# Step 5: Green's Functions % Metadata extracted from parameter files. ```{include} step05_greensfns-synopsis.md ``` ## Simulation parameters In this example we compute static Green's functions for fault slip and use then in Step 6 to invert for fault slip. We generated the "observations" for the slip inversion in Step 4. We impose fault slip impulses over the central portion of the strike-slip fault (-25 km $\le$ y $\le$ +25km), which is slightly larger than where we specified coseismic in Step 4. {numref}`fig:example:strikeslip:2d:step05:diagram` summarizes the boundary conditions and fault slip. The parameters specific to this example are in `step05_greensfns.cfg`. :::{figure-md} fig:example:strikeslip:2d:step05:diagram Boundary conditions for static Green's functions. We set the x and y displacement to zero on the +x and -x boundaries and prescribe left-lateral slip impulses. ::: We use the `GreensFns` problem and specify the fault on which to impose fault slip impulses. As in Step 4, we include output at the fake GNSS stations using `OutputSolnPoints`. In the fault interfaces section we set the fault type to `FaultCohesiveImpulses` for our fault where we want to impose fault slip impulses for the Green's functions. We also use a spatial database to limit the section of the fault where we impose the fault slip impulses to -25 km $\le$ y $\le$ +25 km. :::{important} **Currently, we recommend a basis order of 1 (default) for the slip auxiliary subfield.** The basis order for the slip auxiliary subfield controls the representation of the slip field for the impulses. For a given impulse, a basis order of 1 will impose unit slip at a vertex with zero slip at all other vertices. A basis order of 0 will impose unit slip over a cell with zero slip in all other cells; however, this creates jumps in the slip at the cell boundaries and reduces the accuracy of the slip inversion for a given mesh resolution. A basis order of 2 will impose slip at vertices as well as edge degrees of freedom in the cell; regularization becomes trickier with the higher order discretization, and a basis order of 2 does not always give more accurate results for a given number of impulses. ::: ```{code-block} cfg --- caption: Parameters for computing static Green's functions for fault slip impulses. We change the problem type and specify the fault on which we apply the slip impulses. --- [pylithapp] problem = pylith.problems.GreensFns [pylithapp.greensfns] label = fault label_value = 20 ``` ```{code-block} cfg --- caption: Parameters for the slip impulses. We change the fault type and limit the impulses to the lateral slip component. --- [pylithapp.problem.interfaces] fault = pylith.faults.FaultCohesiveImpulses [pylithapp.problem.interfaces.fault] impulse_dof = [1] db_auxiliary_field = spatialdata.spatialdb.SimpleDB db_auxiliary_field.description = Fault rupture auxiliary field spatial database db_auxiliary_field.iohandler.filename = slip_impulses.spatialdb auxiliary_subfields.slip.basis_order = 1 ``` ## Running the simulation ```{code-block} console --- caption: Run Step 5 simulation --- $ pylith step05_greensfns.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/problems/GreensFns.cc:291:void pylith::problems::GreensFns::solve() -- info (application-flow) -- Component 'greensfns.problem': Computing Green's functions. >> src/cig/pylith/libsrc/pylith/problems/GreensFns.cc:318:void pylith::problems::GreensFns::solve() -- info (application-flow) -- Component 'greensfns.problem': Computing Green's function 1 of 13. 0 SNES Function norm 6.961541624902e-01 Linear solve converged due to CONVERGED_ATOL iterations 9 1 SNES Function norm 6.826069208403e-08 Nonlinear solve converged due to CONVERGED_ITS iterations 1 # -- many lines omitted -- >> /Users/baagaard/src/cig/pylith/libsrc/pylith/problems/GreensFns.cc:318:void pylith::problems::GreensFns::solve() -- info (application-flow) -- Component 'greensfns.problem': Computing Green's function 13 of 13. 0 SNES Function norm 9.567723812071e-01 Linear solve converged due to CONVERGED_ATOL iterations 10 1 SNES Function norm 2.578211184664e-08 Nonlinear solve converged due to CONVERGED_ITS iterations 1 >> /Users/baagaard/software/unix/micromamba/envs/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:222:finalize -- info (application-flow) -- Finalizing problem. WARNING! There are options you set that were not used! WARNING! could be spelling mistake, etc! There are 4 unused database options. They are: Option left: name:-ts_error_if_step_fails (no value) source: code Option left: name:-ts_exact_final_time value: matchstep source: code Option left: name:-ts_monitor (no value) source: code Option left: name:-ts_type value: beuler source: code ``` The beginning of the output written to the terminal matches that in our previous simulations. The second half of the output written to the terminal resembles the output from time-dependent problems, but with the time step information replaced by the impulse information. We get warnings about unused PETSc options because we do not use time stepping. ## Visualizing the results In {numref}`fig:example:strikeslip:2d:step05:impulses` we use the `viz/plot_slip_impulses.py` Python script to visualize the slip impulses. In {numref}`fig:example:strikeslip:2d:step05:solution` we use the `pylith_viz` utility to visualize the y displacement field. You can move the slider or use the `p` and `n` keys to change the increment or decrement slip impulses (shown as different time stamps). ```{code-block} console --- caption: Plot the slip impulses and visualize PyLith output using `pylith_viz`. --- viz/plot_slip_impulses.py pylith_viz --filename=output/step05_greensfns-domain.h5 warp_grid --component=y ``` :::{figure-md} fig:example:strikeslip:2d:step05:impulses Slip impulses for the Green's functions in Step 5. Slip impulses for the Green's functions in Step 5. ::: :::{figure-md} fig:example:strikeslip:2d:step05:solution Solution for Step 5. The colors indicate the y displacement, and the deformation is exaggerated by a factor of 1000. Solution for Step 4. The colors of the shaded surface indicate the y displacement, and the deformation is exaggerated by a factor of 1000. The time value corresponds to the zero-based index of the slip impulses. :::