[cig-commits] commit: More work on text for TPV13.
Mercurial
hg at geodynamics.org
Tue Apr 24 17:16:07 PDT 2012
changeset: 108:01f064fce659
tag: tip
user: Brad Aagaard <baagaard at usgs.gov>
date: Tue Apr 24 17:15:57 2012 -0700
files: faultRup.tex references.bib
description:
More work on text for TPV13.
diff -r a60533730e6c -r 01f064fce659 faultRup.tex
--- a/faultRup.tex Tue Apr 24 15:09:48 2012 -0700
+++ b/faultRup.tex Tue Apr 24 17:15:57 2012 -0700
@@ -6,6 +6,7 @@
\usepackage{array}
\usepackage{rotating}
\usepackage[centertags]{amsmath}
+\usepackage{url}
% :SUBMIT: if draft, comment out this line
\usepackage{graphics}
@@ -182,12 +183,12 @@ discuss later.
Additional motivation for developing PyLith arose from the geophysics
community as part of the Computational Infrastructure for Geodynamics
-(CIG) project \citep{CIG:web:page}. CIG provides guidelines for
-developing robust, open-source code as well as a forum for gathering
-feature requests from the community. Serving the broad needs of the
-community with limited resources generated further incentives for
-designing PyLith to leverage common infrastructure for simulating
-quasi-static and dynamic deformation. Maintaining two
+(CIG) project (\url{http://www.geodynamics.org}). CIG provides
+guidelines for developing robust, open-source code as well as a forum
+for gathering feature requests from the community. Serving the broad
+needs of the community with limited resources generated further
+incentives for designing PyLith to leverage common infrastructure for
+simulating quasi-static and dynamic deformation. Maintaining two
seperate code bases would require a considerably greater development
effort.
@@ -393,7 +394,7 @@ Extensible Toolkit for Scientific Comput
Extensible Toolkit for Scientific Computation (PETSc), which provides
a suite of tools for solving linear systems of algebraic equations
with parallel processing
-\citep{PETSc:web:page,PETSc:manual,PETSC:efficient}. In solving the
+\citep{PETSc:manual,PETSC:efficient}. In solving the
system, we compute the residual (i.e., $\mathbf{r} = \mathbf{b} -
\mathbf{A} \cdot \mathbf{u}$ and the Jacobian of the system
($\mathbf{A}$). In our case the solution is $\mathbf{u} =
@@ -1231,6 +1232,25 @@ the other hand, shows a significant incr
\section{Code Verification Benchmarks}
\label{sec:verification:benchmarks}
+In developing PyLith we verify the numerical implementation using a
+number of techniques. We employ unit testing to verify correct
+implementation of nearly all of the individual routines. Having a test
+for most object methods or functions isolates most bugs at their
+origin during code development and prevents new bugs from occurring as
+code is modified or optimized. We also rely on full-scale benchmarks
+to verify that the code properly solves the numerical problem. In this
+section we focus on two benchmarks that test two different
+applications: quasi-static relaxation of a Maxwell viscoelastic
+material subjected to multiple earthquake cycles involving slip and
+steady creep on a vertical strike-slip fault
+\citep{Savage:Prescott:????} and supeshear spontaneous dynamic rupture
+of a 60 degree dipping normal fault in a Drucker-Prager elastoplastic
+medium. This second benchmark corresponds
+to benchmark TPV13 in the suite of spontaneous dynamic rupture
+benchmarks constructed by the Southern California Earthquake Center
+(SCEC) and the United States Geological Survey
+\citep{Harris:etal:SRL:2009}.
+
\subsection{Quasi-static}
\label{sec:verification:quasi-static}
@@ -1243,12 +1263,96 @@ the other hand, shows a significant incr
\item Geometry
\item profiles for cycles 3 and 10
\end{itemize}
+ \item Table of parameters
\item Spin-up, compare hex8 and tet4 against analytic solution
\end{itemize}
\end{itemize}
+\brad{QUESTIONS FOR CHARLES: The hex8 versus tet4 comparison isn't very
+ useful as both give essentially identical results. Would looking at
+ another quanitity (displacement along a vertical profile, or stress)
+ provide a more stringent test? Is there an easy way to adjust the
+ parameters to give something more numerically challenging
+ (higher/lower viscosity, coarser mesh)?}
\subsection{Dynamic}
\label{sec:verification:dynamic}
+
+SCEC Spontaneous Rupture Benchmark TPV13 focuses on modeling an
+earthquake that produces extreme (very large) ground motions
+associated with supershear rupture towards the ground surface on a
+dipping fault a large stress drop to generate large slip and fast slip
+rates \citep{Harris:etal:SRL:2011}. It uses a Drucker-Prager
+elastoplastic bulk rheology and a slip-weakening friction model in a
+depth-dependent initial stress field. Figure~\ref{fig:tpv13:geometry}
+show the geometry of the benchmark problem and the size of the domain
+we used in our verification test. The benchmark includes both 2-D
+(TPV13-2D is a vertical slice through the fault centerline with plane
+strain conditions) and 3-D versions (TPV13). This benchmark specifies
+a spatial resolution of 100 m on the fault surface. In order to
+examine the effects of cell type and discretization size we consider
+both triangular and quadrilateral discretizations with resolutions on
+the fault of 50 m, 100 m, and 200 m for TPV13-2D and 100 m and 200 m
+for TPV13. We gradually coarsen the mesh with distance from the fault
+by increasing the discretization size at a geometrirc rate of
+2\%. This provides high resolution at the fault surface to resolve the
+small scale features of the rupture process with less resolution at
+the edges of the boundary where the solution is much
+smoother. Figure~\ref{tpv13-2d:mesh} shows the triangular mesh for a
+discretization size of 100 m on the fault.
+
+Rupture initiates due to a low static coefficient of friction in the
+nucleation region. Figure~\ref{fig:tpv13-2d:stress:slip} illustrates
+the depth dependence of the stress field in terms of the fault
+tractions and Table~\ref{tab:tpv13:parameters} summarizes the
+benchmark parameters. \cite{Harris:etal:SRL:2011} provides a more
+complete description with all of the details available from
+\url{http://scecdata.usc.edu/cvws/cgi-bin/cvws.cgi}. An unfortunate
+feature of this, and many other benchmarks in the SCEC Spontaneous
+Rupture Code Verification Exercise, is the use of parameters with
+spatial variations that are not continuous. This includes the
+variation in the static coefficient of friction for the nucleation
+region and the transition to zero deviatoric stresses near the bottom
+of the fault. We impose the geometry of these discontinuities in the
+construction of the finite-element mesh and use the spatial average of
+the parameters where they are discontinuous. This decreases the
+sensitivity of the numerical solution to the discretization size. This
+benchmark also includes fluid pressures. Because PyLith does not
+include fluid pressure, we formulate the simulation parameters in
+terms of effective stresses.
+
+Figure~\ref{fig:tpv13-2d:stress:slip} displays the final slip
+distribution in the TPV13-2D simulation with triangular cells at a
+resolution of 100 m. The large dynamic stress drop and supershear
+rupture generate 20 m of slip at a depth of about 7
+km. Figure~\ref{fig:tpv13-2d:slip:rate}(a) demonstrates the convergence
+of the solution as the discretization size decreases as evidence in
+the normal faulting component of fault slip rate time histories. For a
+resolution of 200 m on the fault, the solution contains some
+high-frequency oscillation due to insufficient resolution of the
+cohesive zone \citep{Rice:????}. The finer meshes provide sufficient
+resolution of the cohesive zone so there is very little high-frequency
+oscillation in the slip rate time histories. The triangular cells
+result in less oscillation compared with quadrilateral cells.
+
+In this problem without an analytical solution, we rely on comparison
+with other spontaneous dynamic rupture modeling codes to verify the
+numerical implementation in
+PyLith. Figure~\ref{fig:tpv13-2d:slip:rate}(b) compares the slip rate
+time histories from PyLith with four other codes (see
+\citep{Harris:etal:SRL:2011} for a discussion of these other
+finite-element and finite-difference codes). The slip rate time
+histories agree very well, although some codes yield more oscillation
+than others. We attribute this to variations in the amount of
+numerical damping used across the various codes.
+
+
+
+From the 2-D and 3-D versions of the SCEC spontaneous rupture
+benchmark TPV13, we conclude that the PyLith performs very similarly
+to other finite-element and finite-difference spontaneous dynamic
+rupture modeling codes in this relatively complex problem involving a
+Drucker-Prager elastoplastic builk rheology, slip-weakening friction,
+and supershear rupture on a dipping normal fault.
\begin{itemize}
\item Spontaneous rupture benchmark: TPV13
@@ -1398,7 +1502,7 @@ MGK acknowledges partial support from NS
\begin{figure}
\noindent\includegraphics{figs/tpv13_geometry}
- \caption{Geometry for SCEC Dynamic Rupture Benchmark TPV13 involving
+ \caption{Geometry for SCEC spontaneous 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
@@ -1414,7 +1518,7 @@ MGK acknowledges partial support from NS
\begin{figure}
\noindent\includegraphics[width=84mm]{figs/tpv13-2d_mesh}
\caption{Finite-element mesh comprised of triangular cells for SCEC
- Dynamic Rupture Benchmark TPV13-2D. The discretization size is 100
+ spontaneous 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.}
@@ -1423,8 +1527,8 @@ MGK acknowledges partial support from NS
\begin{figure}
\noindent\includegraphics{figs/tpv13-2d_tri3_100m_stressslip}
- \caption{(a) Depth-dependent fault tractions in SCEC Dynamic Rupture
- Benchmark TPV13-2D and TPV13. $T_\mathit{shear}$ denotes the
+ \caption{(a) Depth-dependent fault tractions in SCEC spontaneous 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
@@ -1437,7 +1541,6 @@ MGK acknowledges partial support from NS
\label{fig:tpv13-2d:stress:slip}
\end{figure}
-\clearpage
\begin{figure*}[h]
\noindent\includegraphics{figs/cohesivecell}
\caption{Construction of cohesive cells for a fault. (a) Original
@@ -1461,7 +1564,7 @@ MGK acknowledges partial support from NS
\begin{figure*}[h]
\noindent\includegraphics{figs/tpv13-2d_sliprate}
- \caption{Slip rate time histories for SCEC Dynamic Rupture Benchmark
+ \caption{Slip rate time histories for SCEC spontaneous 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
@@ -1475,8 +1578,8 @@ MGK acknowledges partial support from NS
\begin{figure*}[h]
\noindent\includegraphics{figs/tpv13_ruptime}
- \caption{Rupture time contours (0.5 s interval) for SCEC Dynamic
- Rupture Benchmark TPV13. (a) Effect of discretization size and (b)
+ \caption{Rupture time contours (0.5 s interval) for SCEC spontaneous
+ 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
@@ -1487,7 +1590,7 @@ MGK acknowledges partial support from NS
\begin{figure*}[h]
\noindent\includegraphics{figs/tpv13_sliprate}
\caption{Comparison of normal faulting component of slip rate at six
- locations on the fault surface for SCEC Dynamic Rupture Benchmark
+ locations on the fault surface for SCEC spontaneous 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
@@ -1502,7 +1605,7 @@ MGK acknowledges partial support from NS
\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
+ SCEC spontaneous 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
diff -r a60533730e6c -r 01f064fce659 references.bib
--- a/references.bib Tue Apr 24 15:09:48 2012 -0700
+++ b/references.bib Tue Apr 24 17:15:57 2012 -0700
@@ -768,7 +768,7 @@
McInnes, L.~C. and Smith, B.~F. and Zhang, H.",
Title = "{PETSc} {Web} page",
Note = "http://www.mcs.anl.gov/petsc",
- Year = 2011,
+ Year = 2012,
}
@TechReport{PETSc:manual,
@@ -804,14 +804,6 @@
note = {http://www.geodynamics.org/cig/software/pylith/pylith\_manual-1.6.2.pdf}
}
-
- at Misc{CIG:web:page,
- Author = "Kellogg, L.",
- Title = "{CIG} {Web} page",
- Note = "http://geodynamics.org",
- Year = 2011,
-}
-
@book{Saad03,
author = {Yousef Saad},
title = {Iterative Methods for Sparse Linear Systems},
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