Step 1: Static Uniform Coseismic Slip#

Features

  • Triangular cells

  • pylith.problems.TimeDependent

  • pylith.materials.Elasticity

  • pylith.materials.IsotropicLinearElasticity

  • pylith.faults.FaultCohesiveKin

  • pylith.faults.KinSrcStep

  • pylith.bc.DirichletTimeDependent

  • spatialdata.spatialdb.UniformDB

  • pylith.meshio.OutputSolnBoundary

  • pylith.meshio.DataWriterHDF5

  • Static simulation

  • pylith.meshio.MeshIOPetsc

  • Gmsh

Simulation parameters#

This example involves a static simulation that solves for the deformation from prescribed uniform coseismic slip on each of the faults. Fig. 118 shows the boundary conditions on the domain. The parameters specific to this example are in step01_slip.cfg.

Fig. 118 Boundary conditions for static coseismic slip. On the boundary of the domain, we set the displacement component that is perpendicular to the boundary to zero. We prescribe 4.0 m of right-lateral slip on the main fault, 2.0 m of left-lateral slip on the west branch, and 1.0 m of left-lateral slip on the east branch.#

Listing 181 Prescribed slip parameters for Step 1.#
[pylithapp.problem.interfaces.main_fault.eq_ruptures.rupture]
db_auxiliary_field = spatialdata.spatialdb.UniformDB
db_auxiliary_field.description = Fault rupture auxiliary field spatial database
db_auxiliary_field.values = [initiation_time, final_slip_left_lateral, final_slip_opening]
db_auxiliary_field.data = [0.0*s, -4.0*m, 0.0*m]

[pylithapp.problem.interfaces.west_branch.eq_ruptures.rupture]
db_auxiliary_field = spatialdata.spatialdb.UniformDB
db_auxiliary_field.description = Fault rupture auxiliary field spatial database
db_auxiliary_field.values = [initiation_time, final_slip_left_lateral, final_slip_opening]
db_auxiliary_field.data = [0.0*s, 3.0*m, 0.0*m]

[pylithapp.problem.interfaces.east_branch.eq_ruptures.rupture]
db_auxiliary_field = spatialdata.spatialdb.UniformDB
db_auxiliary_field.description = Fault rupture auxiliary field spatial database
db_auxiliary_field.values = [initiation_time, final_slip_left_lateral, final_slip_opening]
db_auxiliary_field.data = [0.0*s, 1.0*m, 0.0*m]

Running the simulation#

Listing 182 Run Step 1 simulation#
$ pylith step01_slip.cfg

# The output should look something like the following.
 >> software/pylith-debug/lib/python3.12/site-packages/pylith/apps/PyLithApp.py:79:main
 -- info (application-flow)
 -- Running on 1 process(es).
 >> src/cig/pylith/libsrc/pylith/utils/PetscOptions.cc:251:static void pylith::utils::_PetscOptions::write(pythia::journal::info_t &, const char *, const PetscOptions &)
 -- info (application-flow)
 -- Setting PETSc options:
    dm_reorder_section = true
    dm_reorder_section_type = cohesive
    ksp_atol = 1.0e-7
    ksp_converged_reason = true
    ksp_error_if_not_converged = true
    ksp_gmres_restart = 100
    ksp_guess_pod_size = 8
    ksp_guess_type = pod
    ksp_rtol = 1.0e-14
    mg_fine_ksp_max_it = 5
    mg_fine_pc_type = vpbjacobi
    pc_type = gamg
    snes_atol = 5.0e-7
    snes_converged_reason = true
    snes_error_if_not_converged = true
    snes_monitor = true
    snes_rtol = 1.0e-14
    ts_error_if_step_fails = true
    ts_exact_final_time = matchstep
    ts_monitor = true
    ts_type = beuler
    viewer_hdf5_collective = true

 >> src/cig/pylith/libsrc/pylith/meshio/MeshIOPetsc.cc:205:virtual void pylith::meshio::MeshIOPetsc::_read()
 -- info (application-flow)
 -- Component 'meshiopetsc.reader': Reading finite-element mesh from 'mesh_tri.msh'.
 >> src/cig/pylith/libsrc/pylith/meshio/MeshIO.cc:76:void pylith::meshio::MeshIO::read(pylith::topology::Mesh *, const bool)
 -- info (application-flow)
 -- Component 'meshiopetsc.reader': Domain bounding box:
    (410000, 490000)
    (3.91e+06, 3.99e+06)
 >> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:316:virtual void pylith::problems::TimeDependent::verifyConfiguration() const
 -- info (application-flow)
 -- Component 'timedependent.problem': Verifying problem configuration.
 >> software/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:238:_printInfo
 -- info (application-flow)
 -- Scales for nondimensionalization:
    Length scale: 1000*m
    Displacement scale: 1*m
    Time scale: 3.15576e+09*s
    Rigidity scale: 1e+10*m**-1*kg*s**-2
    Temperature scale: 1*K
 >> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:342:virtual void pylith::problems::TimeDependent::initialize()
 -- info (application-flow)
 -- Component 'timedependent.problem': Initializing problem.
 >> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:473:void pylith::problems::TimeDependent::solve()
 -- info (application-flow)
 -- Component 'timedependent.problem': Solving equations.
0 TS dt 0.001 time 0.
    0 SNES Function norm 2.419639130581e+01
      Linear solve converged due to CONVERGED_ATOL iterations 13
    1 SNES Function norm 6.875321480887e-08
    Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1
1 TS dt 0.001 time 0.001
 >> software/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:222:finalize
 -- info (application-flow)
 -- Finalizing problem.
 >> software/pylith-debug/lib/python3.12/site-packages/pylith/utils/PetscManager.py:60:finalize
 -- info (application-flow)
 -- Finalizing PETSc.

At the beginning of the output written to the terminal, we see that PyLith is reading the mesh using the MeshIOPetsc reader and that it found the domain to extend from 410000 to 490000 in the x direction and from 3.91e+06 to 3.99e+06 in the y direction. PyLith detects the presence of a fault based on the Lagrange multiplier for the fault in the solution field and selects appropriate preconditioning options as discussed in PETSc Options. The scales for nondimensionalization remain the default values for a quasistatic problem.

At the end of the output written to the terminal, we see that the solver advanced the solution one time step (static simulation). The linear solve converged after 13 iterations and the norm of the residual met the absolute convergence tolerance (ksp_atol) . The nonlinear solve converged in 1 iteration, which we expect because this is a linear problem, and the residual met the absolute convergence tolerance (snes_atol).

Earthquake rupture parameters#

We use the pylith_eqinfo utility to compute rupture information, such as earthquake magnitude, seismic moment, seismic potency, and average slip. For 2D simulations, the average slip provides the most useful information. pylith_eqinfo is a Pyre application and you specify parameters using cfg files and the command line. It writes results to a Python script for use in post-processing of simulation results.

The file eqinfoapp.cfg holds the parameters for pylith_eqinfo in this example. By default, pylith_eqinfo extracts information for the final time step in the output file. In order to compute the seismic moment and moment magnitude, we need the shear modulus, which in this case is uniform over the domain. Consquently, we specify the density and shear wave speed using a UniformDB in eqinfoapp.cfg.

Listing 183 Run pylith_eqinfo for the Step 1 simulation.#
$ pylith_eqinfo
Listing 184 Contents of output/step01_slip-eqinfo.py generated by pylith_eqinfo. The all object includes earthquake rupture information combined from the three the individual faults. The average slip matches the uniform slip prescribed on each fault.#
class RuptureStats(object):
    pass
all = RuptureStats()
all.timestamp = [  3.155760e+07]
all.ruparea = [  5.387992e+04]
all.potency = [  1.733080e+05]
all.moment = [  3.899430e+15]
all.avgslip = [  3.216560e+00]
all.mommag = [  4.360667e+00]
main_fault = RuptureStats()
main_fault.timestamp = [  3.155760e+07]
main_fault.ruparea = [  3.577375e+04]
main_fault.potency = [  1.430950e+05]
main_fault.moment = [  3.219637e+15]
main_fault.avgslip = [  4.000000e+00]
main_fault.mommag = [  4.305205e+00]
east_branch = RuptureStats()
east_branch.timestamp = [  3.155760e+07]
east_branch.ruparea = [  5.999357e+03]
east_branch.potency = [  5.999357e+03]
east_branch.moment = [  1.349855e+14]
east_branch.avgslip = [  1.000000e+00]
east_branch.mommag = [  3.386858e+00]
west_branch = RuptureStats()
west_branch.timestamp = [  3.155760e+07]
west_branch.ruparea = [  1.210682e+04]
west_branch.potency = [  2.421364e+04]
west_branch.moment = [  5.448068e+14]
west_branch.avgslip = [  2.000000e+00]
west_branch.mommag = [  3.790828e+00]

Visualizing the results#

The output directory contains the simulation output. Each “observer” writes its own set of files, so the solution over the domain is in one set of files, the boundary condition information is in another set of files, and the material information is in yet another set of files. The HDF5 (.h5) files contain the mesh geometry and topology information along with the solution fields. The Xdmf (.xmf) files contain metadata that allow visualization tools like ParaView to know where to find the information in the HDF5 files. To visualize the data using ParaView or Visit, load the Xdmf files.

In Fig. 119 we use the pylith_viz utility to visualize the y displacement field.

Listing 185 Visualize PyLith output using pylith_viz.#
pylith_viz --filename=output/step01_slip-domain.h5 warp_grid --component=y
Solution for Step 1. The colors indicate the y displacement, and the deformation is exaggerated by a factor of 1000.

Fig. 119 Solution for Step 1. The colors of the shaded surface indicate the y displacement, and the deformation is exaggerated by a factor of 1000. The undeformed configuration is shown by the gray wireframe. The contrast in material properties across the faults causes the asymmetry in the y displacement field.#

Step 1 with Cubit Mesh#

Using the Cubit mesh rather than the Gmsh mesh involves two changes:

  1. Use the MeshIOCubit reader instead of the MeshIOPetsc reader and change the filename of the mesh file.

  2. Set the label_value to 1 for boundary conditions and faults.
    We must override the label_value settings in pylithapp.cfg that were appropriate for our Gmsh reader but are incorrect for the Cubit reader.

The file step01_slip_cubit.cfg provides these changes and updates the names for output.

Listing 186 Run Step 1 simulation with the Cubit mesh#
$ pylith step01_slip_cubit.cfg

# The output should look something like the following.
 >> software/pylith-debug/lib/python3.12/site-packages/pylith/apps/PyLithApp.py:79:main
 -- info (application-flow)
 -- Running on 1 process(es).
 
 # -- many lines omitted --

 >> src/cig/pylith/libsrc/pylith/meshio/MeshIOCubit.cc:170:virtual void pylith::meshio::MeshIOCubit::_read()
 -- info (application-flow)
 -- Component 'meshiocubit.reader': Reading finite-element mesh from 'mesh_tri.exo'.
 >> src/cig/pylith/libsrc/pylith/meshio/MeshIOCubit.cc:207:virtual void pylith::meshio::MeshIOCubit::_read()
 -- info (application-flow)
 -- Component 'meshiocubit.reader': Read 3125 cells and 1610 vertices.

# -- many lines omitted --

>> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:473:void pylith::problems::TimeDependent::solve()
 -- info (application-flow)
 -- Component 'timedependent.problem': Solving equations.
0 TS dt 0.001 time 0.
    0 SNES Function norm 2.428257473425e+01
      Linear solve converged due to CONVERGED_ATOL iterations 14
    1 SNES Function norm 1.922622064928e-08
    Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1
1 TS dt 0.001 time 0.001
 >> software/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:222:finalize
 -- info (application-flow)
 -- Finalizing problem.