% HOW TO CITE SPECFEM3D CARTESIAN
% HowToCiteSPECFEM3DCartesian.bib
%
% This file includes the bibtex entries necessary for citing SPECFEM3D Cartesian.
%
% Citing software gives proper credit to those who contribute to the
% development of the code and allows CIG to gather citation metrics
% for our community.
%
% There are 3 parts to citing software:
%   I. Acknowledge CIG
%  II. Cite the code
% III. Cite published papers
%
% I. ACKNOWLEDGE CIG
% Use the following text in your “Acknowledgements”:
% We thank the Computational Infrastructure for Geodynamics (geodynamics.org) which is funded by the National Science Foundation under award EAR-0949446, EAR-1550901, and EAR-2149126 for supporting the development of SPECFEM3D Cartesian.


% II. CITE THE CODE
% Select the proper code version from the following:
%
@software{dimitri_komatitsch_2023_10413988,
  author       = {Dimitri Komatitsch and
                  Jeroen Tromp and
                  Rahul Garg and
                  Hom Nath Gharti and
                  Masaru Nagaso and
                  Elif Oral and
                  Daniel Peter and
                  Michael Afanasiev and
                  Rafael Almada and
                  Jean Paul Ampuero and
                  Etienne Bachmann and
                  Kangchen Bai and
                  Piero Basini and
                  Stephen Beller and
                  Jordan Bishop and
                  François Bissey and
                  Celine Blitz and
                  Alexis Bottero and
                  Ebru Bozdag and
                  Emanuele Casarotti and
                  Joseph Charles and
                  Min Chen and
                  Paul Cristini and
                  Clément Durochat and
                  Percy Galvez and
                  Rene Gassmoeller and
                  Dominik Goeddeke and
                  Leopold Grinberg and
                  Aakash Gupta and
                  Eric Heien and
                  Vala Hjoerleifsdottir and
                  Foivos Karakostas and
                  Sue Kientz and
                  Jesus Labarta and
                  Nicolas Le Goff and
                  Pieyre Le Loher and
                  Matthieu Lefebvre and
                  Qinya Liu and
                  Youshan Liu and
                  David Luet and
                  Yang Luo and
                  Alessia Maggi and
                  Federica Magnoni and
                  Roland Martin and
                  Rene Matzen and
                  G. D. McBain and
                  Dennis McRitchie and
                  Matthias Meschede and
                  Peter Messmer and
                  David Michea and
                  David Miller and
                  Ryan Modrak and
                  Vadim Monteiller and
                  Christina Morency and
                  Surendra Nadh Somala and
                  Tarje Nissen-Meyer and
                  Kevin Pouget and
                  Max Rietmann and
                  Elliott Sales de Andrade and
                  Brian Savage and
                  Bernhard Schuberth and
                  Anne Sieminski and
                  James Smith and
                  Leif Strand and
                  Carl Tape and
                  Eduardo Valero Cano and
                  Brice Videau and
                  Jean-Pierre Vilotte and
                  Huihui Weng and
                  Zhinan Xie and
                  Chang-Hua Zhang and
                  Hejun Zhu},
  title        = {SPECFEM/specfem3d: SPECFEM3D v4.1.0},
  month        = dec,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v4.1.0},
  doi          = {10.5281/zenodo.10413988},
  url          = {https://doi.org/10.5281/zenodo.10413988}
}
%
@software{dimitri_komatitsch_2023_7734075,
  author       = {Dimitri Komatitsch and
                  Daniel Peter and
                  Clément Durochat and
                  Vadim Monteiller and
                  Xie Zhinan and
                  1sbeller and
                  Aakash Gupta and
                  Jean Paul Ampuero and
                  Ryan Modrak and
                  Huihui Weng and
                  Emanuele Casarotti and
                  VmontLma and
                  Christina Morency and
                  Rene Gassmoeller and
                  Eric Heien and
                  Carl Tape and
                  Bottero and
                  David Luet and
                  Masaru Nagaso and
                  Kangchen Bai and
                  G. D. McBain and
                  Elif Oral and
                  Eduardo Valero Cano and
                  François Bissey and
                  David Miller and
                  Rafael Almada and
                  buildbot-princeton and
                  EtienneBachmann and
                  Min Chen and
                  Foivos Karakostas},
  title        = {SPECFEM/specfem3d: SPECFEM3D v4.0.0},
  month        = mar,
  year         = 2023,
  publisher    = {Zenodo},
  version      = {v4.0.0},
  doi          = {10.5281/zenodo.7734075},
  url          = {https://doi.org/10.5281/zenodo.7734075}
}
%
@software{specfem3dcartesian-v2.0.2,
  author       = {Komatitsch, D. and Vilotte, J.-P. and Tromp, J. and Ampuero, J.-P. and Bai, K. and Basini, P. and Blitz, C. and Bozdag, E. and Casarotti, E. and Charles, J. and Chen, M. and Galvez, P. and Goddeke, D. and Hjorleifsdottir, V. and Labarta, J. and Le Goff, N. and Le Loher, P. and Lefebvre, M. and Liu, Q. and Luo, Y. and Maggi, A. and Magnoni, F. and Martin, R. and Matzen, R. and McRitchie, D. and Meschede, M. and Messmer, P. and Michea, D. and Nadh Somala, S. and Nissen-Meyer, T. and Peter, D. and Rietmann, M. and de Andrade, E.S.  and Savage, B. and Schuberth, B. and Sieminski, A. and Strand, L. and Tape, C. and Xie, Z. and Zhu, H.},
  title        = {SPECFEM3D Cartesian v2.0.2 [software]},
  year         = 2012,
  version      = {v2.0.2},
  organization = {Computational Infrastructure for Geodynamics},
  optkeywords  = {SPECFEM3D Cartesian},
  doi          = {NoDOI}
}

% III. CITE PUBLISHED PAPERS
% Cite the following:
%
@article{,
  title   = {Spectral-element simulations of global seismic wave propagation-I. Validation},
  author  = {Komatitsch, D. and Tromp, J.},
  journal = {Geophysical Journal International},
  year    = {2002},
  pages   = {390-412},
  volume  = {149},
  number  = {2},
  optkeywords = {SPECFEM3D GLOBE},
  doi     = {10.1046/j.1365-246X.2002.01653.x},
  iSSN    = {0956540X},
  url     = {http://doi.wiley.com/10.1046/j.1365-246X.2002.01653.x}
}
@article{komatitsch2002spectral,
  title   = {Spectral-element simulations of global seismic wave propagation{\textendash}II. Three-dimensional models, oceans, rotation and self-gravitation},
  author  = {Komatitsch, D. and Tromp, J.},
  journal = {Geophysical Journal International},
  year    = {2002},
  pages   = {303-318},
  volume  = {150},
  number  = {1},
  publisher = {Oxford University Press}
}

% In addition, if you use any of the following features
% please cite:

% If you compute on GPU graphics cards for acoustic or seismic wave propagation applications, please cite one or more of the following:
@article{,
  title   = {Fluid-solid coupling on a cluster of GPU graphics cards for seismic wave propagation},
  author  = {Komatitsch, D.},
  journal = {Comptes Rendus Mécanique},
  year    = {2011},
  pages   = {125-135},
  volume  = {339},
  number  = {2-3},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1016/j.crme.2010.11.007},
  iSSN    = {1631-0721},
  url     = {http://linkinghub.elsevier.com/retrieve/pii/S1631072110002081}
}
@article{,
  title   = {Accelerating a three-dimensional finite-difference wave propagation code using GPU graphics cards: Accelerating a wave propagation code using GPUs},
  author  = {Mich{\'e}a, D. and Komatitsch, D.},
  journal = {Geophysical Journal International},
  year    = {2010},
  pages   = {389-402},
  volume  = {182},
  number  = {1},
  optkeywords = {SEISMIC_CPML},
  doi     = {10.1111/j.1365-246X.2010.04616.x},
  iSSN    = {0956540X},
  url     = {http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2010.04616.x}
}
@article{,
  title   = {Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA},
  author  = {Komatitsch, D. and Mich{\'e}a, D. and Erlebacher, G.},
  journal = {Journal of Parallel and Distributed Computing},
  year    = {2009},
  pages   = {451-460},
  volume  = {69},
  number  = {5},
  optkeywords = {SPECFEM3D GLOBE},
  doi     = {10.1016/j.jpdc.2009.01.006},
  iSSN    = {0743-7315},
  url     = {http://linkinghub.elsevier.com/retrieve/pii/S0743731509000069}
}
@article{,
  title   = {High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster},
  author  = {Komatitsch, D. and Erlebacher, G. and G{\"o}ddeke, D. and Mich{\'e}a, D.},
  journal = {Journal of Computational Physics},
  year    = {2010},
  pages   = {7692-7714},
  volume  = {229},
  number  = {20},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1016/j.jcp.2010.06.024},
  iSSN    = {0021-9991},
  url     = {http://linkinghub.elsevier.com/retrieve/pii/S0021999110003396}
}

% If you use this new version, which has non-blocking MPI for much better performance for medium or large runs, please cite at least one of these six articles, in which results of non -blocking MPI runs are presented:
@article{,
  title   = {Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes: SPECFEM3D Version 2.0 'Sesame'},
  author  = {Peter, D. and Komatitsch, D. and Luo, Y. and Martin, R. and Le Goff, N. and Casarotti, E. and Le Loher, P. and Magnoni, F. and Liu, Q. and Blitz, C. and Nissen-Meyer, T. and Basini, P. and Tromp, J.},
  journal = {Geophysical Journal International},
  year    = {2011},
  pages   = {721-739},
  volume  = {186},
  number  = {2},
  optkeywords = {SPECFEM3D Cartesian; SPECFEM3D GLOBE},
  doi     = {10.1111/j.1365-246X.2011.05044.x},
  iSSN    = {0956540X},
  url     = {http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2011.05044.x}
}
@article{,
  title   = {High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster},
  author  = {Komatitsch, D. and Erlebacher, G. and G{\"o}ddeke, D. and Mich{\'e}a, D.},
  journal = {Journal of Computational Physics},
  year    = {2010},
  pages   = {7692-7714},
  volume  = {229},
  number  = {20},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1016/j.jcp.2010.06.024},
  iSSN    = {0021-9991},
  url     = {http://linkinghub.elsevier.com/retrieve/pii/S0021999110003396}
}
@article{,
  title   = {SHdiff-SVdiff splitting in an isotropic Earth},
  author  = {Komatitsch, D. and Vinnik, L.P. and Chevrot, S.},
  journal = {Journal of Geophysical Research},
  year    = {2010},
  volume  = {115},
  number  = {B7},
  optkeywords = {SPECFEM3D GLOBE},
  doi     = {10.1029/2009JB006795},
  iSSN    = {0148-0227},
  url     = {http://doi.wiley.com/10.1029/2009JB006795}
}
@article{,
  title   = {Fluid-solid coupling on a cluster of GPU graphics cards for seismic wave propagation},
  author  = {Komatitsch, D.},
  journal = {Comptes Rendus Mécanique},
  year    = {2011},
  pages   = {125-135},
  volume  = {339},
  number  = {2-3},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1016/j.crme.2010.11.007},
  iSSN    = {1631-0721},
  url     = {http://linkinghub.elsevier.com/retrieve/pii/S1631072110002081}
}
@InProceedings{ref5215501,
  title   = {High-frequency simulations of global seismic wave propagation using SPECFEM3D_GLOBE on 62K processors},
  author  = {Carrington, L. and Komatitsch, D. and Laurenzano, M. and Tikir, M.M. and Michea, D. and Goff, N.L. and Snavely, A. and Tromp, J.},
  journal = {High Performance Computing, Networking, Storage and Analysis, 2008. SC 2008. International Conference for},
  year    = {2008},
  pages   = {1-11},
  optkeywords = {geophysics computing; microcomputers; seismic waves; seismology; solid modelling; wave propagation; 3D Earth models; Jaguar processor system; Ranger processor system; SPECFEM3D GLOBE application; XT4 Franklin processor system; XT4 Kraken processor system; computer speed 28.7 TFLOPS; computer speed 35.7 TFLOPS; global seismic wave propagation; global seismology; memory size 28 KByte; memory size 32 KByte; memory size 62 KByte; time 1.84 s; time 1.94 s; Anisotropic magnetoresistance; Bandwidth; Earth; Frequency; Load management; Scalability; Seismic waves; Seismology; Signal processing; Signal resolution; SPECFEM3D GLOBE},
  doi     = {10.1109/SC.2008.5215501}
}
@InProceedings{martin2008simulation,
  title   = {Simulation of seismic wave propagation in an asteroid based upon an unstructured MPI spectral-element method: blocking and non-blocking communication strategies},
  author  = {Martin, R. and Komatitsch, D. and Blitz, C. and Le Goff, N.},
  journal = {International Conference on High Performance Computing for Computational Science},
  year    = {2008},
  pages   = {350-363}
}

% If you work on simulations in Southern California, you may be interested in citing one or more of the following:
@article{,
  title   = {Simulations of Ground Motion in the Los Angeles Basin Based upon the Spectral-Element Method},
  author  = {Komatitsch, D.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {2004},
  pages   = {187-206},
  volume  = {94},
  number  = {1},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1785/0120030077},
  iSSN    = {0037-1106},
  url     = {http://bssa.geoscienceworld.org/cgi/doi/10.1785/0120030077}
}
@article{,
  title   = {Case Studies of Damage to Tall Steel Moment-Frame Buildings in Southern California during Large San Andreas Earthquakes},
  author  = {Krishnan, S.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {2006},
  pages   = {1523-1537},
  volume  = {96},
  number  = {4a},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1785/0120050145},
  iSSN    = {0037-1106},
  url     = {http://www.bssaonline.org/cgi/doi/10.1785/0120050145}
}
@article{,
  title   = {Performance of Two 18-Story Steel Moment-Frame Buildings in Southern California During Two Large Simulated San Andreas Earthquakes},
  author  = {Krishnan, S. and Ji, C. and Komatitsch, D. and Tromp, J.},
  journal = {Earthquake Spectra},
  year    = {2006},
  pages   = {1035-1061},
  volume  = {22},
  number  = {4},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1193/1.2360698},
  iSSN    = {8755-2930},
  url     = {http://earthquakespectra.org/doi/abs/10.1193/1.2360698}
}

% If you use the 3D Southern California model, you may be interested in citing one or more of the following:
@article{suss2003p,
  title   = {P wave seismic velocity structure derived from sonic logs and industry reflection data in the Los Angeles basin, California},
  author  = {Suss, M.P. and Shaw, J.H.},
  journal = {Journal of Geophysical Research: Solid Earth},
  year    = {2003},
  pages   = {2170},
  volume  = {108},
  number  = {B3},
  publisher = {Wiley Online Library},
  doi     = {10.1029/2001JB001628}
}
@article{lovely2006structural,
  title   = {A structural VP model of the Salton Trough, California, and its implications for seismic hazard},
  author  = {Lovely, P. and Shaw, J.H. and Liu, Q. and Tromp, J.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {2006},
  pages   = {1882-1896},
  volume  = {96},
  number  = {5},
  publisher = {Seismological Society of America}
}
@article{hauksson2000crustal,
  title   = {Crustal structure and seismicity distribution adjacent to the Pacific and North American plate boundary in southern California},
  author  = {Hauksson, E.},
  journal = {Journal of Geophysical Research B},
  year    = {2000},
  pages   = {13875-13903},
  volume  = {105},
  number  = {B6},
  publisher = {American Geophysical Union}
}
@article{zhu2000moho,
  title   = {Moho depth variation in southern California from teleseismic receiver functions},
  author  = {Zhu, L. and Kanamori, H.},
  journal = {Journal of Geophysical Research: Solid Earth},
  year    = {2000},
  pages   = {2969-2980},
  volume  = {105},
  number  = {B2},
  publisher = {Wiley Online Library}
}
@article{dreger1990broadband,
  title   = {Broadband modeling of local earthquakes},
  author  = {Dreger, D.S. and Helmberger, D.V.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {1990},
  pages   = {1162-1179},
  volume  = {80},
  number  = {5},
  publisher = {Seismological Society of America}
}

% If you use anisotropy, you may be interested in citing one or more of the following:
@article{,
  title   = {Theoretical and numerical investigations of global and regional seismic wave propagation in weakly anisotropic earth models},
  author  = {Chen, M. and Tromp, J.},
  journal = {Geophysical Journal International},
  year    = {2007},
  pages   = {1130-1152},
  volume  = {168},
  number  = {3},
  optkeywords = {SPECFEM3D Cartesian; SPECFEM3D GLOBE},
  doi     = {10.1111/j.1365-246X.2006.03218.x},
  iSSN    = {0956540X},
  url     = {http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2006.03218.x}
}
@article{,
  title   = {Rayleigh-Wave Multipathing along the West Coast of North America},
  author  = {Ji, C.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {2005},
  pages   = {2115-2124},
  volume  = {95},
  number  = {6},
  optkeywords = {SPECFEM3D GLOBE},
  doi     = {10.1785/0120040180},
  iSSN    = {0037-1106},
  url     = {http://bssa.geoscienceworld.org/cgi/doi/10.1785/0120040180}
}
@article{,
  title   = {Shear wave splitting in three-dimensional anisotropic media},
  author  = {Chevrot, S. and Favier, N. and Komatitsch, D.},
  journal = {Geophysical Journal International},
  year    = {2004},
  pages   = {711-720},
  volume  = {159},
  number  = {2},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1111/j.1365-246X.2004.02432.x},
  iSSN    = {0956540X},
  url     = {http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2004.02432.x}
}
@article{,
  title   = {Near-field influence on shear wave splitting and traveltime sensitivity kernels},
  author  = {Favier, N. and Chevrot, S. and Komatitsch, D.},
  journal = {Geophysical Journal International},
  year    = {2004},
  pages   = {467-482},
  volume  = {156},
  number  = {3},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1111/j.1365-246X.2004.02178.x},
  iSSN    = {0956540X},
  url     = {http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2004.02178.x}
}
@article{,
  title   = {Effects of crust and mantle heterogeneity on PP/P and SS/S amplitude ratios},
  author  = {Ritsema, J. and Rivera, L.A. and Komatitsch, D. and Tromp, J. and van Heijst, H.-J.},
  journal = {Geophysical Research Letters},
  year    = {2002},
  pages   = {72-1-72-4},
  volume  = {29},
  number  = {10},
  optkeywords = {SPECFEM3D GLOBE},
  doi     = {10.1029/2001GL013831},
  iSSN    = {0094-8276},
  url     = {http://doi.wiley.com/10.1029/2001GL013831}
}
@article{tromp2000spectral,
  title   = {Spectral-element simulations of wave propagation in a laterally homogeneous Earth model},
  author  = {Tromp, J. and Komatitsch, D.},
  journal = {Problems in Geophysics for the New Millennium},
  year    = {2000},
  pages   = {351-372},
  volume  = {INGV},
  publisher = {Ingv}
}

% If you use topography, you may be interested in citing one or more of the following:
@article{,
  title   = {Effects of Topography on Seismic-Wave Propagation: An Example from Northern Taiwan},
  author  = {Lee, S.-J. and Komatitsch, D. and Huang, B.-S. and Tromp, J.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {2009},
  pages   = {314-325},
  volume  = {99},
  number  = {1},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1785/0120080020},
  iSSN    = {0037-1106},
  url     = {http://www.bssaonline.org/cgi/doi/10.1785/0120080020}
}
@article{,
  title   = {Effects of Realistic Surface Topography on Seismic Ground Motion in the Yangminshan Region of Taiwan Based Upon the Spectral-Element Method and LiDAR DTM},
  author  = {Lee, S.-J. and Chan, Y.-C. and Komatitsch, D. and Huang, B.-S. and Tromp, J.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {2009},
  pages   = {681-693},
  volume  = {99},
  number  = {2a},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1785/0120080264},
  iSSN    = {0037-1106},
  url     = {http://www.bssaonline.org/cgi/doi/10.1785/0120080264}
}
@article{,
  title   = {Three-Dimensional Simulations of Seismic-Wave Propagation in the Taipei Basin with Realistic Topography Based upon the Spectral-Element Method},
  author  = {Lee, S.-J. and Chen, H.-W. and Liu, Q. and Komatitsch, D. and Huang, B.-S. and Tromp, J.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {2008},
  pages   = {253-264},
  volume  = {98},
  number  = {1},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1785/0120070033},
  iSSN    = {0037-1106},
  url     = {http://www.bssaonline.org/cgi/doi/10.1785/0120070033}
}
@article{,
  title   = {Numerical Simulation of Ground Rotations along 2D Topographical Profiles under the Incidence of Elastic Plane Waves},
  author  = {Godinho, L. and Amado Mendes, P. and Tadeu, A. and Cadena-Isaza, A. and Smerzini, C. and Sanchez-Sesma, F.J. and Madec, R. and Komatitsch, D.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {2009},
  pages   = {1147-1161},
  volume  = {99},
  number  = {2b},
  optkeywords = {SPECFEM2D},
  doi     = {10.1785/0120080096},
  iSSN    = {0037-1106},
  url     = {http://www.bssaonline.org/cgi/doi/10.1785/0120080096}
}
@article{,
  title   = {Analysis of strong scattering at the micro-scale},
  author  = {van Wijk, K. and Komatitsch, D. and Scales, J.A. and Tromp, J.},
  journal = {The Journal of the Acoustical Society of America},
  year    = {2004},
  pages   = {1006},
  volume  = {115},
  number  = {3},
  optkeywords = {SPECFEM2D},
  doi     = {10.1121/1.1647480},
  iSSN    = {0001-4966},
  url     = {http://scitation.aip.org/content/asa/journal/jasa/115/3/10.1121/1.1647480}
}
%If you use the C-PML absorbing layer capabilities of the code, please cite at least one article written by the developers of the package, for instance:
@article{10.1093/gji/ggu219,
    author = {Xie, Zhinan and Komatitsch, Dimitri and Martin, Roland and Matzen, René},
    title = "{Improved forward wave propagation and adjoint-based sensitivity kernel calculations using a numerically stable finite-element PML}",
    journal = {Geophysical Journal International},
    volume = {198},
    number = {3},
    pages = {1714-1747},
    year = {2014},
    month = {07},
    abstract = "{In recent years, the application of time-domain adjoint methods to improve large, complex underground tomographic models at the regional scale has led to new challenges for the numerical simulation of forward or adjoint elastic wave propagation problems. An important challenge is to design an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D convolution formulation of the complex-frequency-shifted unsplit-field perfectly matched layer (CFS-UPML) derived in previous work more flexible by providing a new treatment to analytically remove singular parameters in the formulation. We also extend this new formulation to 3-D. Furthermore, we derive the auxiliary differential equation (ADE) form of CFS-UPML, which allows for extension to higher order time schemes and is easier to implement. Secondly, we rigorously derive the CFS-UPML formulation for time-domain adjoint elastic wave problems, which to our knowledge has never been done before. Thirdly, in the case of classical low-order FE methods, we show numerically that we achieve long-time stability for both forward and adjoint problems both for the convolution and the ADE formulations. In the case of higher order Legendre spectral-element methods, we show that weak numerical instabilities can appear in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and the main domain only, thus avoiding the need to solve a backward wave propagation problem inside the CFS-UPML, which is known to be highly ill-posed. Finally, by providing several examples we show numerically that our formulation is efficient at absorbing acoustic waves for normal to near-grazing incident body waves as well as surface waves.}",
    issn = {0956-540X},
    doi = {10.1093/gji/ggu219},
    url = {https://doi.org/10.1093/gji/ggu219},
    eprint = {https://academic.oup.com/gji/article-pdf/198/3/1714/1583823/ggu219.pdf},
}
@article{doi:10.1121/1.4954736,
author = {Xie,Zhinan  and Matzen,René  and Cristini,Paul  and Komatitsch,Dimitri  and Martin,Roland },
title = {A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms},
journal = {The Journal of the Acoustical Society of America},
volume = {140},
number = {1},
pages = {165-175},
year = {2016},
doi = {10.1121/1.4954736},
URL = {   https://doi.org/10.1121/1.4954736},
eprint = {    https://doi.org/10.1121/1.4954736}
}
%If you use the attenuation (anelastic/viscoelastic) capabilities of the code, please cite at least one article written by the developers of the package, for instance:
@article{10.1093/gji/ggw024,
    author = {Blanc, Émilie and Komatitsch, Dimitri and Chaljub, Emmanuel and Lombard, Bruno and Xie, Zhinan},
    title = "{Highly accurate stability-preserving optimization of the Zener viscoelastic model, with application to wave propagation in the presence of strong attenuation}",
    journal = {Geophysical Journal International},
    volume = {205},
    number = {1},
    pages = {427-439},
    year = {2016},
    month = {02},
    abstract = "{This paper concerns the numerical modelling of time-domain mechanical waves in viscoelastic media based on a generalized Zener model. To do so, classically in the literature relaxation mechanisms are introduced, resulting in a set of the so-called memory variables and thus in large computational arrays that need to be stored. A challenge is thus to accurately mimic a given attenuation law using a minimal set of relaxation mechanisms. For this purpose, we replace the classical linear approach of Emmerich \\& Korn with a nonlinear optimization approach with constraints of positivity. We show that this technique is more accurate than the linear approach. Moreover, it ensures that physically meaningful relaxation times that always honour the constraint of decay of total energy with time are obtained. As a result, these relaxation times can always be used in a stable way in a modelling algorithm, even in the case of very strong attenuation for which the classical linear approach may provide some negative and thus unusable coefficients.}",
    issn = {0956-540X},
    doi = {10.1093/gji/ggw024},
    url = {https://doi.org/10.1093/gji/ggw024},
    eprint = {https://academic.oup.com/gji/article-pdf/205/1/427/8036946/ggw024.pdf},
}
%If you use the kernel capabilities of the code, please cite at least one article written by the developers of the package, for instance:
@article{tromp2008spectral,
  Title   = {Spectral-element and adjoint methods in seismology},
  Author  = {Tromp, J. and Komatitsch, D. and Liu, Q.},
  Journal = {Communications in Computational Physics},
  Year    = {2008},
  Pages   = {1-32},
  Volume  = {3},
  Number  = {1}
}
@article{,
  title   = {Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes: SPECFEM3D Version 2.0 'Sesame'},
  author  = {Peter, D. and Komatitsch, D. and Luo, Y. and Martin, R. and Le Goff, N. and Casarotti, E. and Le Loher, P. and Magnoni, F. and Liu, Q. and Blitz, C. and Nissen-Meyer, T. and Basini, P. and Tromp, J.},
  journal = {Geophysical Journal International},
  year    = {2011},
  pages   = {721-739},
  volume  = {186},
  number  = {2},
  optkeywords = {SPECFEM3D Cartesian; SPECFEM3D GLOBE},
  doi     = {10.1111/j.1365-246X.2011.05044.x},
  iSSN    = {0956540X},
  url     = {http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2011.05044.x}
}
@article{,
  title   = {Finite-Frequency Kernels Based on Adjoint Methods},
  author  = {Liu, Q. and Tromp, J.},
  journal = {Bulletin of the Seismological Society of America},
  year    = {2006},
  pages   = {2383-2397},
  volume  = {96},
  number  = {6},
  optkeywords = {SPECFEM3D Cartesian},
  doi     = {10.1785/0120060041},
  iSSN    = {0037-1106},
  url     = {http://www.bssaonline.org/cgi/doi/10.1785/0120060041}
}
@article{,
  title   = {Finite-frequency kernels for wave propagation in porous media based upon adjoint methods},
  author  = {Morency, C. and Luo, Y. and Tromp, J.},
  journal = {Geophysical Journal International},
  year    = {2009},
  pages   = {1148-1168},
  volume  = {179},
  number  = {2},
  optkeywords = {SPECFEM2D},
  doi     = {10.1111/j.1365-246X.2009.04332.x},
  iSSN    = {0956540X},
  url     = {http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2009.04332.x}
}
%If you use attenuation, you may be interested in citing one or more of the following:
@article{,
  Title   = {Effects of 3D Attenuation on Seismic Wave Amplitude and Phase Measurements},
  Author  = {Savage, B. and Komatitsch, D. and Tromp, J.},
  Journal = {Bulletin of the Seismological Society of America},
  Year    = {2010},
  Pages   = {1241-1251},
  Volume  = {100},
  Number  = {3},
  optkeywords  = {SPECFEM3D Cartesian},
  iSSN    = {0037-1106},
  doi     = {10.1785/0120090263},
  opturl  = {http://www.bssaonline.org/cgi/doi/10.1785/0120090263}
}
@article{,
  Title   = {Spectral-element simulations of global seismic wave propagation-I. Validation},
  Author  = {Komatitsch, D. and Tromp, J.},
  Journal = {Geophysical Journal International},
  Year    = {2002},
  Pages   = {390-412},
  Volume  = {149},
  Number  = {2},
  optkeywords  = {SPECFEM3D GLOBE},
  iSSN    = {0956540X},
  doi     = {10.1046/j.1365-246X.2002.01653.x},
  opturl  = {http://doi.wiley.com/10.1046/j.1365-246X.2002.01653.x}
}
@article{10.1046/j.1365-246x.1999.00967.x,
    author = {Komatitsch, Dimitri and Tromp, Jeroen},
    title = "{Introduction to the spectral element method for three-dimensional seismic wave propagation}",
    journal = {Geophysical Journal International},
    volume = {139},
    number = {3},
    pages = {806-822},
    year = {1999},
    month = {12},
    abstract = "{We present an introduction to the spectral element method, which provides an innovative numerical approach to the calculation of synthetic seismograms in 3-D earth models. The method combines the flexibility of a finite element method with the accuracy of a spectral method. One uses a weak formulation of the equations of motion, which are solved on a mesh of hexahedral elements that is adapted to the free surface and to the main internal discontinuities of the model. The wavefield on the elements is discretized using high-degree Lagrange interpolants, and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix, which greatly simplifies the algorithm. We illustrate the great potential of the method by comparing it to a discrete wavenumber/reflectivity method for layer-cake models. Both body and surface waves are accurately represented, and the method can handle point force as well as moment tensor sources. For a model with very steep surface topography we successfully benchmark the method against an approximate boundary technique. For a homogeneous medium with strong attenuation we obtain excellent agreement with the analytical solution for a point force.}",
    issn = {0956-540X},
    doi = {10.1046/j.1365-246x.1999.00967.x},
    url = {https://doi.org/10.1046/j.1365-246x.1999.00967.x},
    eprint = {https://academic.oup.com/gji/article-pdf/139/3/806/6006771/139-3-806.pdf},
}