[cig-commits] r22104 - in short/3D/PyLith/trunk/doc/userguide/tutorials/subduction: . figs
brad at geodynamics.org
brad at geodynamics.org
Fri May 17 17:23:27 PDT 2013
Author: brad
Date: 2013-05-17 17:23:27 -0700 (Fri, 17 May 2013)
New Revision: 22104
Added:
short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/cartoon_general.pdf
short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/step01.pdf
short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/step02.pdf
short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/step03.pdf
Removed:
short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/cartoon_general.eps
short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/step01.eps
short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/step02.eps
short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/step03.eps
Modified:
short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/subduction.lyx
Log:
Switch eps to pdf files.
Deleted: short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/cartoon_general.eps
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/cartoon_general.eps 2013-05-18 00:21:58 UTC (rev 22103)
+++ short/3D/PyLith/trunk/doc/userguide/tutorials/subduction/figs/cartoon_general.eps 2013-05-18 00:23:27 UTC (rev 22104)
@@ -1,309 +0,0 @@
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-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-Subduction"
-
-\end_inset
-
-Tutorial for Slip on a Subduction Zone
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Static solution
-\end_layout
-
-\begin_layout Itemize
-Quasi-static solution
-\end_layout
-
-\begin_layout Itemize
-CUBIT mesh generation
-\end_layout
-
-\begin_deeper
-\begin_layout Itemize
-Nonplanar geometry
-\end_layout
-
-\begin_layout Itemize
-Variable mesh resolution
-\end_layout
-
-\begin_layout Itemize
-APREPRO programming language
-\end_layout
-
-\end_deeper
-\begin_layout Itemize
-Linear triangular cells
-\end_layout
-
-\begin_layout Itemize
-HDF5 output
-\end_layout
-
-\begin_layout Itemize
-Dirichlet displacement and velocity boundary conditions
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-UniformDB spatial database
-\end_layout
-
-\begin_layout Itemize
-Multiple materials
-\end_layout
-
-\begin_layout Itemize
-Nonlinear solver
-\end_layout
-
-\begin_layout Itemize
-Plane strain linearly elastic material
-\end_layout
-
-\begin_layout Itemize
-Plane Maxwell linear viscoelastic material
-\end_layout
-
-\begin_layout Itemize
-Prescribed slip
-\end_layout
-
-\begin_deeper
-\begin_layout Itemize
-Static fault rupture
-\end_layout
-
-\begin_layout Itemize
-Multiple faults
-\end_layout
-
-\begin_layout Itemize
-Spatially variable coseismic slip
-\end_layout
-
-\begin_layout Itemize
-Spatially variable aseismic creep
-\end_layout
-
-\end_deeper
-\begin_layout Itemize
-Afterslip via fault friction
-\end_layout
-
-\begin_deeper
-\begin_layout Itemize
-Static fault rupture
-\end_layout
-
-\begin_layout Itemize
-Static friction
-\end_layout
-
-\end_deeper
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/2d/subduction.
-\end_layout
-
-\begin_layout Subsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This tutorial examines quasi-static interseismic and coseismic deformation
- in 2D for a subduction zone (see Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:overview"
-
-\end_inset
-
-).
- It is based on the 2011 M9.0 Tohoku earthquake off the east coast of Japan.
- Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:steps"
-
-\end_inset
-
- shows the three steps of increasing complexity.
- Step 1 focuses on the coseismic slip, Step 2 focuses on interseismic deformatio
-n, and Step 3 combines the two into a pseudo-earthquake cycle deformation
- simulation.
- Step 4 focuses on using the change in tractions from Step 1 to construct
- a simulation with afterslip controlled by frictional sliding.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/cartoon_general.eps
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Cartoon of subduction zone example.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:overview"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="2" columns="3">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<row>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Step 1
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Step 2
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Step 3
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Graphics
- filename figs/step01.eps
- lyxscale 66
- width 2in
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Graphics
- filename figs/step02.eps
- lyxscale 66
- width 2in
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Graphics
- filename figs/step03.eps
- lyxscale 66
- width 2in
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Diagram of fault slip and boundary conditions for each step in the subduction
- zone tutorial.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:steps"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Mesh Description
-\end_layout
-
-\begin_layout Standard
-We construct the mesh in CUBIT by constructing the geometry, prescribing
- the discretization, running the mesher, and then grouping cells and vertices
- for boundary conditions and materials.
- We use the APREPRO programming language within the journal files to enable
- use of units and to set variables for values used many times.
- An appendix in the CUBIT documentation discusses the features available
- with APREPRO in CUBIT.
- The CUBIT commands are in three separate journal files.
- The main driver is in the journal file
-\family typewriter
-mesh_tri3.jou
-\family default
-.
- It calls the journal file
-\family typewriter
-geometry.jou
-\family default
- to construct the geometry and
-\family typewriter
-createbc.jou
-\family default
- to set up the groups associated with boundary conditions and materials.
- The journal files are documented and describe the various steps outlined
- below.
-\end_layout
-
-\begin_layout Enumerate
-Create the geometry defining the domain.
-\end_layout
-
-\begin_deeper
-\begin_layout Enumerate
-Create points.
-\end_layout
-
-\begin_layout Enumerate
-Connect points into spline curves.
-\end_layout
-
-\begin_layout Enumerate
-Split curves to separate them into sections bounding surfaces.
-
-\end_layout
-
-\begin_layout Enumerate
-Connect curves into surfaces.
-\end_layout
-
-\begin_layout Enumerate
-Stitch surfaces together.
-\end_layout
-
-\end_deeper
-\begin_layout Enumerate
-Define meshing scheme and cell size variation.
-\end_layout
-
-\begin_deeper
-\begin_layout Enumerate
-Define cell size along curves near fault.
-\end_layout
-
-\begin_layout Enumerate
-Increase cell size away from fault at a geometric rate (bias).
-\end_layout
-
-\end_deeper
-\begin_layout Enumerate
-Generate mesh.
-\end_layout
-
-\begin_layout Enumerate
-Create blocks for materials and nodesets for boundary conditions.
-\end_layout
-
-\begin_layout Enumerate
-Export mesh.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/subduction_tri3.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Variable resolution finite-element mesh with triangular cells.
- The nominal cell size increases at a geometric rate of 1.2 away from the
- region of coseismic slip.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Common Information
-\end_layout
-
-\begin_layout Standard
-As in the examples discussed in previous sections of these tutorials, we
- place parameters common to the three steps in the
-\family typewriter
-pylithapp.cfg
-\family default
- file so that we do not have to duplicate them for each step.
- The settings contained in
-\family typewriter
-pylithapp.cfg
-\family default
- for this problem consist of:
-\end_layout
-
-\begin_layout Description
-pylithapp.journal.info Settings that control the verbosity of the output written
- to stdout for the different components.
-\end_layout
-
-\begin_layout Description
-pylithapp.mesh_generator Settings that control mesh importing, such as the
- importer type, the filename, and the spatial dimension of the mesh.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Settings that control the problem, such as the total
- time, time-step size, and spatial dimension.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials Settings that control the material type,
- specify which material IDs are to be associated with a particular material
- type, and give the name of the spatial database containing the physical
- properties for the material.
- The quadrature information is also given.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output Settings related output of the solution
- over the domain and subdomain (ground surface).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.
-\shape italic
-MATERIAL
-\shape default
-.output Settings related to output of the state variables for material
-\shape italic
-MATERIAL
-\shape default
-.
-\end_layout
-
-\begin_layout Description
-pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
- type.
-\end_layout
-
-\begin_layout Standard
-The physical properties for each material are specified in spatial database
- files.
- For example, the elastic properties for the continental crust are in
-\family typewriter
-mat_concrust.spatialdb
-\family default
-.
- The provided spatial database files all use just a single point to specify
- uniform physical properties within each material.
- A good exercise is to alter the spatial database files with the physical
- properties to match PREM.
-\end_layout
-
-\begin_layout Subsection
-Step 1: Coseismic Slip Simulation
-\end_layout
-
-\begin_layout Standard
-The first example problem is earthquake rupture involving coseismic slip
- along the interface between the subducting slab and the continental crust
- and uppermost portion of the mantle below the continental crust.
- The spatial variation of slip comes from a cross-section of Gavin Hayes'
- finite-source model
-\begin_inset Flex URL
-status collapsed
-
-\begin_layout Plain Layout
-
-earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/finite_fault.php
-\end_layout
-
-\end_inset
-
-.
- On the lateral and bottom boundaries of the domain, we fix the degrees
- of freedom perpendicular to the boundary as shown in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:steps"
-
-\end_inset
-
-.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step01.cfg
-\family default
-.
- These settings are:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.formulation.time_step Adjust the total simulation time
- to 0 years (static simulation).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies the array of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.
-\shape italic
-BOUNDARY
-\shape default
- Defines the settings for boundary
-\shape italic
-BOUNDARY
-\shape default
-, including which degrees of freedom are being constrained (x or y), the
- label (defined in
-\family typewriter
- mesh_tri3.exo
-\family default
-) corresponding to the nodeset in CUBIT, and a label to the boundary condition
- used in any error messages.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces.fault Specify the coseismic slip along the
- interface between the oceanic crust and continental crust with a small
- amount of slip penetrating into the upper mantle.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain Gives the base filenames for HDF5
- output (for example,
-\family typewriter
-step01.h5
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-We run this example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step01.cfg
-\end_layout
-
-\begin_layout Standard
-The problem will produce twelve pairs of HDF5/Xdmf files.
- The HDF5 files contain the data and the Xdmf files contain the metadata
- required by ParaView and Visit (and possibly other visualization tools
- that use Xdmf files) to access the mesh and data sets in the HDF5 files.
- The files include the solution over the domain and ground surface (two
- pairs of files), physical properties, stress, and strain within each material
- (eight pairs of files), and fault parameters, slip, and traction (two pairs
- of files).
-
-\end_layout
-
-\begin_layout Standard
-Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:step01"
-
-\end_inset
-
-, which was created using ParaView, displays the magnitude of the displacement
- field with the deformation exaggerated by a factor of 1000.
- We construct a three-dimensional displacement vector from the two-dimensional
- displacement components using the Calculator with the expression
-\end_layout
-
-\begin_layout LyX-Code
-displacement_x*iHat + displacement_y*jHat
-\end_layout
-
-\begin_layout Standard
-where we select the displacement components from the Scalars drop-down menu
- and the iHat, jHat, and kHat values from the Calculator buttons.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/step01_soln.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Solution for Step 1.
- The colors indicate the magnitude of the displacement, and the deformation
- is exaggerated by a factor of 1000.
-
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:step01"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Step 2: Interseismic Deformation Simulation
-\end_layout
-
-\begin_layout Standard
-In this example we simulate the interseismic deformation associated with
- the oceanic crust subducting beneath the continental crust and into the
- mantle.
- We prescribe steady aseismic slip of 8 cm/yr along the interfaces between
- the oceanic crust and mantle with the interface between the oceanic crust
- and continental crust locked as shown in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:steps"
-
-\end_inset
-
-.
- We adjust the Dirichlet boundary conditions on the lateral edges and bottom
- of the domain by pinning only the portions of the boundaries in the mantle
- and continental crust (i.e., not part of the oceanic crust).
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step02.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.formulation.time_step Adjust the total simulation time
- to 100 years.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies the array of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.
-\shape italic
-BOUNDARY
-\shape default
- Defines the settings for boundary
-\shape italic
-BOUNDARY
-\shape default
-, including which degrees of freedom are being constrained (x or y), the
- label (defined in
-\family typewriter
- mesh_tri3.exo
-\family default
-) corresponding to the nodeset in CUBIT, and a label to the boundary condition
- used in any error messages.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces Specify the steady aseismic slip as a constant
- slip rate on the fault surfaces.
-
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain Gives the base filename for HDF5
- output (for example,
-\family typewriter
-step02.h5
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-We run this example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step02.cfg
-\end_layout
-
-\begin_layout Standard
-The simulation will produce pairs of HDF5/Xdmf files with separate files
- for each material and fault interface.
- Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:step02"
-
-\end_inset
-
-, which was created using ParaView, displays the magnitude of the displacement
- field with the deformation exaggerated by a factor of 1000.
- Using the animation features within ParaView or Visit you can illustrate
- how the continental crust near the trench subsides during the interseismic
- deformation.
-
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/step02_soln.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Solution for Step 2 at 100 years.
- The colors indicate the magnitude of the displacement, and the deformation
- is exaggerated by a factor of 1000.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:step02"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Step 3: Pseudo-Earthquake Cycle Model
-\end_layout
-
-\begin_layout Standard
-This simulation combines 300 years of interseismic deformation from Step
- 2 with the coseismic deformation from Step 1 applied at 150 years to create
- a simple model of the earthquake cycle.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step03.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.formulation.time_step Adjust the total simulation time
- to 300 years.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies the array of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.
-\shape italic
-BOUNDARY
-\shape default
- The Dirichlet boundary conditions match those in Step 2.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces On the interface between the subducting
- oceanic crust and the mantle, we prescribe the same steady, aseismic slip
- as that in Step 2.
- On the interface along the top of the subducting oceanic crust and the
- continental crust and mantle we create two earthquake ruptures, The first
- rupture applies the coseismic slip form Step 1 at 150 years, while the
- second rupture prescribes the same steady, aseismic slip as in Step 2.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain Gives the base filename for HDF5
- output (for example,
-\family typewriter
-step03.h5
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-We run this example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step03.cfg
-\end_layout
-
-\begin_layout Standard
-The simulation will produce pairs of HDF5/Xdmf files with separate files
- for each material and fault interface.
- Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:step03"
-
-\end_inset
-
-, which was created using ParaView, displays the magnitude of the displacement
- field with the deformation exaggerated by a factor of 1000.
- Using the animation features within ParaView or Visit you can illustrate
- how the continental crust near the trench rebounds during the earthquake
- after subsiding during the interseismic deformation.
-
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/step03_soln.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Solution for Step 3 at 150 years (immediately following the earthquake rupture).
- The colors indicate the magnitude of the displacement, and the deformation
- is exaggerated by a factor of 1000.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:step03"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Step 4: Frictional Afterslip Simulation
-\end_layout
-
-\begin_layout Standard
-This simulation demonstrates how to combine the change in tractions associated
- with coseismic slip with a background stress field to compute afterslip
- controlled by static friction.
- The Python script
-\family typewriter
-afterslip_tractions.py
-\family default
- will create a spatial database file with initial tractions based on the
- change in tractions from Step 1 and a background stress field.
- The background stress field is simply normal tractions consistent with
- the overburden (lithostatic load) for a uniform half-space and shear tractions
- consistent with a coefficient of friction of 0.6.
- The
-\family typewriter
-afterslip_tractions.
-\begin_inset Newline linebreak
-\end_inset
-
-spatialdb
-\family default
- file is provided, so you do not need to run the Python script
-\family typewriter
-afterslip_tractions.py
-\family default
-; however, you can do so by typing
-\end_layout
-
-\begin_layout LyX-Code
-python afterslip_tractions.py
-\end_layout
-
-\begin_layout Standard
-We provide 2.0 MPa of strength excess associated with the background stress
- field by using a cohesion of 2.0 MPa in the static friction model.
- Slip will occur in regions where the coseismic slip increased the shear
- tractions by more than 2.0 MPa.
- On the lateral and bottom boundaries of the domain, we fix the degrees
- of freedom perpendicular to the boundary as shown in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:steps"
-
-\end_inset
-
-.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step04.cfg
-\family default
-.
- These settings are:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.formulation.time_step Adjust the total simulation time
- to 0 years (static simulation).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Selects the nonlinear solver and specifies the array
- of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.
-\shape italic
-BOUNDARY
-\shape default
- Defines the settings for boundary
-\shape italic
-BOUNDARY
-\shape default
-, including which degrees of freedom are being constrained (x or y), the
- label (defined in
-\family typewriter
- mesh_tri3.exo
-\family default
-) corresponding to the nodeset in CUBIT, and a label to the boundary condition
- used in any error messages.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces.fault Specify a fault with a fault constitutive
- model (static friction) and initial fault tractions.
-
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain Gives the base filenames for HDF5
- output (for example,
-\family typewriter
-step04.h5
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-We run this example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step04.cfg
-\end_layout
-
-\begin_layout Standard
-The problem will produce twelve pairs of HDF5/Xdmf files.
- The HDF5 files contain the data and the Xdmf files contain the metadata
- required by ParaView and Visit (and possibly other visualization tools
- that use Xdmf files) to access the mesh and data sets in the HDF5 files.
- The files include the solution over the domain and ground surface (two
- pairs of files), physical properties, stress, and strain within each material
- (eight pairs of files), and fault parameters, slip, and traction (two pairs
- of files).
-
-\end_layout
-
-\begin_layout Standard
-Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:step04"
-
-\end_inset
-
-, which was created using ParaView, displays the magnitude of the displacement
- field with the original configuration.
- Slip occurs down-dip from the coseismic slip as well as in three areas
- with sharp gradients in slip, including the trench.
- The location of the afterslip can be shifted by changing the spatial variation
- of the coseismic slip and background stress field.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/step01_soln.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Solution for Step 4.
- The colors indicate the magnitude of the displacement.
-
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:step04"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Suggested Variations
-\end_layout
-
-\begin_layout Standard
-The list below includes some suggested modifications to the problem that
- will allow you to become more familiar with PyLith while examining some
- interesting physics.
-\end_layout
-
-\begin_layout Itemize
-Change the resolution of the mesh by editing the
-\family typewriter
-mesh_tri3.jou
-\family default
- journal file.
- Change the resolution and bias factor.
-\end_layout
-
-\begin_layout Itemize
-Add depth dependent viscosity to the mantle and crust.
- This requires using the linear Maxwell plane strain bulk constitutive model
- in the crust as well and creating spatial databases that include viscosity
- for the crust.
- Specifying a depth dependent variation in the parameters will require adding
- points, updating num-locs accordingly, and changing data-dim to 1.
-\end_layout
-
-\begin_layout Itemize
-Modify the spatial database files for the material properties to use depth-depen
-dent elastic properties based on PREM (Dziewonski and Anderson, 1981, 10.1016/003
-1-9201(81)90046-7).
- See
-\begin_inset Flex URL
-status open
-
-\begin_layout Plain Layout
-
-geophysics.ou.edu/solid_earth/prem.html
-\end_layout
-
-\end_inset
-
- for a simple table of values.
- Add points, update num-locs accordingly, and change data-dim to 1.
-\end_layout
-
-\begin_layout Itemize
-Modify the CUBIT journal files to use quad4 cells rather than tri3 cells.
- This requires using the pave mesh scheme.
-\end_layout
-
-\begin_layout Itemize
-Create a simulation with multiple earthquake cycles by lengthening the duration
- of the simulation and adding additional earthquake ruptures.
- See
-\family typewriter
-examples/3d/hex8/step06.cfg
-\family default
- for an example with multiple earthquake ruptures.
- Examine spinup towards a steady-state solution.
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 1in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-Subduction"
+
+\end_inset
+
+Tutorial for Slip on a Subduction Zone
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Static solution
+\end_layout
+
+\begin_layout Itemize
+Quasi-static solution
+\end_layout
+
+\begin_layout Itemize
+CUBIT mesh generation
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Nonplanar geometry
+\end_layout
+
+\begin_layout Itemize
+Variable mesh resolution
+\end_layout
+
+\begin_layout Itemize
+APREPRO programming language
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Linear triangular cells
+\end_layout
+
+\begin_layout Itemize
+HDF5 output
+\end_layout
+
+\begin_layout Itemize
+Dirichlet displacement and velocity boundary conditions
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+UniformDB spatial database
+\end_layout
+
+\begin_layout Itemize
+Multiple materials
+\end_layout
+
+\begin_layout Itemize
+Nonlinear solver
+\end_layout
+
+\begin_layout Itemize
+Plane strain linearly elastic material
+\end_layout
+
+\begin_layout Itemize
+Plane Maxwell linear viscoelastic material
+\end_layout
+
+\begin_layout Itemize
+Prescribed slip
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Static fault rupture
+\end_layout
+
+\begin_layout Itemize
+Multiple faults
+\end_layout
+
+\begin_layout Itemize
+Spatially variable coseismic slip
+\end_layout
+
+\begin_layout Itemize
+Spatially variable aseismic creep
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Afterslip via fault friction
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Static fault rupture
+\end_layout
+
+\begin_layout Itemize
+Static friction
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/2d/subduction.
+\end_layout
+
+\begin_layout Subsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This tutorial examines quasi-static interseismic and coseismic deformation
+ in 2D for a subduction zone (see Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:overview"
+
+\end_inset
+
+).
+ It is based on the 2011 M9.0 Tohoku earthquake off the east coast of Japan.
+ Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:steps"
+
+\end_inset
+
+ shows the three steps of increasing complexity.
+ Step 1 focuses on the coseismic slip, Step 2 focuses on interseismic deformatio
+n, and Step 3 combines the two into a pseudo-earthquake cycle deformation
+ simulation.
+ Step 4 focuses on using the change in tractions from Step 1 to construct
+ a simulation with afterslip controlled by frictional sliding.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/cartoon_general.pdf
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Cartoon of subduction zone example.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:overview"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="3">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Step 1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Step 2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Step 3
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+ filename figs/step01.pdf
+ lyxscale 66
+ width 2in
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+ filename figs/step02.pdf
+ lyxscale 66
+ width 2in
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+ filename figs/step03.pdf
+ lyxscale 66
+ width 2in
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Diagram of fault slip and boundary conditions for each step in the subduction
+ zone tutorial.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:steps"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Mesh Description
+\end_layout
+
+\begin_layout Standard
+We construct the mesh in CUBIT by constructing the geometry, prescribing
+ the discretization, running the mesher, and then grouping cells and vertices
+ for boundary conditions and materials.
+ We use the APREPRO programming language within the journal files to enable
+ use of units and to set variables for values used many times.
+ An appendix in the CUBIT documentation discusses the features available
+ with APREPRO in CUBIT.
+ The CUBIT commands are in three separate journal files.
+ The main driver is in the journal file
+\family typewriter
+mesh_tri3.jou
+\family default
+.
+ It calls the journal file
+\family typewriter
+geometry.jou
+\family default
+ to construct the geometry and
+\family typewriter
+createbc.jou
+\family default
+ to set up the groups associated with boundary conditions and materials.
+ The journal files are documented and describe the various steps outlined
+ below.
+\end_layout
+
+\begin_layout Enumerate
+Create the geometry defining the domain.
+\end_layout
+
+\begin_deeper
+\begin_layout Enumerate
+Create points.
+\end_layout
+
+\begin_layout Enumerate
+Connect points into spline curves.
+\end_layout
+
+\begin_layout Enumerate
+Split curves to separate them into sections bounding surfaces.
+
+\end_layout
+
+\begin_layout Enumerate
+Connect curves into surfaces.
+\end_layout
+
+\begin_layout Enumerate
+Stitch surfaces together.
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Define meshing scheme and cell size variation.
+\end_layout
+
+\begin_deeper
+\begin_layout Enumerate
+Define cell size along curves near fault.
+\end_layout
+
+\begin_layout Enumerate
+Increase cell size away from fault at a geometric rate (bias).
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Generate mesh.
+\end_layout
+
+\begin_layout Enumerate
+Create blocks for materials and nodesets for boundary conditions.
+\end_layout
+
+\begin_layout Enumerate
+Export mesh.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/subduction_tri3.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Variable resolution finite-element mesh with triangular cells.
+ The nominal cell size increases at a geometric rate of 1.2 away from the
+ region of coseismic slip.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Common Information
+\end_layout
+
+\begin_layout Standard
+As in the examples discussed in previous sections of these tutorials, we
+ place parameters common to the three steps in the
+\family typewriter
+pylithapp.cfg
+\family default
+ file so that we do not have to duplicate them for each step.
+ The settings contained in
+\family typewriter
+pylithapp.cfg
+\family default
+ for this problem consist of:
+\end_layout
+
+\begin_layout Description
+pylithapp.journal.info Settings that control the verbosity of the output written
+ to stdout for the different components.
+\end_layout
+
+\begin_layout Description
+pylithapp.mesh_generator Settings that control mesh importing, such as the
+ importer type, the filename, and the spatial dimension of the mesh.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Settings that control the problem, such as the total
+ time, time-step size, and spatial dimension.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials Settings that control the material type,
+ specify which material IDs are to be associated with a particular material
+ type, and give the name of the spatial database containing the physical
+ properties for the material.
+ The quadrature information is also given.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output Settings related output of the solution
+ over the domain and subdomain (ground surface).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials.
+\shape italic
+MATERIAL
+\shape default
+.output Settings related to output of the state variables for material
+\shape italic
+MATERIAL
+\shape default
+.
+\end_layout
+
+\begin_layout Description
+pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
+ type.
+\end_layout
+
+\begin_layout Standard
+The physical properties for each material are specified in spatial database
+ files.
+ For example, the elastic properties for the continental crust are in
+\family typewriter
+mat_concrust.spatialdb
+\family default
+.
+ The provided spatial database files all use just a single point to specify
+ uniform physical properties within each material.
+ A good exercise is to alter the spatial database files with the physical
+ properties to match PREM.
+\end_layout
+
+\begin_layout Subsection
+Step 1: Coseismic Slip Simulation
+\end_layout
+
+\begin_layout Standard
+The first example problem is earthquake rupture involving coseismic slip
+ along the interface between the subducting slab and the continental crust
+ and uppermost portion of the mantle below the continental crust.
+ The spatial variation of slip comes from a cross-section of Gavin Hayes'
+ finite-source model
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/finite_fault.php
+\end_layout
+
+\end_inset
+
+.
+ On the lateral and bottom boundaries of the domain, we fix the degrees
+ of freedom perpendicular to the boundary as shown in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:steps"
+
+\end_inset
+
+.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step01.cfg
+\family default
+.
+ These settings are:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.formulation.time_step Adjust the total simulation time
+ to 0 years (static simulation).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies the array of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.
+\shape italic
+BOUNDARY
+\shape default
+ Defines the settings for boundary
+\shape italic
+BOUNDARY
+\shape default
+, including which degrees of freedom are being constrained (x or y), the
+ label (defined in
+\family typewriter
+ mesh_tri3.exo
+\family default
+) corresponding to the nodeset in CUBIT, and a label to the boundary condition
+ used in any error messages.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces.fault Specify the coseismic slip along the
+ interface between the oceanic crust and continental crust with a small
+ amount of slip penetrating into the upper mantle.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.domain Gives the base filenames for HDF5
+ output (for example,
+\family typewriter
+step01.h5
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+We run this example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step01.cfg
+\end_layout
+
+\begin_layout Standard
+The problem will produce twelve pairs of HDF5/Xdmf files.
+ The HDF5 files contain the data and the Xdmf files contain the metadata
+ required by ParaView and Visit (and possibly other visualization tools
+ that use Xdmf files) to access the mesh and data sets in the HDF5 files.
+ The files include the solution over the domain and ground surface (two
+ pairs of files), physical properties, stress, and strain within each material
+ (eight pairs of files), and fault parameters, slip, and traction (two pairs
+ of files).
+
+\end_layout
+
+\begin_layout Standard
+Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:step01"
+
+\end_inset
+
+, which was created using ParaView, displays the magnitude of the displacement
+ field with the deformation exaggerated by a factor of 1000.
+ We construct a three-dimensional displacement vector from the two-dimensional
+ displacement components using the Calculator with the expression
+\end_layout
+
+\begin_layout LyX-Code
+displacement_x*iHat + displacement_y*jHat
+\end_layout
+
+\begin_layout Standard
+where we select the displacement components from the Scalars drop-down menu
+ and the iHat, jHat, and kHat values from the Calculator buttons.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/step01_soln.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Solution for Step 1.
+ The colors indicate the magnitude of the displacement, and the deformation
+ is exaggerated by a factor of 1000.
+
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:step01"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Step 2: Interseismic Deformation Simulation
+\end_layout
+
+\begin_layout Standard
+In this example we simulate the interseismic deformation associated with
+ the oceanic crust subducting beneath the continental crust and into the
+ mantle.
+ We prescribe steady aseismic slip of 8 cm/yr along the interfaces between
+ the oceanic crust and mantle with the interface between the oceanic crust
+ and continental crust locked as shown in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:steps"
+
+\end_inset
+
+.
+ We adjust the Dirichlet boundary conditions on the lateral edges and bottom
+ of the domain by pinning only the portions of the boundaries in the mantle
+ and continental crust (i.e., not part of the oceanic crust).
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step02.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.formulation.time_step Adjust the total simulation time
+ to 100 years.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies the array of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.
+\shape italic
+BOUNDARY
+\shape default
+ Defines the settings for boundary
+\shape italic
+BOUNDARY
+\shape default
+, including which degrees of freedom are being constrained (x or y), the
+ label (defined in
+\family typewriter
+ mesh_tri3.exo
+\family default
+) corresponding to the nodeset in CUBIT, and a label to the boundary condition
+ used in any error messages.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces Specify the steady aseismic slip as a constant
+ slip rate on the fault surfaces.
+
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.domain Gives the base filename for HDF5
+ output (for example,
+\family typewriter
+step02.h5
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+We run this example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step02.cfg
+\end_layout
+
+\begin_layout Standard
+The simulation will produce pairs of HDF5/Xdmf files with separate files
+ for each material and fault interface.
+ Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:step02"
+
+\end_inset
+
+, which was created using ParaView, displays the magnitude of the displacement
+ field with the deformation exaggerated by a factor of 1000.
+ Using the animation features within ParaView or Visit you can illustrate
+ how the continental crust near the trench subsides during the interseismic
+ deformation.
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/step02_soln.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Solution for Step 2 at 100 years.
+ The colors indicate the magnitude of the displacement, and the deformation
+ is exaggerated by a factor of 1000.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:step02"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Step 3: Pseudo-Earthquake Cycle Model
+\end_layout
+
+\begin_layout Standard
+This simulation combines 300 years of interseismic deformation from Step
+ 2 with the coseismic deformation from Step 1 applied at 150 years to create
+ a simple model of the earthquake cycle.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step03.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.formulation.time_step Adjust the total simulation time
+ to 300 years.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies the array of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.
+\shape italic
+BOUNDARY
+\shape default
+ The Dirichlet boundary conditions match those in Step 2.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces On the interface between the subducting
+ oceanic crust and the mantle, we prescribe the same steady, aseismic slip
+ as that in Step 2.
+ On the interface along the top of the subducting oceanic crust and the
+ continental crust and mantle we create two earthquake ruptures, The first
+ rupture applies the coseismic slip form Step 1 at 150 years, while the
+ second rupture prescribes the same steady, aseismic slip as in Step 2.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.domain Gives the base filename for HDF5
+ output (for example,
+\family typewriter
+step03.h5
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+We run this example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step03.cfg
+\end_layout
+
+\begin_layout Standard
+The simulation will produce pairs of HDF5/Xdmf files with separate files
+ for each material and fault interface.
+ Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:step03"
+
+\end_inset
+
+, which was created using ParaView, displays the magnitude of the displacement
+ field with the deformation exaggerated by a factor of 1000.
+ Using the animation features within ParaView or Visit you can illustrate
+ how the continental crust near the trench rebounds during the earthquake
+ after subsiding during the interseismic deformation.
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/step03_soln.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Solution for Step 3 at 150 years (immediately following the earthquake rupture).
+ The colors indicate the magnitude of the displacement, and the deformation
+ is exaggerated by a factor of 1000.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:step03"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Step 4: Frictional Afterslip Simulation
+\end_layout
+
+\begin_layout Standard
+This simulation demonstrates how to combine the change in tractions associated
+ with coseismic slip with a background stress field to compute afterslip
+ controlled by static friction.
+ The Python script
+\family typewriter
+afterslip_tractions.py
+\family default
+ will create a spatial database file with initial tractions based on the
+ change in tractions from Step 1 and a background stress field.
+ The background stress field is simply normal tractions consistent with
+ the overburden (lithostatic load) for a uniform half-space and shear tractions
+ consistent with a coefficient of friction of 0.6.
+ The
+\family typewriter
+afterslip_tractions.
+\begin_inset Newline linebreak
+\end_inset
+
+spatialdb
+\family default
+ file is provided, so you do not need to run the Python script
+\family typewriter
+afterslip_tractions.py
+\family default
+; however, you can do so by typing
+\end_layout
+
+\begin_layout LyX-Code
+python afterslip_tractions.py
+\end_layout
+
+\begin_layout Standard
+We provide 2.0 MPa of strength excess associated with the background stress
+ field by using a cohesion of 2.0 MPa in the static friction model.
+ Slip will occur in regions where the coseismic slip increased the shear
+ tractions by more than 2.0 MPa.
+ On the lateral and bottom boundaries of the domain, we fix the degrees
+ of freedom perpendicular to the boundary as shown in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:steps"
+
+\end_inset
+
+.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step04.cfg
+\family default
+.
+ These settings are:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.formulation.time_step Adjust the total simulation time
+ to 0 years (static simulation).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Selects the nonlinear solver and specifies the array
+ of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.
+\shape italic
+BOUNDARY
+\shape default
+ Defines the settings for boundary
+\shape italic
+BOUNDARY
+\shape default
+, including which degrees of freedom are being constrained (x or y), the
+ label (defined in
+\family typewriter
+ mesh_tri3.exo
+\family default
+) corresponding to the nodeset in CUBIT, and a label to the boundary condition
+ used in any error messages.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces.fault Specify a fault with a fault constitutive
+ model (static friction) and initial fault tractions.
+
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.domain Gives the base filenames for HDF5
+ output (for example,
+\family typewriter
+step04.h5
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+We run this example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step04.cfg
+\end_layout
+
+\begin_layout Standard
+The problem will produce twelve pairs of HDF5/Xdmf files.
+ The HDF5 files contain the data and the Xdmf files contain the metadata
+ required by ParaView and Visit (and possibly other visualization tools
+ that use Xdmf files) to access the mesh and data sets in the HDF5 files.
+ The files include the solution over the domain and ground surface (two
+ pairs of files), physical properties, stress, and strain within each material
+ (eight pairs of files), and fault parameters, slip, and traction (two pairs
+ of files).
+
+\end_layout
+
+\begin_layout Standard
+Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:step04"
+
+\end_inset
+
+, which was created using ParaView, displays the magnitude of the displacement
+ field with the original configuration.
+ Slip occurs down-dip from the coseismic slip as well as in three areas
+ with sharp gradients in slip, including the trench.
+ The location of the afterslip can be shifted by changing the spatial variation
+ of the coseismic slip and background stress field.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/step01_soln.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Solution for Step 4.
+ The colors indicate the magnitude of the displacement.
+
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:step04"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Suggested Variations
+\end_layout
+
+\begin_layout Standard
+The list below includes some suggested modifications to the problem that
+ will allow you to become more familiar with PyLith while examining some
+ interesting physics.
+\end_layout
+
+\begin_layout Itemize
+Change the resolution of the mesh by editing the
+\family typewriter
+mesh_tri3.jou
+\family default
+ journal file.
+ Change the resolution and bias factor.
+\end_layout
+
+\begin_layout Itemize
+Add depth dependent viscosity to the mantle and crust.
+ This requires using the linear Maxwell plane strain bulk constitutive model
+ in the crust as well and creating spatial databases that include viscosity
+ for the crust.
+ Specifying a depth dependent variation in the parameters will require adding
+ points, updating num-locs accordingly, and changing data-dim to 1.
+\end_layout
+
+\begin_layout Itemize
+Modify the spatial database files for the material properties to use depth-depen
+dent elastic properties based on PREM (Dziewonski and Anderson, 1981, 10.1016/003
+1-9201(81)90046-7).
+ See
+\begin_inset Flex URL
+status open
+
+\begin_layout Plain Layout
+
+geophysics.ou.edu/solid_earth/prem.html
+\end_layout
+
+\end_inset
+
+ for a simple table of values.
+ Add points, update num-locs accordingly, and change data-dim to 1.
+\end_layout
+
+\begin_layout Itemize
+Modify the CUBIT journal files to use quad4 cells rather than tri3 cells.
+ This requires using the pave mesh scheme.
+\end_layout
+
+\begin_layout Itemize
+Create a simulation with multiple earthquake cycles by lengthening the duration
+ of the simulation and adding additional earthquake ruptures.
+ See
+\family typewriter
+examples/3d/hex8/step06.cfg
+\family default
+ for an example with multiple earthquake ruptures.
+ Examine spinup towards a steady-state solution.
+\end_layout
+
+\end_body
+\end_document
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