[cig-commits] commit: Added figure captions.
Mercurial
hg at geodynamics.org
Tue Apr 24 15:09:58 PDT 2012
changeset: 107:a60533730e6c
tag: tip
user: Brad Aagaard <baagaard at usgs.gov>
date: Tue Apr 24 15:09:48 2012 -0700
files: faultRup.tex figs/savageprescott_soln.png figs/solvertest_mesh.png references.bib
description:
Added figure captions.
diff -r bcb3dd2fb96d -r a60533730e6c faultRup.tex
--- a/faultRup.tex Tue Apr 24 13:18:27 2012 -0700
+++ b/faultRup.tex Tue Apr 24 15:09:48 2012 -0700
@@ -1325,6 +1325,7 @@ MGK acknowledges partial support from NS
% ------------------------------------------------------------------
% FIGURES
% ------------------------------------------------------------------
+\pagebreak
\begin{figure}
\noindent\includegraphics{figs/domaindecomp}
@@ -1333,27 +1334,6 @@ MGK acknowledges partial support from NS
across the fault, whereas the tractions are continuous.}
\label{fig:domain:decomposition}
\end{figure}
-
-\begin{figure*}
- \noindent\includegraphics{figs/cohesivecell}
- \caption{Construction of cohesive cells for a fault. (a) Original
- mesh with fault normal and fault vertices identified. (b) For each
- vertex on the fault, introduce a vertex on the positive side of
- the fault $S_{f^+}$ and a vertex corresponding to the Lagrange
- multiplier constraint between the pair of vertices on the positive
- and negative sides of the fault. (c) Identify cells with faces on
- the fault. Use the orientation of each face to identify cells on
- the positive and negative sides of the fault. Replace vertices in
- cells on the positive side of the fault with the newly created
- vertices. (d) Classify remaining cells with vertices on the fault
- using breadth-first search, and replace original vertices in cells
- on positive side of the fault with newly created
- vertices. Construct cohesive cells with zero volume from the
- vertices on the positive side of the fault, negative side of the
- fault, and Lagrange multiplier constraints.}
- \label{fig:cohesive:cell}
-\end{figure*}
-
\begin{figure}
\noindent\includegraphics{figs/solvertest_geometry}
@@ -1387,61 +1367,155 @@ MGK acknowledges partial support from NS
\begin{figure}
\noindent\includegraphics[width=84mm]{figs/savageprescott_soln}
- \caption{ADD CAPTION}
+ \caption{Deformation (exaggerated by a factor of 5000) 95\% of the
+ way through earthquake cycle 10 of the Savage and Prescott
+ benchmark involving viscoelastic relaxation over multiple
+ earthquake cycles on a vertical, strike-slip fault. The
+ coordinates are in units of locking depth and the displacement
+ field is in units of coseismic slip. The locking depth is one-half
+ of the thickness of the elastic layer. We refine the mesh by a
+ factor of three near the center of the
+ domain. Figure~\ref{fig:savage:prescott:profiles} compares
+ profiles along y=0 with the analytic solution.}
\label{fig:savage:prescott::solution}
\end{figure}
-\clearpage
+
\begin{figure}
\noindent\includegraphics{figs/savageprescott_profiles}
- \caption{ADD CAPTION}
+ \caption{Comparison of displacement profiles perpendicular to the
+ fault in the Savage and Prescott benchmark during earthquake
+ cycles 3 and 10. The displacements values shown are
+ relative to the values at the beginning of the earthquake cycle to
+ faciliate comparison between the analytical solution and the
+ numerical models which require spinup to reach the steady-state
+ solution. Both the hexahedral (Hex8) and tetrahedral (Tet4)
+ discretizations resolve the viscoelastic deformation and display
+ excellent agreement with the steady-state solution by the tenth
+ earthquake cycle.}
\label{fig:savage:prescott:profiles}
\end{figure}
\begin{figure}
\noindent\includegraphics{figs/tpv13_geometry}
- \caption{ADD CAPTION}
+ \caption{Geometry for SCEC Dynamic Rupture Benchmark TPV13 involving
+ a Drucker-Prager elastoplastic bulk rheology, slip-weakening
+ friction, a depth-dependent stress field, and normal fault with a
+ 60 degree dip angle. The 2-D version corresponds to the vertical
+ slice shown by the dashed line. The red dotes denote locations on
+ the fault used in the comparison of the vertical slip dates
+ (Figures~\ref{fig:tpv13-2d:slip:rate}
+ and~\ref{fig:tpv13:slip:rate}). The blue dots indicate locations
+ on the ground surface used in the comparison of fault normal and
+ vertical velocity time histories (Figure~\ref{fig:tpv13:velocity}).}
\label{fig:tpv13:geometry}
\end{figure}
-\clearpage
\begin{figure}
\noindent\includegraphics[width=84mm]{figs/tpv13-2d_mesh}
- \caption{ADD CAPTION}
+ \caption{Finite-element mesh comprised of triangular cells for SCEC
+ Dynamic Rupture Benchmark TPV13-2D. The discretization size is 100
+ m on the fault surface and increases at a geometric rate of 2\%
+ with distance from the fault. We employ this same spatial
+ variation of the discretization size in the 3-D model.}
\label{fig:tpv13-2d:mesh}
\end{figure}
\begin{figure}
\noindent\includegraphics{figs/tpv13-2d_tri3_100m_stressslip}
- \caption{ADD CAPTION}
+ \caption{(a) Depth-dependent fault tractions in SCEC Dynamic Rupture
+ Benchmark TPV13-2D and TPV13. $T_\mathit{shear}$ denotes the
+ initial shear traction, $T_\mathit{normal}$ denotes the initial
+ effective normal traction, $T_\mathit{failure}$ denotes the
+ frictional failure stress corresponding to the initial effective
+ normal traction, and $T_\mathit{sliding}$ denotes the dynamic
+ sliding stress corresponding to the initial effective normal
+ traction. Positive shear tractions correspond to normal faulting
+ and negative normal tractions correspond to compression. (b) Final
+ slip as a function of depth in TPV13-2D for the triangular mesh
+ with a resolution of 100 m on the fault.}
\label{fig:tpv13-2d:stress:slip}
\end{figure}
-\begin{figure*}
+\clearpage
+\begin{figure*}[h]
+ \noindent\includegraphics{figs/cohesivecell}
+ \caption{Construction of cohesive cells for a fault. (a) Original
+ mesh with fault normal and fault vertices identified. (b) For each
+ vertex on the fault, introduce a vertex on the positive side of
+ the fault $S_{f^+}$ and a vertex corresponding to the Lagrange
+ multiplier constraint between the pair of vertices on the positive
+ and negative sides of the fault. (c) Identify cells with faces on
+ the fault. Use the orientation of each face to identify cells on
+ the positive and negative sides of the fault. Replace vertices in
+ cells on the positive side of the fault with the newly created
+ vertices. (d) Classify remaining cells with vertices on the fault
+ using breadth-first search, and replace original vertices in cells
+ on positive side of the fault with newly created
+ vertices. Construct cohesive cells with zero volume from the
+ vertices on the positive side of the fault, negative side of the
+ fault, and Lagrange multiplier constraints.}
+ \label{fig:cohesive:cell}
+\end{figure*}
+
+
+\begin{figure*}[h]
\noindent\includegraphics{figs/tpv13-2d_sliprate}
- \caption{ADD CAPTION}
+ \caption{Slip rate time histories for SCEC Dynamic Rupture Benchmark
+ TPV13-2D. Locations correspond to the red dots along the
+ centerline of the fault shown in
+ Figure~\ref{fig:tpv13:geometry}. Panels (a)--(d) show convergence
+ of the solution for quadrilateral and triangular cells as a
+ function of discretization size, and panels (e)--(h) demonstrate
+ of code verification via excellent agreement among PyLith and four
+ other dynamic rupture modeling codes
+ \citep{Harris:etal:SRL:2011}.}
\label{fig:tpv13-2d:slip:rate}
\end{figure*}
-\begin{figure*}
+\begin{figure*}[h]
\noindent\includegraphics{figs/tpv13_ruptime}
- \caption{ADD CAPTION}
+ \caption{Rupture time contours (0.5 s interval) for SCEC Dynamic
+ Rupture Benchmark TPV13. (a) Effect of discretization size and (b)
+ demonstration of code verification via excellent agreement among
+ PyLith and three other dynamic rupture modeling codes
+ \citep{Harris:etal:SRL:2011}. The contours for PyLith and Kaneko
+ (spectral element code) are nearly identical.}
\label{fig:tpv13:rupture:time}
\end{figure*}
-\clearpage
-\begin{figure*}
+\begin{figure*}[h]
\noindent\includegraphics{figs/tpv13_sliprate}
- \caption{ADD CAPTION}
+ \caption{Comparison of normal faulting component of slip rate at six
+ locations on the fault surface for SCEC Dynamic Rupture Benchmark
+ TPV13. (a)--(c) are at a depth of 0 km and (d)--(f) are at a depth
+ of 7.5 km. The slip rate time histories for all four dynamic
+ rupture modeling codes agree very well. At 12 km along strike and
+ 7.5 km down dip, there is a small discrepancy between two groups
+ of codes (PyLith and Kaneko versus Barall and Ma) that we
+ attribute to how the modelers handled the discontinuity in the
+ initial stress field and parameters.}
\label{fig:tpv13:slip:rate}
+\end{figure*}
+
+\begin{figure*}[h]
+ \noindent\includegraphics{figs/tpv13_velth}
+ \caption{Comparison of fault normal and vertical components of
+ velocity time histories at two sites on the ground surface for
+ SCEC Dynamic Rupture Benchmark TPV13. Panels (a)--(b) are
+ associated with a site that is on the hanging wall 3 km from the
+ fault trace and 12 km along strike, and panels (c)--(d) are
+ assocaited with a site that is on the footwall 3 km from the fault
+ trace along the fault centerline. As expected based on the close
+ agreement in the rupture time contours and fault slip rates, the
+ velocity time histories from the difference dynamic rupture
+ modeling codes agree very closely.}
+ \label{fig:tpv13:velocity}
\end{figure*}
% ------------------------------------------------------------------
% TABLES
% ------------------------------------------------------------------
-\clearpage
-\pagebreak
-
\begin{table*}
\caption{Example Preconditioners for the Saddle Point Problem in
Equation~(\ref{eqn:saddle:point})\tablenotemark{a}}
diff -r bcb3dd2fb96d -r a60533730e6c figs/savageprescott_soln.png
Binary file figs/savageprescott_soln.png has changed
diff -r bcb3dd2fb96d -r a60533730e6c figs/solvertest_mesh.png
Binary file figs/solvertest_mesh.png has changed
diff -r bcb3dd2fb96d -r a60533730e6c references.bib
--- a/references.bib Tue Apr 24 13:18:27 2012 -0700
+++ b/references.bib Tue Apr 24 15:09:48 2012 -0700
@@ -245,6 +245,42 @@
note = {in press},
doi = {10.1111/j.1365-246X.2011.05117.x},
abstract = {},
+}
+
+ at Article{Harris:etal:SRL:2011,
+ author = {Harris, R.~A. and Barall, M. and Andrews, D.~J. and
+ Duan, B. and Ma, S. and Dunham, E.~M. and Gabriel,
+ A.~A. and Kaneko, Y. and Kase, Y. and Aagaard,
+ B.~T. and Oglesby, D.~D. and Ampuero, J.~P. and
+ Hanks, T.~C. and Abrahamson, N.},
+ title = {Verifying a computational method for predicting
+ extreme ground motion},
+ journal = SRL,
+ year = {2011},
+ volume = {82},
+ number = {5},
+ month = {sep #{/} oct},
+ pages = {638--644},
+ doi = {10.1785/gssrl.82.5.638}
+}
+
+ at Article{Harris:etal:SRL:2009,
+ author = {Harris, R.~A. and Barall, M. and Archuleta, R. and
+ Dunham, E. and Aagaard, B. and Ampuero, J.~P. and
+ Bhat, H. and Cruz-Atienza, V. and Dalguer, L. and
+ Dawson, P. and Day, S. and Duan, B. and Ely, G. and
+ Kase, Y. and Lapusta, N. and Liu, Y. and Ma, S. and
+ Oglesby, D. and Olsen, K. and Pitarka, A. and Song,
+ S. and Templeton, E.},
+ title = {The {SCEC}/{USGS} Dynamic Earthquake Rupture Code
+ Verification Exercise},
+ journal = SRL,
+ year = {2009},
+ volume = 80,
+ number = 1,
+ month = jan #{/} #feb,
+ pages = {119--126},
+ doi = {10.1785/gssrl.80.1.119}
}
@Article{Kaneko:etal:????,
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