# 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/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:
(-50000, 50000)
(-75000, 75000)
# -- many lines omitted --
>> /src/cig/pylith/libsrc/pylith/problems/GreensFns.cc:322:void pylith::problems::GreensFns::solve()
-- greensfns(info)
-- Component 'problem': Computing Green's function 12 of 12.
0 SNES Function norm 3.027654014246e-03
Linear solve converged due to CONVERGED_ATOL iterations 18
1 SNES Function norm 1.850212226728e-12
Nonlinear solve converged due to CONVERGED_ITS iterations 1
>> /software/unix/py3.12-venv/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:199:finalize
-- greensfns(info)
-- Finalizing problem.
WARNING! There are options you set that were not used!
WARNING! could be spelling mistake, etc!
There are 3 unused database options. They are:
Option left: name:-ts_error_if_step_fails (no value) 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.
The journal info associated with the `GreensFns` component (`journal.info.greensfns`) turns on 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` Pyhon 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.
:::
:::{figure-md} fig:example:strikeslip:2d:step05:solution
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.
:::