdisplayskip\abovedisplayskip
+\belowdisplayshortskip\abovedisplayskip
+\abovedisplayshortskip\abovedisplayskip
+$$\halign
+to \linewidth\bgroup\@eqnsel\hskip\@centering$\displaystyle\tabskip\z@
+ {##}$&\global\@eqcnt\@ne \hskip 2\arraycolsep \hfil${##}$\hfil
+ &\global\@eqcnt\tw@ \hskip 2\arraycolsep $\displaystyle{##}$\hfil
+ \tabskip\@centering&\llap{##}\tabskip\z@\cr}
+
+\def\endeqnarray{\@@eqncr\egroup
+ \global\advance\c at equation\m at ne$$\global\@ignoretrue}
+
+\newdimen\mathindent
+\mathindent = \z@
+
+\ifGJ at mreferee
+ \setlength {\mathindent} {2 mm}
+\fi
+
+% ****************************************
+% * MISCELLANEOUS *
+% ****************************************
+%
+% DATE
+\def\today{\number\day\ \ifcase\month\or
+ January\or February\or March\or April\or May\or June\or
+ July\or August\or September\or October\or November\or December
+ \fi \ \number\year}
+
+% ****************************************
+% * INITIALIZATION *
+% ****************************************
+%
+\flushbottom
+\ps at headings
+\ifGJ at galley
+ \raggedbottom
+ \ps at empty
+\fi
+\ifGJ at referee
+ \raggedbottom
+\fi
+\pagenumbering{arabic}
+\if at twocolumn
+ \twocolumn
+ \sloppy
+\else
+ \onecolumn
+\fi
+\frenchspacing
+
+
+%%% ACKNOWLEDGEMENTS
+
+\newenvironment{acknowledgments}{\section*{ACKNOWLEDGMENTS}}{}%
+\newenvironment{acknowledgment}{\section*{ACKNOWLEDGMENT}}{}%
+
+
+%%% COMMON JOURNALS
+
+\newcommand{\areps}{\textit{Ann.\ Rev.\ Earth Planet\ Sci.}, }
+\newcommand{\bssa}{\textit{Bull.\ seism.\ Soc.\ Am.}, }
+\newcommand{\eos}{\textit{Eos Trans.\ AGU}, }
+\newcommand{\eps}{\textit{Earth~Planets~Space},}
+\newcommand{\epsl}{\textit{Earth~Planet.\ Sci.\ Lett.}, }
+\newcommand{\gca}{\textit{Geochim.\ Cosmochim.\ Acta}, }
+\newcommand{\geo}{\textit{Geology}, }
+\newcommand{\geop}{\textit{Geophysics}, }
+\newcommand{\gji}{\textit{Geophys.\ J\ Int.}, }
+\newcommand{\gjras}{\textit{Geophys.\ J.\ R.\ astr.\ Soc.}, }
+\newcommand{\grl}{\textit{Geophys.\ Res.\ Lett.}, }
+\newcommand{\gsab}{\textit{Geol.\ Soc.\ Am.\ Bull.},}
+\newcommand{\gs}{\textit{Geophys.\ Surv.}, }
+\newcommand{\jgr}{\textit{J.\ geophys.\ Res.}, }
+\newcommand{\jpo}{\textit{J.\ Phys.\ Oceanogr.}, }
+\newcommand{\jseis}{\textit{J.~Seismology}, }
+\newcommand{\mnras}{\textit{Mon.\ Not.\ R.\ astr.\ Soc.}, }
+\newcommand{\pag}{\textit{Pure Appl.\ Geophys.},}
+\newcommand{\pepi}{\textit{Phys.\ Earth Planet.\ Inter.}, }
+\newcommand{\rg}{\textit{Rev.\ Geophys.}, }
+\newcommand{\tecto}{\textit{Tectonophysics}, }
+
+\ifGJ at extra
+\def\refname{REFERENCES}
+\usepackage{gji_extra}
+\fi
+% end of GJI.cls
Added: seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/newcommands.tex
===================================================================
--- seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/newcommands.tex (rev 0)
+++ seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/newcommands.tex 2012-08-07 23:03:13 UTC (rev 20558)
@@ -0,0 +1,478 @@
+%bold lowercase roman letters
+
+\newcommand{\ba}{\mbox{${\bf a}$}}
+\newcommand{\bb}{\mbox{${\bf b}$}}
+\newcommand{\bc}{\mbox{${\bf c}$}}
+\newcommand{\bd}{\mbox{${\bf d}$}}
+\newcommand{\be}{\mbox{${\bf e}$}}
+\newcommand{\bef}{\mbox{${\bf f}$}}
+\newcommand{\bg}{\mbox{${\bf g}$}}
+\newcommand{\bh}{\mbox{${\bf h}$}}
+\newcommand{\bi}{\mbox{${\bf i}$}}
+\newcommand{\bj}{\mbox{${\bf j}$}}
+\newcommand{\bk}{\mbox{${\bf k}$}}
+\newcommand{\bl}{\mbox{${\bf l}$}}
+\newcommand{\bm}{\mbox{${\bf m}$}}
+\newcommand{\bn}{\mbox{${\bf n}$}}
+\newcommand{\bo}{\mbox{${\bf o}$}}
+\newcommand{\bp}{\mbox{${\bf p}$}}
+\newcommand{\bq}{\mbox{${\bf q}$}}
+\newcommand{\br}{\mbox{${\bf r}$}}
+\newcommand{\bs}{\mbox{${\bf s}$}}
+\newcommand{\bt}{\mbox{${\bf t}$}}
+\newcommand{\bu}{\mbox{${\bf u}$}}
+\newcommand{\bv}{\mbox{${\bf v}$}}
+\newcommand{\bw}{\mbox{${\bf w}$}}
+\newcommand{\bx}{\mbox{${\bf x}$}}
+\newcommand{\by}{\mbox{${\bf y}$}}
+\newcommand{\bz}{\mbox{${\bf z}$}}
+
+%bold uppercase roman letters
+
+\newcommand{\bA}{\mbox{${\bf A}$}}
+\newcommand{\bB}{\mbox{${\bf B}$}}
+\newcommand{\bC}{\mbox{${\bf C}$}}
+\newcommand{\bD}{\mbox{${\bf D}$}}
+\newcommand{\bE}{\mbox{${\bf E}$}}
+\newcommand{\bF}{\mbox{${\bf F}$}}
+\newcommand{\bG}{\mbox{${\bf G}$}}
+\newcommand{\bH}{\mbox{${\bf H}$}}
+\newcommand{\bI}{\mbox{${\bf I}$}}
+\newcommand{\bJ}{\mbox{${\bf J}$}}
+\newcommand{\bK}{\mbox{${\bf K}$}}
+\newcommand{\bL}{\mbox{${\bf L}$}}
+\newcommand{\bM}{\mbox{${\bf M}$}}
+\newcommand{\bN}{\mbox{${\bf N}$}}
+\newcommand{\bO}{\mbox{${\bf O}$}}
+\newcommand{\bP}{\mbox{${\bf P}$}}
+\newcommand{\bQ}{\mbox{${\bf Q}$}}
+\newcommand{\bR}{\mbox{${\bf R}$}}
+\newcommand{\bS}{\mbox{${\bf S}$}}
+\newcommand{\bT}{\mbox{${\bf T}$}}
+\newcommand{\bU}{\mbox{${\bf U}$}}
+\newcommand{\bV}{\mbox{${\bf V}$}}
+\newcommand{\bW}{\mbox{${\bf W}$}}
+\newcommand{\bX}{\mbox{${\bf X}$}}
+\newcommand{\bY}{\mbox{${\bf Y}$}}
+\newcommand{\bZ}{\mbox{${\bf Z}$}}
+
+%script upper case letters
+
+\newcommand{\sA}{\mbox{$\cal A$}}
+\newcommand{\sB}{\mbox{$\cal B$}}
+\newcommand{\sC}{\mbox{$\cal C$}}
+\newcommand{\sD}{\mbox{$\cal D$}}
+\newcommand{\sE}{\mbox{$\cal E$}}
+\newcommand{\sF}{\mbox{$\cal F$}}
+\newcommand{\sG}{\mbox{$\cal G$}}
+\newcommand{\sH}{\mbox{$\cal H$}}
+\newcommand{\sI}{\mbox{$\cal I$}}
+\newcommand{\sJ}{\mbox{$\cal J$}}
+\newcommand{\sK}{\mbox{$\cal K$}}
+\newcommand{\sL}{\mbox{$\cal L$}}
+\newcommand{\sM}{\mbox{$\cal M$}}
+\newcommand{\sN}{\mbox{$\cal N$}}
+\newcommand{\sO}{\mbox{$\cal O$}}
+\newcommand{\sP}{\mbox{$\cal P$}}
+\newcommand{\sQ}{\mbox{$\cal Q$}}
+\newcommand{\sR}{\mbox{$\cal R$}}
+\newcommand{\sS}{\mbox{$\cal S$}}
+\newcommand{\sT}{\mbox{$\cal T$}}
+\newcommand{\sU}{\mbox{$\cal U$}}
+\newcommand{\sV}{\mbox{$\cal V$}}
+\newcommand{\sW}{\mbox{$\cal W$}}
+\newcommand{\sX}{\mbox{$\cal X$}}
+\newcommand{\sY}{\mbox{$\cal Y$}}
+\newcommand{\sZ}{\mbox{$\cal Z$}}
+
+%bold upper case script letters
+
+\newcommand{\bsA}{\mbox{\boldmath$\cal A$}}
+\newcommand{\bsB}{\mbox{\boldmath$\cal B$}}
+\newcommand{\bsC}{\mbox{\boldmath$\cal C$}}
+\newcommand{\bsD}{\mbox{\boldmath$\cal D$}}
+\newcommand{\bsE}{\mbox{\boldmath$\cal E$}}
+\newcommand{\bsF}{\mbox{\boldmath$\cal F$}}
+\newcommand{\bsG}{\mbox{\boldmath$\cal G$}}
+\newcommand{\bsH}{\mbox{\boldmath$\cal H$}}
+\newcommand{\bsI}{\mbox{\boldmath$\cal I$}}
+\newcommand{\bsJ}{\mbox{\boldmath$\cal J$}}
+\newcommand{\bsK}{\mbox{\boldmath$\cal K$}}
+\newcommand{\bsL}{\mbox{\boldmath$\cal L$}}
+\newcommand{\bsM}{\mbox{\boldmath$\cal M$}}
+\newcommand{\bsN}{\mbox{\boldmath$\cal N$}}
+\newcommand{\bsO}{\mbox{\boldmath$\cal O$}}
+\newcommand{\bsP}{\mbox{\boldmath$\cal P$}}
+\newcommand{\bsQ}{\mbox{\boldmath$\cal Q$}}
+\newcommand{\bsR}{\mbox{\boldmath$\cal R$}}
+\newcommand{\bsS}{\mbox{\boldmath$\cal S$}}
+\newcommand{\bsT}{\mbox{\boldmath$\cal T$}}
+\newcommand{\bsU}{\mbox{\boldmath$\cal U$}}
+\newcommand{\bsV}{\mbox{\boldmath$\cal V$}}
+\newcommand{\bsW}{\mbox{\boldmath$\cal W$}}
+\newcommand{\bsX}{\mbox{\boldmath$\cal X$}}
+\newcommand{\bsY}{\mbox{\boldmath$\cal Y$}}
+\newcommand{\bsZ}{\mbox{\boldmath$\cal Z$}}
+
+%upper case sans serif letters
+
+\newcommand{\ssA}{\mbox{${\sf A}$}}
+\newcommand{\ssB}{\mbox{${\sf B}$}}
+\newcommand{\ssC}{\mbox{${\sf C}$}}
+\newcommand{\ssD}{\mbox{${\sf D}$}}
+\newcommand{\ssE}{\mbox{${\sf E}$}}
+\newcommand{\ssF}{\mbox{${\sf F}$}}
+\newcommand{\ssG}{\mbox{${\sf G}$}}
+\newcommand{\ssH}{\mbox{${\sf H}$}}
+\newcommand{\ssI}{\mbox{${\sf I}$}}
+\newcommand{\ssJ}{\mbox{${\sf J}$}}
+\newcommand{\ssK}{\mbox{${\sf K}$}}
+\newcommand{\ssL}{\mbox{${\sf L}$}}
+\newcommand{\ssM}{\mbox{${\sf M}$}}
+\newcommand{\ssN}{\mbox{${\sf N}$}}
+\newcommand{\ssO}{\mbox{${\sf O}$}}
+\newcommand{\ssP}{\mbox{${\sf P}$}}
+\newcommand{\ssQ}{\mbox{${\sf Q}$}}
+\newcommand{\ssR}{\mbox{${\sf R}$}}
+\newcommand{\ssS}{\mbox{${\sf S}$}}
+\newcommand{\ssT}{\mbox{${\sf T}$}}
+\newcommand{\ssU}{\mbox{${\sf U}$}}
+\newcommand{\ssV}{\mbox{${\sf V}$}}
+\newcommand{\ssW}{\mbox{${\sf W}$}}
+\newcommand{\ssX}{\mbox{${\sf X}$}}
+\newcommand{\ssY}{\mbox{${\sf Y}$}}
+\newcommand{\ssZ}{\mbox{${\sf Z}$}}
+
+%lower case sans serif letters
+
+\newcommand{\ssa}{\mbox{${\sf a}$}}
+\newcommand{\ssb}{\mbox{${\sf b}$}}
+\newcommand{\ssc}{\mbox{${\sf c}$}}
+\newcommand{\ssd}{\mbox{${\sf d}$}}
+\newcommand{\sse}{\mbox{${\sf e}$}}
+\newcommand{\ssf}{\mbox{${\sf f}$}}
+\newcommand{\ssg}{\mbox{${\sf g}$}}
+\newcommand{\ssh}{\mbox{${\sf h}$}}
+\newcommand{\ssi}{\mbox{${\sf i}$}}
+\newcommand{\ssj}{\mbox{${\sf j}$}}
+\newcommand{\ssk}{\mbox{${\sf k}$}}
+\newcommand{\ssl}{\mbox{${\sf l}$}}
+\newcommand{\ssm}{\mbox{${\sf m}$}}
+\newcommand{\ssn}{\mbox{${\sf n}$}}
+\newcommand{\sso}{\mbox{${\sf o}$}}
+\newcommand{\ssp}{\mbox{${\sf p}$}}
+\newcommand{\ssq}{\mbox{${\sf q}$}}
+\newcommand{\ssr}{\mbox{${\sf r}$}}
+\newcommand{\sss}{\mbox{${\sf s}$}}
+\newcommand{\sst}{\mbox{${\sf t}$}}
+\newcommand{\ssu}{\mbox{${\sf u}$}}
+\newcommand{\ssv}{\mbox{${\sf v}$}}
+\newcommand{\ssw}{\mbox{${\sf w}$}}
+\newcommand{\ssx}{\mbox{${\sf x}$}}
+\newcommand{\ssy}{\mbox{${\sf y}$}}
+\newcommand{\ssz}{\mbox{${\sf z}$}}
+
+%bold lowercase greek letters
+
+\newcommand{\balpha}{\mbox{\boldmath $\bf \alpha$}}
+\newcommand{\bbeta}{\mbox{\boldmath $\bf \beta$}}
+\newcommand{\bgamma}{\mbox{\boldmath $\bf \gamma$}}
+\newcommand{\bdelta}{\mbox{\boldmath $\bf \delta$}}
+\newcommand{\bepsilon}{\mbox{\boldmath $\bf \varepsilon$}}
+\newcommand{\beps}{\mbox{\boldmath $\bf \varepsilon$}}
+\newcommand{\bzeta}{\mbox{\boldmath $\bf \zeta$}}
+\newcommand{\boeta}{\mbox{\boldmath $\bf \eta$}}
+\newcommand{\btheta}{\mbox{\boldmath $\bf \theta$}}
+\newcommand{\bkappa}{\mbox{\boldmath $\bf \kappa$}}
+\newcommand{\blambda}{\mbox{\boldmath $\bf \lambda$}}
+\newcommand{\bmu}{\mbox{\boldmath $\bf \mu$}}
+\newcommand{\bnu}{\mbox{\boldmath $\bf \nu$}}
+\newcommand{\bxi}{\mbox{\boldmath $\bf \xi$}}
+\newcommand{\bpi}{\mbox{\boldmath $\bf \pi$}}
+\newcommand{\bsigma}{\mbox{\boldmath $\bf \sigma$}}
+\newcommand{\btau}{\mbox{\boldmath $\bf \tau$}}
+\newcommand{\bupsilon}{\mbox{\boldmath $\bf \upsilon$}}
+\newcommand{\bphi}{\mbox{\boldmath $\bf \phi$}}
+\newcommand{\bchi}{\mbox{\boldmath $\bf \chi$}}
+\newcommand{\bpsi}{\mbox{\boldmath$ \bf \psi$}}
+\newcommand{\bomega}{\mbox{\boldmath $\bf \omega$}}
+\newcommand{\bom}{\mbox{\boldmath $\bf \omega$}}
+
+%bold uppercase greek letters
+
+\newcommand{\bGamma}{\mbox{\boldmath $\bf \Gamma$}}
+\newcommand{\bDelta}{\mbox{\boldmath $\bf \Delta$}}
+\newcommand{\bLambda}{\mbox{\boldmath $\bf \Lambda$}}
+\newcommand{\bXi}{\mbox{\boldmath $\bf \Xi$}}
+\newcommand{\bPi}{\mbox{\boldmath $\bf \Pi$}}
+\newcommand{\bSigma}{\mbox{\boldmath $\bf \Sigma$}}
+\newcommand{\bUpsilon}{\mbox{\boldmath $\bf \Upsilon$}}
+\newcommand{\bPhi}{\mbox{\boldmath $\bf \Phi$}}
+\newcommand{\bPsi}{\mbox{\boldmath $\bf \Psi$}}
+\newcommand{\bOmega}{\mbox{\boldmath $\bf \Omega$}}
+\newcommand{\bOm}{\mbox{\boldmath $\bf \Omega$}}
+
+%sans serif greek letters and numbers
+
+\newcommand{\ssDelta}{\mbox{${\sf \Delta}$}}
+\newcommand{\ssLambda}{\mbox{${\sf \Lambda}$}}
+\newcommand{\ssGamma}{\mbox{${\sf \Gamma}$}}
+\newcommand{\ssOmega}{\mbox{${\sf \Omega}$}}
+\newcommand{\ssSigma}{\mbox{${\sf \Sigma}$}}
+\newcommand{\sszero}{\mbox{${\sf 0}$}}
+
+%bold unit vectors
+
+\newcommand{\bCh}{\mbox{$\hat{\mbox{${\bf C}$}}$}}
+\newcommand{\bGh}{\mbox{$\hat{\mbox{${\bf G}$}}$}}
+\newcommand{\bah}{\mbox{$\hat{\mbox{${\bf a}$}}$}}
+\newcommand{\bbh}{\mbox{$\hat{\mbox{${\bf b}$}}$}}
+\newcommand{\beh}{\mbox{$\hat{\mbox{${\bf e}$}}$}}
+\newcommand{\bgh}{\mbox{$\hat{\mbox{${\bf g}$}}$}}
+\newcommand{\bkh}{\mbox{$\hat{\mbox{${\bf k}$}}$}}
+\newcommand{\bnh}{\mbox{$\hat{\mbox{${\bf n}$}}$}}
+\newcommand{\bph}{\mbox{$\hat{\mbox{${\bf p}$}}$}}
+\newcommand{\brh}{\mbox{$\hat{\mbox{${\bf r}$}}$}}
+\newcommand{\bth}{\mbox{$\hat{\mbox{${\bf t}$}}$}}
+\newcommand{\bxh}{\mbox{$\hat{\mbox{${\bf x}$}}$}}
+\newcommand{\byh}{\mbox{$\hat{\mbox{${\bf y}$}}$}}
+\newcommand{\bzh}{\mbox{$\hat{\mbox{${\bf z}$}}$}}
+\newcommand{\bnuh}{\mbox{$\hat{\mbox{\boldmath $\bf \nu$}}$}}
+\newcommand{\betah}{\mbox{$\hat{\mbox{\boldmath $\bf \eta$}}$}}
+\newcommand{\bthetah}{\mbox{$\hat{\mbox{\boldmath $\bf \theta$}}$}}
+\newcommand{\bphih}{\mbox{$\hat{\mbox{\boldmath $\bf \phi$}}$}}
+\newcommand{\bDeltah}{\mbox{$\hat{\mbox{\boldmath $\bf \Delta$}}$}}
+\newcommand{\bThetah}{\mbox{$\hat{\mbox{\boldmath $\bf \Theta$}}$}}
+\newcommand{\bPhih}{\mbox{$\hat{\mbox{\boldmath $\bf \Phi$}}$}}
+\newcommand{\bsigmah}{\mbox{$\hat{\mbox{\boldmath $\bf \sigma$}}$}}
+\newcommand{\bthetahpr}{\mbox{$\hat{\mbox{\boldmath $\bf \theta$}}
+ ^{\raise-.5ex\hbox{$\scriptstyle\prime$}}$}}
+\newcommand{\bphihpr}{\mbox{$\hat{\mbox{\boldmath $\bf \phi$}}
+ ^{\raise-.5ex\hbox{$\scriptstyle\prime$}}$}}
+\newcommand{\bThetahpr}{\mbox{$\hat{\mbox{\boldmath $\bf \Theta$}}
+ ^{\raise-.5ex\hbox{$\scriptstyle\prime$}}$}}
+\newcommand{\bPhihpr}{\mbox{$\hat{\mbox{\boldmath $\bf \Phi$}}
+ ^{\raise-.5ex\hbox{$\scriptstyle\prime$}}$}}
+
+%subscripts
+
+\newcommand{\spar}{\mbox{$\scriptstyle\partial$}}
+\newcommand{\sbdel}{\mbox{\boldmath $\scriptstyle\nabla$}}
+\newcommand{\subk}{\mbox{\scriptsize\bf k}}
+\newcommand{\subp}{\mbox{\scriptsize\bf p}}
+\newcommand{\subr}{\mbox{\scriptsize\bf r}}
+\newcommand{\subs}{\mbox{\scriptsize\bf s}}
+\newcommand{\subx}{\mbox{\scriptsize\bf x}}
+\newcommand{\subxi}{\mbox{$\scriptstyle{\bf \xi}$}}
+\newcommand{\subrho}{\mbox{$\scriptstyle\rho$}}
+\newcommand{\subphi}{\mbox{$\scriptstyle\phi$}}
+\newcommand{\subpsi}{\mbox{$\scriptstyle\psi$}}
+\newcommand{\subnhat}{\mbox{\scriptsize{$\hat{\mbox{${\bf n}$}}$}}}
+\newcommand{\subearth}{\raise.15ex\hbox{$\scriptstyle\oplus$}}
+\newcommand{\subhalf}{\mbox{$\scriptstyle\frac{1}{2}$}}
+\newcommand{\subspace}{\raise.25ex\hbox{$\scriptscriptstyle\bigcirc$}}
+
+%fractions
+
+\newcommand{\half}{\mbox{$\frac{1}{2}$}}
+\newcommand{\third}{\mbox{$\frac{1}{3}$}}
+\newcommand{\fifth}{\mbox{$\frac{1}{5}$}}
+\newcommand{\fourth}{\mbox{$\frac{1}{4}$}}
+% DK DK for GJI style file \newcommand{\twothirds}{\mbox{$\frac{2}{3}$}}
+\newcommand{\fourthirds}{\mbox{$\frac{4}{3}$}}
+\newcommand{\threehalves}{\mbox{$\frac{3}{2}$}}
+\newcommand{\fivehalves}{\mbox{$\frac{5}{2}$}}
+\newcommand{\threefourths}{\mbox{$\frac{3}{4}$}}
+\newcommand{\threeeighths}{\mbox{$\frac{3}{8}$}}
+\newcommand{\fivesixteenths}{\mbox{$\frac{5}{16}$}}
+\newcommand{\fivefourths}{\mbox{$\frac{5}{4}$}}
+\newcommand{\ninefourths}{\mbox{$\frac{9}{4}$}}
+\newcommand{\threefifths}{\mbox{$\frac{3}{5}$}}
+\newcommand{\fivethirds}{\mbox{$\frac{5}{3}$}}
+\newcommand{\eightthirds}{\mbox{$\frac{8}{3}$}}
+\newcommand{\fourninths}{\mbox{$\frac{4}{9}$}}
+\newcommand{\fiveninths}{\mbox{$\frac{5}{9}$}}
+\newcommand{\sixteenthirds}{\mbox{$\frac{16}{3}$}}
+\newcommand{\sixteenninths}{\mbox{$\frac{16}{9}$}}
+\newcommand{\nineteenhalves}{\mbox{$\frac{19}{2}$}}
+\newcommand{\quart}{\mbox{$\frac{1}{4}$}}
+\newcommand{\eighth}{\mbox{$\frac{1}{8}$}}
+\newcommand{\ninth}{\mbox{$\frac{1}{9}$}}
+\newcommand{\tenth}{\mbox{$\frac{1}{10}$}}
+\newcommand{\fifteenth}{\mbox{$\frac{1}{15}$}}
+\newcommand{\sixth}{\mbox{$\frac{1}{6}$}}
+\newcommand{\seventhirds}{\mbox{$\frac{7}{3}$}}
+\newcommand{\invpi}{\mbox{$\frac{1}{\pi}$}}
+\newcommand{\twoinvpi}{\mbox{$\frac{2}{\pi}$}}
+\newcommand{\invtwopi}{\mbox{$\frac{1}{2\pi}$}}
+
+%other miscellaneous definitions
+
+\newcommand{\om}{\mbox{$\omega$}}
+\newcommand{\Om}{\mbox{$\Omega$}}
+\newcommand{\ep}{\mbox{$\varepsilon$}}
+% DK DK for GJI style file \newcommand{\eps}{\mbox{$\varepsilon$}}
+\newcommand{\p}{\mbox{$\partial$}}
+\newcommand{\del}{\mbox{$\nabla$}}
+\newcommand{\bdel}{\mbox{\boldmath $\nabla$}}
+\newcommand{\bzero}{\mbox{${\bf 0}$}}
+\renewcommand{\Re}{\mbox{${\rm R}$}}
+\renewcommand{\Im}{\mbox{${\rm I}$}}
+\newcommand{\real}{\mbox{$\Re{\rm e}$}}
+\newcommand{\imag}{\mbox{$\Im{\rm m}$}}
+\newcommand{\sqL}{\mbox{$k$}}
+\newcommand{\sqLinv}{\mbox{$k^{-1}$}}
+\newcommand{\nunl}{\mbox{${}_n\nu_l$}}
+% DK DK for GJI style file \newcommand{\earth}{\raise.15ex\hbox{$\oplus$}}
+\newcommand{\tdot}{\,.\hspace{-0.98 mm}\raise.6ex\hbox{.}
+ \hspace{-0.98 mm}\raise1.2ex\hbox{.}\,}
+\newcommand{\pvint}{\mathbin{\int{\mkern-19.2mu}-}}
+\newcommand{\allspace}{\raise.25ex\hbox{$\scriptstyle\bigcirc$}}
+
+%miscellaneous definitions jeroen paris visit
+
+\newcommand{\bTt}{\mbox{$\widetilde{{\bf T}}$}}
+\newcommand{\ylm}{\mbox{${\cal Y}_{lm}$}}
+\newcommand{\Un}{\mbox{$U_n$}}
+\newcommand{\Vn}{\mbox{$V_n$}}
+\newcommand{\Fn}{\mbox{$F_n$}}
+\newcommand{\Hn}{\mbox{$H_n$}}
+\newcommand{\Pn}{\mbox{$P_n$}}
+\newcommand{\Wn}{\mbox{$W_n$}}
+\newcommand{\Gn}{\mbox{$G_n$}}
+\newcommand{\an}{\mbox{$a_n$}}
+\newcommand{\kn}{\mbox{$k_n$}}
+\newcommand{\omn}{\mbox{$\omega_n$}}
+\newcommand{\alphan}{\mbox{$\alpha_n$}}
+\newcommand{\Unl}{\mbox{${}_nU_l$}}
+\newcommand{\sUnl}{\mbox{${}_{n\hspace{0.2 mm}}\sU_l$}}
+\newcommand{\sVnl}{\mbox{${}_{n\hspace{-0.4 mm}}\sV_l$}}
+\newcommand{\sWnl}{\mbox{${}_{n\hspace{-0.3 mm}}\sW_l$}}
+\newcommand{\sPnl}{\mbox{${}_n\sP_l$}}
+\newcommand{\Fnl}{\mbox{${}_nF_l$}}
+\newcommand{\Gnl}{\mbox{${}_nG_l$}}
+\newcommand{\Anl}{\mbox{${}_nA_l$}}
+\newcommand{\Hnl}{\mbox{${}_nH_l$}}
+\newcommand{\Vnl}{\mbox{${}_nV_l$}}
+\newcommand{\Wnl}{\mbox{${}_nW_l$}}
+\newcommand{\Pnl}{\mbox{${}_nP_l$}}
+\newcommand{\Rnl}{\mbox{${}_nR_l$}}
+\newcommand{\Snl}{\mbox{${}_nS_l$}}
+\newcommand{\Tnl}{\mbox{${}_nT_l$}}
+\newcommand{\Knl}{\mbox{${}_nK_l$}}
+\newcommand{\bAnlm}{\mbox{${}_n\bA_{lm}$}}
+\newcommand{\bBnlm}{\mbox{${}_n\bB_{lm}$}}
+\newcommand{\bAnm}{\mbox{${}_n\bA_{m}$}}
+\newcommand{\bBnm}{\mbox{${}_n\bB_{m}$}}
+\newcommand{\bGnm}{\mbox{${}_n\bG_{m}$}}
+\newcommand{\bRnl}{\mbox{${}_n\bR_l$}}
+\newcommand{\bDnl}{\mbox{${}_n\bD_l$}}
+\newcommand{\bsDnl}{\mbox{${}_{n\hspace{-0.2 mm}}\bsD_l$}}
+\newcommand{\bEnl}{\mbox{${}_n\bE_l$}}
+\newcommand{\bsEnl}{\mbox{${}_n\bsE_l$}}
+\newcommand{\bTnlm}{\mbox{${}_n\bT_{lm}$}}
+\newcommand{\bsnlm}{\mbox{${}_n\bs_{lm}$}}
+\newcommand{\phinlm}{\mbox{${}_n\phi_{lm}$}}
+\newcommand{\dUnl}{\mbox{${}_n\dot{U}_l$}}
+\newcommand{\dVnl}{\mbox{${}_n\dot{V}_l$}}
+\newcommand{\dWnl}{\mbox{${}_n\dot{W}_l$}}
+\newcommand{\dPnl}{\mbox{${}_n\dot{P}_l$}}
+\newcommand{\Unlm}{\mbox{${}_nU_{lm}$}}
+\newcommand{\Vnlm}{\mbox{${}_nV_{lm}$}}
+\newcommand{\Wnlm}{\mbox{${}_nW_{lm}$}}
+\newcommand{\Rnlm}{\mbox{${}_nR_{lm}$}}
+\newcommand{\Snlm}{\mbox{${}_nS_{lm}$}}
+\newcommand{\Tnlm}{\mbox{${}_nT_{lm}$}}
+\newcommand{\Pnlm}{\mbox{${}_nP_{lm}$}}
+\newcommand{\dRnl}{\mbox{${}_n\dot{R}_l$}}
+\newcommand{\dSnl}{\mbox{${}_n\dot{S}_l$}}
+\newcommand{\dTnl}{\mbox{${}_n\dot{T}_l$}}
+\newcommand{\dKnl}{\mbox{${}_n\dot{K}_l$}}
+\newcommand{\omnl}{\mbox{${}_{n\hspace{-0.2 mm}}\omega_l$}}
+\newcommand{\gammanl}{\mbox{${}_{n\hspace{-0.5 mm}}\gamma_l$}}
+\newcommand{\omnlm}{\mbox{${}_n\omega_{lm}$}}
+\newcommand{\dU}{\mbox{$\dot{U}$}}
+\newcommand{\dV}{\mbox{$\dot{V}$}}
+\newcommand{\dW}{\mbox{$\dot{W}$}}
+\newcommand{\dP}{\mbox{$\dot{P}$}}
+\newcommand{\dR}{\mbox{$\dot{R}$}}
+\newcommand{\dS}{\mbox{$\dot{S}$}}
+\newcommand{\dT}{\mbox{$\dot{T}$}}
+\newcommand{\dK}{\mbox{$\dot{K}$}}
+\newcommand{\dsU}{\mbox{$\dot{\sU}$}}
+\newcommand{\dsV}{\mbox{$\dot{\sV}$}}
+\newcommand{\dsW}{\mbox{$\dot{\sW}$}}
+\newcommand{\dsP}{\mbox{$\dot{\sP}$}}
+\newcommand{\dg}{\mbox{$\dot{g}$}}
+\newcommand{\dy}{\mbox{$\dot{y}$}}
+\newcommand{\ddy}{\mbox{$\ddot{y}$}}
+\newcommand{\dr}{\mbox{$\dot{r}$}}
+\newcommand{\dearth}{\mbox{$\dot{\earth}$}}
+\newcommand{\dpp}{\mbox{$\dot{p}$}}
+\newcommand{\ds}{\mbox{$\dot{s}$}}
+\newcommand{\dphi}{\mbox{$\dot{\phi}$}}
+\newcommand{\dkappa}{\mbox{$\dot{\kappa}$}}
+\newcommand{\dmu}{\mbox{$\dot{\mu}$}}
+\newcommand{\drho}{\mbox{$\dot{\rho}$}}
+\newcommand{\dPhi}{\mbox{$\dot{\Phi}$}}
+\newcommand{\ddU}{\mbox{$\ddot{U}$}}
+\newcommand{\ddV}{\mbox{$\ddot{V}$}}
+\newcommand{\ddW}{\mbox{$\ddot{W}$}}
+\newcommand{\ddP}{\mbox{$\ddot{P}$}}
+\newcommand{\ddphi}{\mbox{$\ddot{\phi}$}}
+\newcommand{\ddPhi}{\mbox{$\ddot{\Phi}$}}
+
+%miscellaneous definitions jeroen appendix D
+
+\newcommand{\uu}{\mbox{$u$}}
+\newcommand{\du}{\mbox{$\dot{u}$}}
+\newcommand{\vv}{\mbox{$v$}}
+\newcommand{\dv}{\mbox{$\dot{v}$}}
+\newcommand{\w}{\mbox{$w$}}
+\newcommand{\dw}{\mbox{$\dot{w}$}}
+\newcommand{\ph}{\mbox{$p$}}
+\newcommand{\dph}{\mbox{$\dot{p}$}}
+\newcommand{\f}{\mbox{$f$}}
+\newcommand{\x}{\mbox{$x$}}
+\newcommand{\z}{\mbox{$z$}}
+\newcommand{\el}{\mbox{$k^2$}}
+%%%%%%%%\newcommand{\up}{\mbox{$u'$}}
+\newcommand{\dup}{\mbox{$\dot{u}'$}}
+\newcommand{\vp}{\mbox{$v'$}}
+\newcommand{\dvp}{\mbox{$\dot{v}'$}}
+\newcommand{\wwp}{\mbox{$w'$}}
+\newcommand{\dwp}{\mbox{$\dot{w}'$}}
+\newcommand{\php}{\mbox{$p'$}}
+\newcommand{\dphp}{\mbox{$\dot{p}'$}}
+% DK DK for GJI style file \newcommand{\fp}{\mbox{$f'$}}
+\newcommand{\xp}{\mbox{$x'$}}
+\newcommand{\zp}{\mbox{$z'$}}
+\newcommand{\lp}{\mbox{$k'^2$}}
+
+%miscellaneous definitions jeroen chapter 14
+
+\newcommand{\dombar}{\mbox{$\delta\bar{\omega}$}}
+\newcommand{\otheta}{{\bar{\theta}}}
+\newcommand{\ophi}{{\bar{\phi}}}
+\newcommand{\eightfifteenths}{\mbox{$\frac{8}{15}$}}
+\newcommand{\twentyfivefourths}{\mbox{$\frac{25}{4}$}}
+\newcommand{\twofifteenth}{\mbox{$\frac{2}{15}$}}
+
+%equation formatting
+
+\newcommand{\eq}{\begin{equation}}
+\newcommand{\en}{\end{equation}}
+\newcommand{\eqa}{\begin{eqnarray}}
+\newcommand{\ena}{\end{eqnarray}}
+
+%fattened bold Greek subscripts
+
+\newcommand{\subtau}{\mbox{\boldmath $\scriptstyle{\tau}$}}
+\newcommand{\subLambda}{\mbox{\boldmath $\scriptstyle{\Lambda}$}}
+\newcommand{\subGamma}{\mbox{\boldmath $\scriptstyle{\Gamma}$}}
+
+%sans serif lower case delta and eta
+
+\newcommand{\grss}{\fontencoding{LGR}\fontfamily{cmss}\selectfont}
+\newcommand{\ssdelta}{\mbox{\grss d}}
+\newcommand{\sseta}{\mbox{\grss h}}
Added: seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/notes_about_CPML_for_SPECFEM3D.tex
===================================================================
--- seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/notes_about_CPML_for_SPECFEM3D.tex (rev 0)
+++ seismo/3D/SPECFEM3D/trunk/doc/notes_about_CPML/notes_about_CPML_for_SPECFEM3D.tex 2012-08-07 23:03:13 UTC (rev 20558)
@@ -0,0 +1,696 @@
+%
+% new Latex2E GJI class file
+% don't use "times" package because of a bug
+\documentclass[onecolumn,extra]{gji_modified_cours_UPPA}
+%
+% T1 encoding gives better PDF and allows for 8 bits
+\usepackage[T1]{fontenc}
+\usepackage{times}
+\usepackage{graphicx}
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% A4 paper
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\textwidth 17cm
+\textheight 24.8cm
+\oddsidemargin -4.5mm
+\evensidemargin -4.5mm
+\topmargin -11mm
+
+% biblio GJI
+\bibliographystyle{gji}
+\renewcommand{\cite}[1]{\citet{#1}}
+% roman d for dV in integrals
+\newcommand{\rmd}{\mathrm{d}}
+
+% roman i for complex number
+\newcommand{\myiomega}{\mathrm{i} \omega}
+
+\input{newcommands}
+
+\begin{document}
+
+\title{Notes about 3D C-PML equations for SPECFEM3D}
+%
+\author[Dimitri Komatitsch, Zhinan Xie]{Dimitri Komatitsch, Zhinan Xie\\
+CNRS Marseille, France}
+%
+\date{August 8, 2012}
+
+\maketitle
+
+\begin{figure}
+\includegraphics[scale=0.5]{pml_schematic.png}
+\caption{Schematic of a typical wave-equation problem, in which there is some finite region of interest where sources,
+inhomogeneous media, nonlinearities and etc are being investigated, from which some radiative waves escape to infinity.
+The perfect absorbing layer, which was used to truncated out computational region, is placed adjacent to the edges of the
+computational region}
+\end{figure}
+
+\noindent
+Adjacent to 3DCPML, we assume the motion is governed by 3D elastic wave equation. In differential form it is given by:
+%
+\begin{eqnarray}
+\varepsilon_{xx} & = & \partial_x u_x \nonumber \\
+\varepsilon_{yy} & = & \partial_y u_y \nonumber \\
+\varepsilon_{zz} & = & \partial_z u_z \nonumber \\
+\varepsilon_{xy} & = & \frac{1}{2} (\partial_x u_y + \partial_y u_x) \,\, , \,\, \varepsilon_{yx} = \varepsilon_{xy} \nonumber \\
+\varepsilon_{xz} & = & \frac{1}{2} (\partial_x u_z + \partial_z u_x) \,\, , \,\, \varepsilon_{zx} = \varepsilon_{xz} \nonumber \\
+\varepsilon_{yz} & = & \frac{1}{2} (\partial_y u_z + \partial_z u_y) \,\, , \,\, \varepsilon_{zy} = \varepsilon_{yz}
+\end{eqnarray}
+%
+\noindent and
+%
+\begin{eqnarray}
+\sigma_{xx} & = & (\lambda + 2 \mu) \, \varepsilon_{xx} + \lambda \, \varepsilon_{yy} + \lambda \, \varepsilon_{zz} \nonumber \\
+\sigma_{yy} & = & \lambda \, \varepsilon_{xx} + (\lambda + 2 \mu) \, \varepsilon_{yy} + \lambda \, \varepsilon_{zz} \nonumber \\
+\sigma_{zz} & = & \lambda \, \varepsilon_{xx} + \lambda \, \varepsilon_{yy} + (\lambda + 2 \mu) \, \varepsilon_{zz} \nonumber \\
+\sigma_{xy} & = & 2 \mu \, \varepsilon_{xy} \,\, , \,\, \sigma_{yx} = \sigma_{xy} \nonumber \\
+\sigma_{xz} & = & 2 \mu \, \varepsilon_{xz} \,\, , \,\, \sigma_{zx} = \sigma_{xz} \nonumber \\
+\sigma_{yz} & = & 2 \mu \, \varepsilon_{yz} \,\, , \,\, \sigma_{yz} = \sigma_{zy}
+\end{eqnarray}
+%
+\noindent and
+%
+\begin{eqnarray}
+\rho \, \frac{\partial^2 u_x}{\partial t^2} & = & \partial_x \sigma_{xx} + \partial_y \sigma_{xy} + \partial_z \sigma_{xz} + f_x \nonumber \\
+\rho \, \frac{\partial^2 u_y}{\partial t^2} & = & \partial_x \sigma_{yx} + \partial_y \sigma_{yy} + \partial_z \sigma_{yz} + f_y \nonumber \\
+\rho \, \frac{\partial^2 u_z}{\partial t^2} & = & \partial_x \sigma_{zx} + \partial_y \sigma_{zy} + \partial_z \sigma_{zz} + f_z
+\end{eqnarray}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+\clearpage
+%
+%\noindent To obtain the CPML form, we just need to replace each spatial derivative with that same derivative multiplied by $1/s$.
+%Thus, with CPML, in differential form in 2D this gives (noting $\frac{\partial^2 u_x}{\partial t^2}$ instead of $-\omega^2 u_x$ for now, even though we perform a Fourier transform,
+%because we will perform an inverse Fourier transform later and thus get the term $\frac{\partial^2 u_x}{\partial t^2}$ back):
+%
+\noindent To obtain the CPML form, we firstly perform a Fourier transform on above equation,
+then replace each spatial derivative with that same derivative multiplied by $1/s$
+to make the plane wave entering into CPML without reflection and decaying exponentially along the x, y, z or in all directions.
+Thus,in differential form in 3D the frequency-domain equation govened the motion in CPML gives:
+%
+\begin{eqnarray}
+\varepsilon_{xx} & = & \frac{1}{s_x}\partial_x u_x \nonumber \\
+\varepsilon_{yy} & = & \frac{1}{s_y}\partial_y u_y \nonumber \\
+\varepsilon_{zz} & = & \frac{1}{s_z}\partial_z u_z \nonumber \\
+\varepsilon_{xy} & = & \frac{1}{2} (\frac{1}{s_x} \partial_x u_y + \frac{1}{s_y} \partial_y u_x) \,\, , \,\, \varepsilon_{yx} = \varepsilon_{xy} \nonumber \\
+\varepsilon_{xz} & = & \frac{1}{2} (\frac{1}{s_x} \partial_x u_z + \frac{1}{s_z} \partial_z u_x) \,\, , \,\, \varepsilon_{zx} = \varepsilon_{xz} \nonumber \\
+\varepsilon_{yz} & = & \frac{1}{2} (\frac{1}{s_y} \partial_y u_z + \frac{1}{s_z} \partial_z u_y) \,\, , \,\, \varepsilon_{zy} = \varepsilon_{yz}
+\end{eqnarray}
+%
+\noindent and
+%
+\begin{eqnarray}
+\sigma_{xx} & = & (\lambda + 2 \mu) \, \varepsilon_{xx} + \lambda \, \varepsilon_{yy} + \lambda \, \varepsilon_{zz} \nonumber \\
+\sigma_{yy} & = & \lambda \, \varepsilon_{xx} + (\lambda + 2 \mu) \, \varepsilon_{yy} + \lambda \, \varepsilon_{zz} \nonumber \\
+\sigma_{zz} & = & \lambda \, \varepsilon_{xx} + \lambda \, \varepsilon_{yy} + (\lambda + 2 \mu) \, \varepsilon_{zz} \nonumber \\
+\sigma_{xy} & = & 2 \mu \, \varepsilon_{xy} \,\, , \,\, \sigma_{yx} = \sigma_{xy} \nonumber \\
+\sigma_{xz} & = & 2 \mu \, \varepsilon_{xz} \,\, , \,\, \sigma_{zx} = \sigma_{xz} \nonumber \\
+\sigma_{yz} & = & 2 \mu \, \varepsilon_{yz} \,\, , \,\, \sigma_{yz} = \sigma_{zy}
+\end{eqnarray}
+%
+\noindent and
+%
+\begin{eqnarray}
+- \rho \, \omega^2 u_x & = & \frac{1}{s_x} \partial_x \sigma_{xx} + \frac{1}{s_y} \partial_y \sigma_{xy} + \frac{1}{s_z} \partial_z \sigma_{xz} + f_x \nonumber \\
+- \rho \, \omega^2 u_y & = & \frac{1}{s_x} \partial_x \sigma_{yx} + \frac{1}{s_y} \partial_y \sigma_{yy} + \frac{1}{s_z} \partial_z \sigma_{yz} + f_y \nonumber \\
+- \rho \, \omega^2 u_z & = & \frac{1}{s_x} \partial_x \sigma_{zx} + \frac{1}{s_y} \partial_y \sigma_{zy} + \frac{1}{s_z} \partial_z \sigma_{zz} + f_z
+\end{eqnarray}
+%
+where $s_x = \kappa_x + \frac{d_x}{\alpha_x + \myiomega}$ , $s_y = \kappa_y + \frac{d_y}{\alpha_y + \myiomega}$ and
+$s_z = \kappa_z + \frac{d_z}{\alpha_z + \myiomega}$. $\kappa_x ,d_x,\alpha_x;\kappa_y ,d_y,\alpha_y;\kappa_z ,d_z,\alpha_z$
+valued following the way used in paper \cite{FeVi05}.
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\noindent In the frequency domain we define:
+\begin{equation}
+\partial_{\tilde{x}} = \frac{1}{s_x}\, \partial_ x,
+\label{diffmapping}
+\end{equation}
+%
+and we know from \cite{KoMa07} that $\partial_x$ is then transformed in the time domain into:
+\begin{equation}
+\partial_{\tilde{x}}= \frac{1}{\kappa_x} \partial_{x}
+- \frac{d_x}{\kappa_x^2} H(t) e^{-(d_x/\kappa_x + \alpha_x)t} * \partial_ x \, .
+\end{equation}
+
+\noindent This means that $\frac{1}{s_x}$ is transformed by inverse Fourier transform into
+$\frac{1}{\kappa_x} - \frac{d_x}{\kappa_x^2} H(t) e^{-(d_x/\kappa_x + \alpha_x)t} *$.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\clearpage
+
+\noindent
+Here we extended the approach used in \cite{Mat11} to get an stable CPML implementation for spectral element method: Let us multiply the set of equation (6) by $s_x s_y s_z$,
+This will results in a more complex mass matrix on the left-hand side.
+And let us get rid of the source term because there is no source in the PML layers, we have:
+\begin{eqnarray}
+- \rho s_x s_y s_z \omega^2 u_x & = & s_y s_z \partial_x \sigma_{xx} + s_x s_z \partial_y \sigma_{xy} + s_x s_y \partial_z \sigma_{xz} \nonumber \\
+- \rho s_x s_y s_z \omega^2 u_y & = & s_y s_z \partial_x \sigma_{yx} + s_x s_z \partial_y \sigma_{yy} + s_x s_y \partial_z \sigma_{yz} \nonumber \\
+- \rho s_x s_y s_z \omega^2 u_z & = & s_y s_z \partial_x \sigma_{zx} + s_x s_z \partial_y \sigma_{zy} + s_x s_y \partial_z \sigma_{zz}
+\end{eqnarray}
+%
+\noindent since $s_y s_z$ does not depend on $x$ ,
+$s_x s_z$ does not depend on $y$ and $s_x s_y$ does not depend on $z$:
+%
+\begin{eqnarray}
+- \rho s_x s_y s_z \omega^2 u_x & = & \partial_x (s_y s_z \sigma_{xx}) + \partial_y (s_x s_z \sigma_{xy}) + \partial_z (s_x s_y \sigma_{xz}) \nonumber \\
+- \rho s_x s_y s_z \omega^2 u_y & = & \partial_x (s_y s_z \sigma_{yx}) + \partial_y (s_x s_z \sigma_{yy}) + \partial_z (s_x s_y \sigma_{yz}) \nonumber \\
+- \rho s_x s_y s_z \omega^2 u_z & = & \partial_x (s_y s_z \sigma_{zx}) + \partial_y (s_x s_z \sigma_{zy}) + \partial_z (s_x s_y \sigma_{zz})
+\end{eqnarray}
+\noindent By inserting the definition of the stress tensor we get:
+\begin{eqnarray}
+- \rho s_x s_y s_z \omega^2 u_x & = & \partial_x (s_y s_z ((\lambda + 2 \mu) \, \varepsilon_{xx} + \lambda \, \varepsilon_{yy} + \lambda \, \varepsilon_{zz}))
++ \partial_y (s_x s_z (2 \mu \, \varepsilon_{xy})) + \partial_z (s_x s_y (2 \mu \, \varepsilon_{xz})) \nonumber \\
+- \rho s_x s_y s_z \omega^2 u_y & = & \partial_x (s_y s_z (2 \mu \, \varepsilon_{xy}))
++ \partial_y (s_x s_z (\lambda \, \varepsilon_{xx} + (\lambda + 2 \mu) \, \varepsilon_{yy} + \lambda \, \varepsilon_{zz}))
++ \partial_z (s_x s_y (2 \mu \, \varepsilon_{yz})) \nonumber \\
+- \rho s_x s_y s_z \omega^2 u_z & = & \partial_x (s_y s_z (2 \mu \, \varepsilon_{xz}))
++ \partial_y (s_x s_z (2 \mu \, \varepsilon_{yz}))
++ \partial_z (s_x s_y (\lambda \, \varepsilon_{xx} + \lambda \, \varepsilon_{yy} + (\lambda + 2 \mu) \, \varepsilon_{zz}))
+\end{eqnarray}
+
+\noindent Then, inserting the definition of the strain tensor we get:
+\begin{eqnarray}
+-\rho s_x s_y s_z \omega^2 u_x& = &\partial_x (s_y s_z ((\lambda + 2 \mu)\frac{1}{s_x}\partial_x u_x + \lambda\frac{1}{s_y}\partial_y u_y + \lambda\frac{1}{s_z}\partial_z u_z))
++ \partial_y (s_x s_z (\mu (\frac{1}{s_x} \partial_x u_y + \frac{1}{s_y} \partial_y u_x))) \nonumber \\
+&\,& \,+\,\, \partial_z (s_x s_y (\mu(\frac{1}{s_x} \partial_x u_z + \frac{1}{s_z}\partial_z u_x)) \nonumber \\
+-\rho s_x s_y s_z \omega^2 u_y & = & \partial_x (s_y s_z (\mu(\frac{1}{s_x} \partial_x u_y + \frac{1}{s_y}\partial_y u_x)))
++ \partial_y (s_x s_z (\lambda\frac{1}{s_x}\partial_x u_x + (\lambda + 2 \mu)\frac{1}{s_y}\partial_y u_y + \lambda\frac{1}{s_z}\partial_z u_z))\nonumber \\
+&\,& \,+\,\, \partial_z (s_x s_y (\mu(\frac{1}{s_y} \partial_y u_z + \frac{1}{s_z} \partial_z u_y))) \nonumber \\
+- \rho s_x s_y s_z \omega^2 u_z & = & \partial_x (s_y s_z (\mu(\frac{1}{s_x} \partial_x u_z + \frac{1}{s_z} \partial_z u_x)))
++ \partial_y (s_x s_z (\mu(\frac{1}{s_y} \partial_y u_z + \frac{1}{s_z} \partial_z u_y))) \nonumber \\
+&\,& \,+\,\, \partial_z (s_x s_y (\lambda\frac{1}{s_x}\partial_x u_x + \lambda\frac{1}{s_y}\partial_y u_y + (\lambda + 2 \mu)(\frac{1}{s_z}\partial_z u_z)))
+\end{eqnarray}
+\noindent Grouping the $s_x$,$s_y$ and $s_z$ factors we get:
+\begin{eqnarray}
+-\rho s_x s_y s_z \omega^2 u_x& = &\partial_x ((\lambda + 2 \mu)\frac{s_y s_z}{s_x}\partial_x u_x + \lambda s_z \partial_y u_y + \lambda s_y \partial_z u_z)
++ \partial_y (\mu s_z \partial_x u_y + \mu \frac{s_x s_z}{s_y} \partial_y u_x) \nonumber \\
+&\,& \,+\,\, \partial_z (\mu s_y \partial_x u_z + \mu \frac{s_x s_y}{s_z}\partial_z u_x) \nonumber \\
+-\rho s_x s_y s_z \omega^2 u_y & = & \partial_x (\mu \frac{s_y s_z}{s_x} \partial_x u_y + \mu s_z \partial_y u_x )
++ \partial_y (\lambda s_z \partial_x u_x + (\lambda + 2 \mu)\frac{s_x s_z}{s_y}\partial_y u_y + \lambda s_x \partial_z u_z)\nonumber \\
+&\,& \,+\,\, \partial_z ( \mu s_x \partial_y u_z + \mu \frac{s_x s_y}{s_z} \partial_z u_y) \nonumber \\
+- \rho s_x s_y s_z \omega^2 u_z & = & \partial_x ( \mu \frac{s_y s_z}{s_x} \partial_x u_z + \mu s_y \partial_z u_x )
++ \partial_y ( \mu \frac{s_x s_z}{s_y} \partial_y u_z + \mu s_x \partial_z u_y ) \nonumber \\
+&\,& \,+\,\, \partial_z ( \lambda s_y\partial_x u_x + \lambda s_x \partial_y u_y + (\lambda + 2 \mu)\frac{s_x s_y}{s_z}\partial_z u_z)
+\end{eqnarray}
+
+\noindent Let us note that the above equation, if interpreted in terms of an equivalent stress tensor, implies that such a stress tensor is not symmetric any more.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\clearpage
+
+\noindent
+With CPML, in variational form, in 3D with a test vector $\mathbf{w} = (w_x,w_y,w_z)$ this gives
+(let us get rid of the source term because there is no source in the PML layers):
+%
+\begin{eqnarray}
+%
+\int_\Omega -\rho s_x s_y s_z \omega^2 u_x & = & \int_\Omega \Bigg( w_x \partial_x ((\lambda + 2 \mu)\frac{s_y s_z}{s_x}\partial_x u_x + \lambda s_z \partial_y u_y + \lambda s_y \partial_z u_z)
++ w_x \partial_y (\mu s_z \partial_x u_y + \mu \frac{s_x s_z}{s_y} \partial_y u_x) \nonumber \\
+&\,& \,+\,\, w_x \partial_z (\mu s_y \partial_x u_z + \mu \frac{s_x s_y}{s_z}\partial_z u_x)\Bigg) \nonumber \\
+%
+\int_\Omega -\rho s_x s_y s_z \omega^2 u_y & = & \int_\Omega \Bigg( w_y \partial_x (\mu \frac{s_y s_z}{s_x} \partial_x u_y + \mu s_z \partial_y u_x )
++ w_y \partial_y (\lambda s_z \partial_x u_x + (\lambda + 2 \mu)\frac{s_x s_z}{s_y}\partial_y u_y + \lambda s_x \partial_z u_z)\nonumber \\
+&\,& \,+\,\, w_y \partial_z ( \mu s_x \partial_y u_z + \mu \frac{s_x s_y}{s_z} \partial_z u_y) \Bigg) \nonumber \\
+%
+\int_\Omega - \rho s_x s_y s_z \omega^2 u_z & = & \int_\Omega \Bigg( w_z \partial_x ( \mu \frac{s_y s_z}{s_x} \partial_x u_z + \mu s_y \partial_z u_x )
++ w_z \partial_y ( \mu \frac{s_x s_z}{s_y} \partial_y u_z + \mu s_x \partial_z u_y ) \nonumber \\
+&\,& \,+\,\, w_z \partial_z ( \lambda s_y\partial_x u_x + \lambda s_x \partial_y u_y + (\lambda + 2 \mu)\frac{s_x s_y}{s_z}\partial_z u_z)\Bigg)
+\end{eqnarray}
+%
+Integrating by parts (and ignoring the boundary integral term because of the Dirichlet conditions that we will apply
+later on that boundary, because its contribution would be erased by the Dirichlet condition) we get
+%
+\begin{eqnarray}
+%
+\int_\Omega -\rho s_x s_y s_z \omega^2 u_x & = & \int_\Omega \Bigg(((\lambda + 2 \mu)\frac{s_y s_z}{s_x}\partial_x u_x + \lambda s_z \partial_y u_y + \lambda s_y \partial_z u_z) \partial_x w_x
++ (\mu s_z \partial_x u_y + \mu \frac{s_x s_z}{s_y} \partial_y u_x) \partial_y w_x \nonumber \\
+&\,& \,+\,\, (\mu s_y \partial_x u_z + \mu \frac{s_x s_y}{s_z}\partial_z u_x) \partial_z w_x \Bigg) \nonumber \\
+%
+\int_\Omega -\rho s_x s_y s_z \omega^2 u_y & = & \int_\Omega \Bigg((\mu \frac{s_y s_z}{s_x} \partial_x u_y + \mu s_z \partial_y u_x )\partial_x w_y
++ (\lambda s_z \partial_x u_x + (\lambda + 2 \mu)\frac{s_x s_z}{s_y}\partial_y u_y + \lambda s_x \partial_z u_z) \partial_y w_y \nonumber \\
+&\,& \,+\,\, ( \mu s_x \partial_y u_z + \mu \frac{s_x s_y}{s_z} \partial_z u_y) \partial_z w_y \Bigg) \nonumber \\
+%
+\int_\Omega - \rho s_x s_y s_z \omega^2 u_z & = & \int_\Omega \Bigg( ( \mu \frac{s_y s_z}{s_x} \partial_x u_z + \mu s_y \partial_z u_x ) \partial_x w_z
++ ( \mu \frac{s_x s_z}{s_y} \partial_y u_z + \mu s_x \partial_z u_y ) \partial_y w_z \nonumber \\
+&\,& \,+\,\,( \lambda s_y\partial_x u_x + \lambda s_x \partial_y u_y + (\lambda + 2 \mu)\frac{s_x s_y}{s_z}\partial_z u_z) \partial_z w_z \Bigg)
+\end{eqnarray}
+%
+\noindent
+Inverse FT of $- \omega^2 s_x s_y s_z$ computed using MAPLE for left-hand side:
+$$A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)$$
+with
+$$A_0 = \kappa_x \kappa_y \kappa_z \, , \, A_1 =d_x \kappa_y \kappa_z + d_y \kappa_x \kappa_z + d_z \kappa_x \kappa_y $$
+$$A_2 = d_x d_y \kappa_z +d_x d_z \kappa_y + d_y d_z \kappa_x-\alpha( d_x \kappa_y \kappa_z + d_y \kappa_x \kappa_z + d_z \kappa_x \kappa_y)$$
+$$A_3= d_x d_y d_z - 2 \alpha (d_x d_y \kappa_z +d_x d_z \kappa_y + d_y d_z \kappa_x )
+ +\alpha ^2 (d_x \kappa_y \kappa_z + d_y \kappa_x \kappa_z + d_z \kappa_x \kappa_y) $$
+$$A_4= -2 \alpha d_x d_y d_z+\alpha ^2 (d_x d_y \kappa_z + d_x d_z \kappa_y + d_y d_z \kappa_x), A_5=\frac{1}{2} \alpha ^2 d_x d_y d_z$$
+Here in order to solve the singularity problem arised using definition of $\alpha_x$, $\alpha_y$ and $\alpha_z$, we set $$\alpha_x=\alpha_y=\alpha_z=const=\alpha$$
+where $\alpha_x, \alpha_y$ or $\alpha_z$ is nonzero \\
+
+\noindent
+Inverse FT of $\frac{s_y s_z}{s_x}$ computed using MAPLE for right-hand side:\\\\
+a): $d_x \neq 0 $
+$$A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t) $$
+with
+$$A_6=\frac{\kappa_y \kappa_z}{\kappa_x},\,A_7=\frac{d_y d_z}{d_x},
+\,A_8=\frac{(d_y \kappa_x - d_x \kappa_y )(d_x \kappa_z - d_z \kappa_x )}{d_x \kappa^{2}_x}$$\\
+b): $d_x = 0 $
+$$A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-\alpha\,t} \, t \, H(t) $$
+with
+$$A_6=\frac{\kappa_y \kappa_z}{\kappa_x},\,A_7=\frac{d_z \kappa_y + d_y \kappa_z}{\kappa_x},\,
+A_8=\frac{d_y d_z}{\kappa_x}
+$$
+\\
+\noindent
+Inverse FT of $\frac{s_x s_z}{s_y}$ computed using MAPLE for right-hand side:\\\\
+a): $d_y \neq 0 $
+$$A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t) $$
+with
+$$A_9=\frac{\kappa_x \kappa_z}{\kappa_y},\,A_{10}=\frac{d_x d_z}{d_y},
+\,A_{11}=\frac{(d_x \kappa_y - d_y \kappa_x )(d_y \kappa_z - d_z \kappa_y )}{d_y \kappa^{2}_y}$$\\
+b): $d_y = 0 $
+$$A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-\alpha\,t} \, t \, H(t) $$
+with
+$$A_9=\frac{\kappa_x \kappa_z}{\kappa_y},\,A_{10}=\frac{d_z \kappa_x + d_x \kappa_z}{\kappa_y},\,
+A_{11}=\frac{d_x d_z}{\kappa_y}
+$$
+\\
+\noindent
+Inverse FT of $\frac{s_x s_y}{s_z}$ computed using MAPLE for right-hand side:\\\\
+a): $d_z \neq 0 $
+$$A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t) $$
+with
+$$A_{12}=\frac{\kappa_x \kappa_y}{\kappa_z},\,A_{13}=\frac{d_x d_y}{d_z},
+\,A_{14}=\frac{(d_x \kappa_z - d_z \kappa_x )(d_z \kappa_y - d_y \kappa_z )}{d_z \kappa^{2}_z}$$\\
+b): $d_z = 0 $
+$$A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-\alpha\,t} \, t \, H(t) $$
+with
+$$A_{12}=\frac{\kappa_x \kappa_y}{\kappa_z},\,A_{13}=\frac{d_y \kappa_x + d_x \kappa_y}{\kappa_z},\,
+A_{14}=\frac{d_x d_y}{\kappa_z}
+$$
+\\
+\noindent
+Inverse FT of $s_x$ computed using MAPLE for right-hand side:
+$$A_{15}\delta(t) + A_{16} {\rm e}^{-\alpha\,t} \, H(t) $$
+with
+$$A_{15}= \kappa_x, \, A_{16}=d_x $$
+\\
+\noindent
+Inverse FT of $s_y$ computed using MAPLE for right-hand side:
+$$A_{17}\delta(t) + A_{18} {\rm e}^{-\alpha\,t} \, H(t) $$
+with
+$$A_{17}= \kappa_y, \, A_{18}=d_y $$
+\\
+\noindent
+Inverse FT of $s_z$ computed using MAPLE for right-hand side:
+$$A_{19}\delta(t) + A_{20} {\rm e}^{-\alpha\,t} \, H(t) $$
+with
+$$A_{19}= \kappa_z, \, A_{20}=d_z $$
+
+Thus going back to the time domain, in which a product in the Fourier transform domain becomes a convolution in the time domain, we get
+%
+\begin{eqnarray}
+%
+&&\int_\Omega \rho \Big(A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)\Big) \ast u_x \nonumber \\
+&& = \int_\Omega \Bigg(\Big((\lambda + 2 \mu)(A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t))\ast\partial_x u_x
++\lambda (A_{19}\delta(t) + A_{20} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t)) \ast \partial_y u_y \nonumber\\
+&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + \lambda (A_{17}\delta(t) + A_{18} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t))\ast \partial_z u_z\Big) \partial_x w_x\nonumber\\
+&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+ \Big(\mu (A_{19}\delta(t) + A_{20} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t)) \ast \partial_x u_y
++ \mu (A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t) ) \ast\partial_y u_x\Big) \partial_y w_x \nonumber \\
+&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+ \Big(\mu (A_{17}\delta(t) + A_{18} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t))\ast \partial_x u_z
++ \mu (A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t))\ast\partial_z u_x\Big) \partial_z w_x \Bigg) \nonumber \\ \nonumber \\
+%
+&&\int_\Omega \rho \Big(A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)\Big) \ast u_y \nonumber \\
+&&= \int_\Omega \Bigg(\Big(\mu (A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t) )\ast \partial_x u_y
++ \mu (A_{19}\delta(t) + A_{20} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t)) \ast\partial_y u_x \Big)\partial_x w_y \nonumber\\
+&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+ \Big(\lambda (A_{19}\delta(t) + A_{20} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t)) \ast \partial_x u_x
++ (\lambda + 2 \mu)(A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t) )\ast\partial_y u_y\nonumber\\
+&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+ \lambda (A_{15}\delta(t) + A_{16} {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t))\ast \partial_z u_z\Big) \partial_y w_y \nonumber \\
+&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+ \Big( \mu (A_{15}\delta(t) + A_{16} {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t))\ast \partial_y u_z
++ \mu (A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t))\ast \partial_z u_y\Big) \partial_z w_y \Bigg) \nonumber \\ \nonumber \\
+%
+&&\int_\Omega \rho \Big(A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)\Big) \ast u_z \nonumber \\
+&& = \int_\Omega \Bigg( \Big( \mu (A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t))\ast \partial_x u_z
++ \mu (A_{17}\delta(t) + A_{18} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t)) \ast \partial_z u_x \Big) \partial_x w_z \nonumber \\
+&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + \Big( \mu (A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t)) \ast \partial_y u_z
++ \mu (A_{15}\delta(t) + A_{16} {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t)) \ast \partial_z u_y \Big) \partial_y w_z \nonumber \\
+&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+\Big( \lambda (A_{17}\delta(t) + A_{18} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t))\ast \partial_x u_x
++ \lambda (A_{15}\delta(t) + A_{16} {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t)) \ast \partial_y u_y\nonumber \\
+&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+ (\lambda + 2 \mu)(A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t))\ast\partial_z u_z\Big) \partial_z w_z \Bigg)
+\end{eqnarray}
+%
+Take the first equation of set (16) as example,Remembering that $u * \delta'(t) = u' * \delta(t)$ and $u * \delta''(t) = u'' * \delta(t)$, we
+expanding the left hand side of the equation
+%
+$$\int_\Omega \rho A_0 \frac{\partial^2 u_x}{\partial t^2}w_x+
+\int_\Omega \rho A_1 \frac{\partial u_x}{\partial t} w_x +
+\int_\Omega \rho A_2 u_x w_x +
+\int_\Omega \rho (A_3 {\rm e}^{-\alpha\,t} \, H(t)) \ast u_x+
+\int_\Omega \rho (A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)) \ast u_x +
+\int_\Omega \rho (A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)) \ast u_x
+$$
+%
+
+Note that, following \cite{Hug87} equation (9.1.12) page 491, and as also mentioned by \cite{Mat11}, the term $\rho \, A_1$ is a damping
+matrix $C$ related to velocity and thus it adds a $\rho \, \frac{\Delta t}{2} \, A_1$ term to the mass matrix in the
+explicit Newmark scheme ($\alpha = \frac{1}{2}$, $\beta = 0$).
+
+Eq. 16 is the equation set of corner PML where $\kappa_x,d_x,\alpha_x;\kappa_y,d_y,\alpha_y; and \kappa_z,d_z,\alpha_z$ are not zero everywhere. But in the edge PML
+like XYPML, XZPML and YZPML or surface PML like XPML, YPML and ZPML, it is not the same. In that case, we have:\\
+a):XYPML\\
+$\kappa_x,d_x$ and $\kappa_y,d_y$ defined as usual; $\alpha_x=\alpha_y=\alpha$ but $\kappa_z = 1 ,d_z= 0,\alpha_z= 0$.\\
+In this case inverse FT of $-\omega^2 s_x s_y s_z$ is:
+$$A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)$$
+with
+$$A_0 = \kappa_x \kappa_y \, , \, A_1 =d_x \kappa_y + d_y \kappa_x \, , \,A_2 = d_x d_y -\alpha(d_y \kappa_x + d_x \kappa_y)$$
+$$A_3= - 2 \alpha d_x d_y +\alpha ^2 (d_x \kappa_y + d_y \kappa_x),A_4= \alpha ^2 d_x d_y, A_5=0 $$
+\noindent
+Inverse FT of $\frac{s_y s_z}{s_x}$ computed using MAPLE for right-hand side:\\
+$$A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t) $$
+with
+$$A_6=\frac{\kappa_y}{\kappa_x},\,A_7=0,\,A_8=\frac{d_y \kappa_x-d_x \kappa_y }{\kappa^2_x} $$\\
+\noindent
+Inverse FT of $\frac{s_x s_z}{s_y}$ computed using MAPLE for right-hand side:\\
+$$A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t) $$
+with
+$$A_9=\frac{\kappa_x}{\kappa_y},\,A_{10}=0,
+\,A_{11}=\frac{(d_x \kappa_y - d_y \kappa_x )}{\kappa^{2}_y}$$\\
+\noindent
+Inverse FT of $\frac{s_x s_y}{s_z}$ computed using MAPLE for right-hand side:\\
+$$ A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-\alpha \,t} t H(t) $$
+with
+$$A_{12}=\kappa_x \kappa_y,\,A_{13}=d_x\kappa_y+d_y\kappa_x,
+\,A_{14}=d_xd_y$$\\
+\noindent
+Inverse FT of $s_x$ computed using MAPLE for right-hand side:
+$$A_{15}\delta(t) + A_{16} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{15}= \kappa_x, \, A_{16}=d_x $$
+\noindent
+Inverse FT of $s_y$ computed using MAPLE for right-hand side:
+$$A_{17}\delta(t) + A_{18} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{17}= \kappa_y, \, A_{18}=d_y $$
+\noindent
+Inverse FT of $s_z$ computed using MAPLE for right-hand side:
+$$A_{19}\delta(t) + A_{20} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{19}= 1, \, A_{20}=0 $$
+b):XZPML\\
+$\kappa_x,d_x$ and $\kappa_z,d_z$ defined as usual; $\alpha_x=\alpha_z=\alpha$ but $\kappa_y = 1 ,d_y= 0,\alpha_y= 0$\\
+In this case inverse FT of $-\omega^2 s_x s_y s_z$ is:
+$$A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)$$
+with
+$$A_0 = \kappa_x \kappa_z \, , \, A_1 =d_x \kappa_z + d_z \kappa_x \, , \,A_2 = d_x d_z -\alpha(d_z \kappa_x + d_x \kappa_z)$$
+$$A_3= - 2 \alpha d_x d_z +\alpha ^2 (d_x \kappa_z + d_z \kappa_x),A_4= \alpha ^2 d_x d_z, A_5=0 $$
+\noindent
+Inverse FT of $\frac{s_y s_z}{s_x}$ computed using MAPLE for right-hand side:\\
+$$A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t) $$
+with
+$$A_6=\frac{\kappa_z}{\kappa_x},\,A_7=0,\,A_8=\frac{d_z \kappa_x-d_x \kappa_z }{\kappa^2_x} $$\\
+\noindent
+Inverse FT of $\frac{s_x s_z}{s_y}$ computed using MAPLE for right-hand side:\\
+$$A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-\alpha\,t} \, tH(t) $$
+with
+$$A_9=\kappa_x \kappa_z,\,A_{10}=d_x\kappa_z+d_z\kappa_x,
+\,A_{11}=d_xd_z$$\\
+\noindent
+Inverse FT of $\frac{s_x s_y}{s_z}$ computed using MAPLE for right-hand side:\\
+$$A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t) $$
+with
+$$A_{12}=\frac{\kappa_x}{\kappa_z},\,A_{13}=0,
+\,A_{14}=\frac{d_x \kappa_z-d_z \kappa_x }{\kappa^2_z}$$\\
+\noindent
+Inverse FT of $s_x$ computed using MAPLE for right-hand side:
+$$A_{15}\delta(t) + A_{16} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{15}= \kappa_x, \, A_{16}=d_x $$
+\noindent
+Inverse FT of $s_y$ computed using MAPLE for right-hand side:
+$$A_{17}\delta(t) + A_{18} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{17}= 1, \, A_{18}=0 $$
+\noindent
+Inverse FT of $s_z$ computed using MAPLE for right-hand side:
+$$A_{19}\delta(t) + A_{20} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{19}= \kappa_z, \, A_{20}=d_z $$
+c):YZPML\\
+$\kappa_y,d_y$ and $\kappa_z,d_z$ defined as usual; $\alpha_y=\alpha_z=\alpha$ but $\kappa_x = 1 ,d_x= 0,\alpha_x= 0$\\
+In this case inverse FT of $-\omega^2 s_x s_y s_z$ is:
+$$A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)$$
+with
+$$A_0 = \kappa_y \kappa_z \, , \, A_1 =d_y \kappa_z + d_z \kappa_y \, , \,A_2 = d_y d_z -\alpha(d_z \kappa_y + d_y \kappa_z)$$
+$$A_3= - 2 \alpha d_y d_z +\alpha ^2 (d_y \kappa_z + d_z \kappa_y),A_4= \alpha ^2 d_y d_z, A_5=0 $$
+\noindent
+Inverse FT of $\frac{s_y s_z}{s_x}$ computed using MAPLE for right-hand side:\\
+$$A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-\alpha\,t} \, tH(t) $$
+with
+$$A_6=\kappa_y \kappa_z,\,A_7=d_y \kappa_z+\kappa_y d_z,\,A_8=d_y d_z $$\\
+\noindent
+Inverse FT of $\frac{s_x s_z}{s_y}$ computed using MAPLE for right-hand side:\\
+$$A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t) $$
+with
+$$A_9=\frac{\kappa_z}{\kappa_y},\,A_{10}=0,
+\,A_{11}=\frac{d_z \kappa_y-d_y \kappa_z }{\kappa^2_y}$$\\
+\noindent
+Inverse FT of $\frac{s_x s_y}{s_z}$ computed using MAPLE for right-hand side:\\
+$$A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t) $$
+with
+$$A_{12}=\frac{\kappa_y}{\kappa_z},\,A_{13}=0,
+\,A_{14}=\frac{d_y \kappa_z-d_z \kappa_y }{\kappa^2_z}$$\\
+\noindent
+Inverse FT of $s_x$ computed using MAPLE for right-hand side:
+$$A_{15}\delta(t) + A_{16} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{15}= 1, \, A_{16}=0 $$
+\noindent
+Inverse FT of $s_y$ computed using MAPLE for right-hand side:
+$$A_{17}\delta(t) + A_{18} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{17}= \kappa_y, \, A_{18}=d_y $$
+\noindent
+Inverse FT of $s_z$ computed using MAPLE for right-hand side:
+$$A_{19}\delta(t) + A_{20} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{19}= \kappa_z, \, A_{20}=d_z $$
+d):XPML\\
+$\kappa_x,d_x$ defined as usual; $\alpha_x=\alpha$ but $\kappa_y = 1 ,d_y= 0,\alpha_y= 0$;$\,$ $\kappa_z = 1 ,d_z= 0,\alpha_z= 0$\\
+In this case inverse FT of $-\omega^2 s_x s_y s_z$ is:
+$$A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)$$
+with
+$$A_0 = \kappa_x \, , \, A_1 =d_x\, , \,A_2 = -\alpha d_x $$
+$$A_3= \alpha ^2 d_x , A_4= 0, A_5=0 $$
+\noindent
+Inverse FT of $\frac{s_y s_z}{s_x}$ computed using MAPLE for right-hand side:\\
+$$A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t) $$
+with
+$$A_6=\frac{1}{\kappa_x},\,A_7=0,\,A_8=-\frac{d_x}{\kappa^2_x} $$\\
+\noindent
+Inverse FT of $\frac{s_x s_z}{s_y}$ computed using MAPLE for right-hand side:\\
+$$A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t) $$
+with
+$$A_9=\kappa_x,\,A_{10}=d_x,
+\,A_{11}= 0 $$\\
+\noindent
+Inverse FT of $\frac{s_x s_y}{s_z}$ computed using MAPLE for right-hand side:\\
+$$ A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t) $$
+with
+$$A_{12}=\kappa_x ,\,A_{13}=d_x,
+\,A_{14}=0$$\\
+\noindent
+Inverse FT of $s_x$ computed using MAPLE for right-hand side:
+$$A_{15}\delta(t) + A_{16} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{15}= \kappa_x, \, A_{16}=d_x $$
+\noindent
+Inverse FT of $s_y$ computed using MAPLE for right-hand side:
+$$A_{17}\delta(t) + A_{18} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{17}= 1, \, A_{18}=0 $$
+\noindent
+Inverse FT of $s_z$ computed using MAPLE for right-hand side:
+$$A_{19}\delta(t) + A_{20} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{19}= 1, \, A_{20}=0 $$
+e):YPML\\
+$\kappa_y,d_y$ defined as usual; $\alpha_y=\alpha$ but $\kappa_x = 1 ,d_x= 0,\alpha_x= 0$;$\,$ $\kappa_z = 1 ,d_z= 0,\alpha_z= 0$\\
+In this case inverse FT of $-\omega^2 s_x s_y s_z$ is:
+$$A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)$$
+with
+$$A_0 = \kappa_y \, , \, A_1 =d_x\, , \,A_2 = -\alpha d_y $$
+$$A_3= \alpha ^2 d_y , A_4= 0, A_5=0 $$
+\noindent
+Inverse FT of $\frac{s_y s_z}{s_x}$ computed using MAPLE for right-hand side:\\
+$$A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t) $$
+with
+$$A_6=\kappa_y,\,A_7=d_y,\,A_8=0 $$\\
+\noindent
+Inverse FT of $\frac{s_x s_z}{s_y}$ computed using MAPLE for right-hand side:\\
+$$A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t) $$
+with
+$$A_9=\frac{1}{\kappa_y},\,A_{10}=0,
+\,A_{11}= -\frac{d_y}{\kappa^2_y} $$\\
+\noindent
+Inverse FT of $\frac{s_x s_y}{s_z}$ computed using MAPLE for right-hand side:\\
+$$ A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t) $$
+with
+$$A_{12}=\kappa_y ,\,A_{13}=d_y,
+\,A_{14}=0$$\\
+\noindent
+Inverse FT of $s_x$ computed using MAPLE for right-hand side:
+$$A_{15}\delta(t) + A_{16} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{15}= 1, \, A_{16}=0 $$
+\noindent
+Inverse FT of $s_y$ computed using MAPLE for right-hand side:
+$$A_{17}\delta(t) + A_{18} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{17}= \kappa_y, \, A_{18}=d_y $$
+\noindent
+Inverse FT of $s_z$ computed using MAPLE for right-hand side:
+$$A_{19}\delta(t) + A_{20} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{19}= 1, \, A_{20}=0 $$
+f):ZPML\\
+$\kappa_z,d_z$ defined as usual; $\alpha_z=\alpha$ but $\kappa_x = 1 ,d_x= 0,\alpha_x= 0$;$\,$ $\kappa_y = 1 ,d_y= 0,\alpha_y= 0$\\
+In this case inverse FT of $-\omega^2 s_x s_y s_z$ is:
+$$A_0 \delta''(t) + A_1 \delta'(t) + A_2 \delta(t)
++ A_3 {\rm e}^{-\alpha\,t} \, H(t)
++ A_4 {\rm e}^{-\alpha\,t} \,t\, H(t)
++ A_5 {\rm e}^{-\alpha\,t} \,t^{2} \,H(t)$$
+with
+$$A_0 = \kappa_z \, , \, A_1 =d_z\, , \,A_2 = -\alpha d_z $$
+$$A_3= \alpha ^2 d_z , A_4= 0, A_5=0 $$
+\noindent
+Inverse FT of $\frac{s_y s_z}{s_x}$ computed using MAPLE for right-hand side:\\
+$$A_6\delta(t) + A_7 {\rm e}^{-\alpha\,t} \, H(t) + A_8 {\rm e}^{-t(\alpha+\frac{d_x}{\kappa_x})} \, H(t) $$
+with
+$$A_6=\kappa_z,\,A_7=d_z,\,A_8=0 $$\\
+\noindent
+Inverse FT of $\frac{s_x s_z}{s_y}$ computed using MAPLE for right-hand side:\\
+$$A_9\delta(t) + A_{10} {\rm e}^{-\alpha\,t} \, H(t) + A_{11} {\rm e}^{-t(\alpha+\frac{d_y}{\kappa_y})} \, H(t) $$
+with
+$$A_9=\kappa_z,\,A_{10}=d_z,
+\,A_{11}=0 $$\\
+\noindent
+Inverse FT of $\frac{s_x s_y}{s_z}$ computed using MAPLE for right-hand side:\\
+$$ A_{12}\delta(t) + A_{13} {\rm e}^{-\alpha\,t} \, H(t) + A_{14} {\rm e}^{-t(\alpha+\frac{d_z}{\kappa_z})} \, H(t) $$
+with
+$$A_{12}=\frac{1}{\kappa_z} ,\,A_{13}=0,
+\,A_{14}=-\frac{d_z}{\kappa^2_z}$$\\
+\noindent
+Inverse FT of $s_x$ computed using MAPLE for right-hand side:
+$$A_{15}\delta(t) + A_{16} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{15}= 1, \, A_{16}=0 $$
+\noindent
+Inverse FT of $s_y$ computed using MAPLE for right-hand side:
+$$A_{17}\delta(t) + A_{18} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{17}= 1, \, A_{18}=0 $$
+\noindent
+Inverse FT of $s_z$ computed using MAPLE for right-hand side:
+$$A_{19}\delta(t) + A_{20} {\rm e}^{-\alpha \,t} \, H(t) $$
+with
+$$A_{19}= \kappa_y, \, A_{20}=d_z $$
+\\
+The time domain equation of CPML in edge-PML and surface-PML can be derived directly following the above way used to get the
+time domain equation of CPML in corner-PML
+\\
+\section{Time scheme for the convolution terms}
+The last step is to find a recursive way of computing all the convolutions.
+Equations for first-order convolution
+performed using the first-order-accurate recursive approach of \cite{LuHu92}
+(but they are unstable in practice):
+\begin{equation}
+\partial_{\tilde{x}} = \frac{1}{\kappa_x} \partial_ x + \psi_x
+\label{memory_variable_replace}
+\end{equation}
+%
+with
+\begin{equation}
+\psi_x^n = b_x \psi_x^{n - 1} + a_x \left(\partial_ x\right)^{n - \frac{1}{2}} \, .
+\label{time_evolution_psi}
+\end{equation}
+%
+Equations for second-order convolution:
+%
+To get a stable time scheme we thus use the second-order-accurate recursive approach developed recently in in Wang and Texeira 2006,
+which is that for a mathematical convolution
+$$f(t) = a {\rm e}^{-bt} H(t) * u(t) = a \psi_(t)$$
+from Wang and Texeira 2006 we know that we can compute the discrete form using
+\begin{equation}
+\psi^n = {\rm e}^{-b \Delta t} \psi^{n-1} + (\frac{1}{b} (1 - {\rm e}^{-b \Delta t /2})) u^n
++ (\frac{1}{b} (1 - {\rm e}^{-b \Delta t /2 }) {\rm e}^{-b \Delta t /2} \ ) u^{n-1}
+\end{equation}
+%
+It can also used to compute mathematical convolutions as following
+$$g(t) = [a {\rm e}^{-bt} t H(t)] * u(t)$$
+which gives
+$$g(t) = \int_{-\infty}^{t} a {\rm e}^{-b (t-\tau)} (t-\tau) H(t-\tau) u(\tau) d \tau$$
+according to linearity of convolution we have
+$$g(t) = at\int_{-\infty}^{t} {\rm e}^{-b (t-\tau)} H(t-\tau) u(\tau) d \tau - a\int_{-\infty}^{t} {\rm e}^{-b (t-\tau)} H(t-\tau) \tau u(\tau) d \tau $$
+or
+$$g(t) = at [ {\rm e}^{-bt} H(t) * u(t)] - a [ {\rm e}^{-bt} H(t) * (t u(t))] $$
+Then the same discrete scheme (19) can be used to compute the first and second square brackets term on the right hand.
+%
+Also we can used to compute mathematical convolutions as following
+$$g(t) = [a {\rm e}^{-bt} t^2 H(t)] * u(t)$$
+which gives
+$$g(t) = \int_{-\infty}^{t} a {\rm e}^{-b (t-\tau)} (t-\tau)^2 H(t-\tau) u(\tau) d \tau$$
+according to linearity of convolution we have
+$$g(t) = at^2\int_{-\infty}^{t} {\rm e}^{-b (t-\tau)} H(t-\tau) u(\tau) d \tau -
+2at\int_{-\infty}^{t} {\rm e}^{-b (t-\tau)} \tau H(t-\tau) u(\tau) d \tau+
+\int_{-\infty}^{t} a {\rm e}^{-b (t-\tau)} \tau^2 H(t-\tau) u(\tau) d \tau$$
+or
+$$g(t) = at^2[{\rm e}^{-bt} H(t) * u(t)] -
+2at[{\rm e}^{-bt} H(t) * (t u(t))]+
+[ {\rm e}^{-bt} H(t) * (t^2 u(t))]$$
+Then the same discrete scheme (19) can be used to compute the first, second and third square brackets term on the right hand.
+%
+%
+%
+%
+%
+%
+%%%%%%%%% BIBLIOGRAPHY %%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%\newpage
+\bibliography{Biblio1}
+%
+\end{document}
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Name: svn:mime-type
+ application/octet-stream
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