Skip to content


Download Jupyter Notebook

This page is automatically generated from a Jupyter Notebook.

Note that everything here is fully automatically tested against - and thus guaranteed to work - only for the latest versions of all the Salvus packages. So please update if anything works differently on your machine.

In this notebook will use Gar6more2D to generate a set of of semi-analytic solutions to the 2-D acoustic wave equation, and then compare these solutions to those computed within Salvus. To make things a bit more interesting, we will consider a domain bounded by one stress-free (free-surface) boundary, in an analogue to Lamb's problem in elastic media.

# Stdlib packages
import os
import pathlib
import shutil
import subprocess

# Third party packages
import matplotlib.pyplot as plt
import numpy as np
import obspy
import pyasdf

# Import things from SalvusFlow
import salvus_flow.api
# Configuration helpers from SalvusFlow.
from salvus_flow.simple_config import (
    CartesianMomentTensorSource2D, CartesianReceiver2D,
    RickerSTF, WaveformSimulation)

# And some helper functions to run the integration tests.
from integration_test_mesh_helper import (
    get_mesh, Physics, AnalyticCode, read_gar6more)

# Number of processes SalvusCompute will run with.
# Get it from the environment or default to 4.
MPI_RANKS = int(os.environ.get('NUM_MPI_RANKS', 4))
# Choose on which site to run this.


First we must compile and run Gar6more2D. As the Gar6more2D git repository is included here as a submodule, as long as the module has been pulled the following paths should work on your machine. The next cell should compile Gar6more2D in the default location (if it has not been compiled yet).

# Set up the paths for the Gar6more2D data and binaries.
gar6more2d_base_path = pathlib.Path("gar6more2d")
gar6more2d_build_path = gar6more2d_base_path / "build"
gar6more2d_bin = gar6more2d_build_path / "Gar6more2D.out"
gar6more2d_par_file_path = gar6more2d_build_path / "Gar6more2D.dat"

# Compile Gar6more2D
os.makedirs(gar6more2d_build_path, exist_ok=True)
if not os.path.exists(gar6more2d_bin):
    assert['cmake', '..'], cwd=gar6more2d_build_path).returncode == 0
    assert['make'], cwd=gar6more2d_build_path).returncode == 0

Now we generate the parameter file to pass to Gar6more2D. We choose a medium which is infinite on 3 sides, and which has a free-surface at the bottom boundary. We use a ricker source-time function to generate the acoustic wavefield, with a center frequency of 100 Hz. We place this source 250 m above the free surface boundary (0, 250), and place 5 receivers 50 m above the same boundary, spaced equidistantly from x = -200 m to x = +200 m. We compute the solution between 0 and 0.1 seconds, with a sampling interval of 1 \times 10^{-4} seconds, for a total of 1000 time samples. We also choose an acoustic wave velocity of 5800 m/s and a density of 2600 kg/m^3, which corresponds to a bulk modulus \mu of 8.7464 \times 10^{10}.

# Generate and write the parameter file.
amplitude = 1e2
time_step = 1e-4
center_frequency = 100.0
gar6more2d_par_file = """3 infinite medium (1), free surface (2), wall boundary (3) or bilayered medium(4)
1 first layer : acoustic (0) elastodynamic (1), poroelastic (2)
1d2 Central frequency of the source
1d9 Amplitude of the P source
0d0 Amplitude of the S source
2d-2 0d0 Delay of the source
250d0 Height of the source
50d0 Height of the line of receivers
-200d0 Abscissa of the first receiver
200d0  Abscissa of the last receiver
5 Numbers of receivers
0 Start time
1d-1 Stop time
1e-4 Time step
1000 Number of intervals for the numerical computation of the convolution
41600000000 4264000000 2600 mu, lambda and rho
with open(gar6more2d_par_file_path, 'w') as fh:

Now, we generate the semi-analytic pressure solution, and read the results into an obspy stream object.

# Run code.
assert['./Gar6more2D.out'], cwd=gar6more2d_build_path).returncode == 0

# Read data.
gar6more2d_data_file_x = gar6more2d_build_path / "Ux.dat"
gar6more2d_data_file_y = gar6more2d_build_path / "Uy.dat"
gar6more2d_data_x = obspy.Stream(read_gar6more(gar6more2d_data_file_x))
gar6more2d_data_y = obspy.Stream(read_gar6more(gar6more2d_data_file_y))


Now, we will run a fully numerical simulations in Salvus, and attempt to replicate the semi-analytic seismograms. For the sake of brevity, we've left the specifics of the mesh and parameter file generation to the module, which is shared between all integration test instances. Feel free to peak inside to see how the meshes are made -- or alternatively check out the meshing tutorials for a more in-depth explanation.

# Adjust the scaling of the source term to be equivalent to what is
# used in GAR6MORE.
bulk_modulus = 8.7464e10
gar6more_scale = bulk_modulus / (2 * np.pi ** 2 * center_frequency ** 2)
source_amplitude = amplitude / gar6more_scale

Generate Source and Receivers

Use the helper objects in SalvusFlow to generate sources, receivers, and boundary conditions.

source = CartesianMomentTensorSource2D(
    x=500.0, y=250.0,
    mxx=1e9, myy=1e9, mxy=0.0,
# Generate 5 cartesian receivers, spaced between X=300 and X=700 meters.
receivers = [
        x=x, y=50, fields=["displacement"])
    for i, x in enumerate(range(300, 701, 100))
boundary = HomogeneousDirichletBoundary(side_sets=["y0"])

Finally run the simulations for a number of different shape mapping orders.

output_dirs = []

# Run for a number of different shape orders.
for shape_order in [1, 2, 4]:

    # Setup the mesh for this simulation.
    mesh = get_mesh(dimension=2,

    # Unique job name. 
    job_name = f"GAR6MORE2D_ELASTIC_SHAPE_ORDER_{shape_order}"
    output_dirs.append(pathlib.Path(job_name) / "output")

    # Configure Salvus
    w = WaveformSimulation()

    w.physics.wave_equation.start_time_in_seconds = -2e-2
    w.physics.wave_equation.end_time_in_seconds = 8e-2
    w.physics.wave_equation.time_step_in_seconds = time_step


    # The input files can optionally be already validated.
    w.validate(), output_folder=output_dirs[-1], 
                        input_file=w, ranks=MPI_RANKS, get_all=True,  

Compare Both

Finally, we'll now read in the seismograms from Salvus, and plot them overtop the semi-analytic solutions we generated in Gar6more2D. If you've used all the default settings, things should match up exactly. However, feel free to play with some parameters to see how the accuracy can be increased or decreased. Note that, since these are our actual analytic tests, a reduction in accuracy may cause the np.testing.assert_allclose line to fail. If you encounter this, and would still like to see the effect of your changes on the seismograms, feel free to comment out that line.

# Setup the figure.
f, ax = plt.subplots(5, 1, figsize=(15, 30), sharex=True)
ax[0].set_title('Integration Test (Gar6more2D // Elastic)')

# Plot analytic data.
for _i, (a, gx, gy) in enumerate(zip(ax, gar6more2d_data_x, gar6more2d_data_y)):
    if _i != 2:
        a.plot(-gx.copy().differentiate().normalize().data, label='Gar6more2D [x]')
    a.plot(-gy.copy().differentiate().normalize().data, label='Gar6more2D [y]')

# Read in the data produced by Salvus.
for output_dir in output_dirs:

    with pyasdf.ASDFDataSet(output_dir / 'receivers.h5', mode='r') as dataset:

        # Loop over the receivers in both Gar6more2D and Salvus, 
        # and plot them overtop of one another.
        for _i, (a, s, gx, gy) in enumerate(zip(
            ax, dataset.waveforms, gar6more2d_data_x, gar6more2d_data_y)):

            # Get both solutions.
            if _i != 2:
                analytic_x = gx.copy().differentiate().normalize().data
            analytic_y = -gy.copy().differentiate().normalize().data
            salvus_x = s.displacement[0].copy().normalize().data
            salvus_y = s.displacement[1].copy().normalize().data

            # Plot (should deploy these to some server).
            order ="_")[-1][0]

            if _i != 2:
                a.plot(salvus_x, label=f"Salvus [x] (Shape order {order})", ls="dashed")
            a.plot(salvus_y, label=f"Salvus [y] (Shape order {order})", ls="dashed")
            a.set_xlabel('Time sample')
            a.set_ylabel('Displacement (m)')

            # Nodal line.
            if _i != 2:
                np.testing.assert_allclose(analytic_x, salvus_x, atol=1e1)                
            np.testing.assert_allclose(analytic_y, salvus_y, atol=1e-1)

Last but not least clean up.

for d in output_dirs: