Step 2: Static Spatially Variable 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

  • spatially variable slip

Simulation parameters#

This example involves a static simulation that solves for the deformation from prescribed spatially variable coseismic slip on each of the faults. Fig. 117 shows the boundary conditions on the domain. The parameters specific to this example are in step02_varslip.cfg.

Fig. 117 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 piecewise linear variations in slip along strike on each of the faults.#

We prescribe piecewise linear variations in slip along strike on each of the faults using SimpleDB spatial databases. The spatial databases contain coordinates of points in geographic coordinates. PyLith will transform each the coordinates of point on the fault to the geographic coordinates and interpolate the values in the spatial database to the point on the fault.

Listing 168 Prescribed slip parameters for Step 2.#
[pylithapp.problem.interfaces.main_fault.eq_ruptures.rupture]
db_auxiliary_field = spatialdata.spatialdb.SimpleDB
db_auxiliary_field.description = Slip parameters for fault 'main'
db_auxiliary_field.iohandler.filename = fault_main_slip.spatialdb
db_auxiliary_field.query_type = linear

[pylithapp.problem.interfaces.west_branch.eq_ruptures.rupture]
db_auxiliary_field = spatialdata.spatialdb.SimpleDB
db_auxiliary_field.description = Slip parameters for fault 'west'
db_auxiliary_field.iohandler.filename = fault_west_slip.spatialdb
db_auxiliary_field.query_type = linear

[pylithapp.problem.interfaces.east_branch.eq_ruptures.rupture]
db_auxiliary_field = spatialdata.spatialdb.SimpleDB
db_auxiliary_field.description = Slip parameters for fault 'east'
db_auxiliary_field.iohandler.filename = fault_east_slip.spatialdb
db_auxiliary_field.query_type = linear

Running the simulation#

Listing 169 Run Step 2 simulation#
$ pylith step02_varslip.cfg

# The output should look something like the following.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/apps/PyLithApp.py:77:main
 -- pylithapp(info)
 -- Running on 1 process(es).
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/meshio/MeshIOObj.py:38:read
 -- meshiopetsc(info)
 -- Reading finite-element mesh
 >> /src/cig/pylith/libsrc/pylith/meshio/MeshIO.cc:85:void pylith::meshio::MeshIO::read(pylith::topology::Mesh *, const bool)
 -- meshiopetsc(info)
 -- Component 'reader': Domain bounding box:
    (410000, 490000)
    (3.91e+06, 3.99e+06)
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/faults/FaultCohesiveKin.py:87:preinitialize
 -- faultcohesivekin(info)
 -- Pre-initializing fault 'fault_main'.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/faults/FaultCohesiveKin.py:87:preinitialize
 -- faultcohesivekin(info)
 -- Pre-initializing fault 'fault_west'.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/faults/FaultCohesiveKin.py:87:preinitialize
 -- faultcohesivekin(info)
 -- Pre-initializing fault 'fault_east'.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:116:preinitialize
 -- timedependent(info)
 -- Performing minimal initialization before verifying configuration.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/problems/Solution.py:39:preinitialize
 -- solution(info)
 -- Performing minimal initialization of solution.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/faults/FaultCohesiveKin.py:87:preinitialize
 -- faultcohesivekin(info)
 -- Pre-initializing fault 'fault_main'.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/faults/FaultCohesiveKin.py:87:preinitialize
 -- faultcohesivekin(info)
 -- Pre-initializing fault 'fault_west'.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/faults/FaultCohesiveKin.py:87:preinitialize
 -- faultcohesivekin(info)
 -- Pre-initializing fault 'fault_east'.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:174:verifyConfiguration
 -- timedependent(info)
 -- Verifying compatibility of problem configuration.
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:219:_printInfo
 -- timedependent(info)
 -- Scales for nondimensionalization:
    Length scale: 1000*m
    Time scale: 3.15576e+09*s
    Pressure scale: 3e+10*m**-1*kg*s**-2
    Density scale: 2.98765e+23*m**-3*kg
    Temperature scale: 1*K
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:185:initialize
 -- timedependent(info)
 -- Initializing timedependent problem with quasistatic formulation.
 >> /src/cig/pylith/libsrc/pylith/utils/PetscOptions.cc:239:static void pylith::utils::_PetscOptions::write(pythia::journal::info_t &, const char *, const PetscOptions &)
 -- petscoptions(info)
 -- Setting PETSc options:
ksp_converged_reason = true
ksp_guess_pod_size = 8
ksp_guess_type = pod
snes_converged_reason = true
snes_monitor = true
ts_error_if_step_fails = true
ts_monitor = true

 >> /src/cig/pylith/libsrc/pylith/utils/PetscOptions.cc:239:static void pylith::utils::_PetscOptions::write(pythia::journal::info_t &, const char *, const PetscOptions &)
 -- petscoptions(info)
 -- Using user values rather then the following default PETSc options:
ksp_atol = 1.0e-12
ksp_error_if_not_converged = true
ksp_rtol = 1.0e-12
snes_atol = 1.0e-9
snes_error_if_not_converged = true
snes_rtol = 1.0e-12

 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/problems/TimeDependent.py:132:run
 -- timedependent(info)
 -- Solving problem.
0 TS dt 0.01 time 0.
    0 SNES Function norm 4.696586307427e-02
      Linear solve converged due to CONVERGED_ATOL iterations 19
    1 SNES Function norm 7.572811652012e-13
    Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1
1 TS dt 0.01 time 0.01
 >> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:199:finalize
 -- timedependent(info)
 -- Finalizing 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 19 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).

Visualizing the results#

In Fig. 118 we use the pylith_viz utility to visualize the y displacement field.

Listing 170 Visualize PyLith output using pylith_viz.#
pylith_viz --filename=output/step02_varslip-domain.h5 warp_grid --component=y
Solution for Step 2. The colors indicate the y displacement, and the deformation is exaggerated by a factor of 1000.

Fig. 118 Solution for Step 2. 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.#