Mondaic DocumentationThis micro-tutorial compares different parameterizations of acoustic media and demonstrates how to run VTI acoustic simulations with SalvusProject. The concept is shown for a simple 2-D layered medium, but it works just the same in 3-D by just adding an extra dimension.
import numpy as np
import os
import salvus.namespace as sn
# Run simulations on this site.
SALVUS_FLOW_SITE_NAME = os.environ.get("SITE_NAME", "local")# Either load an existing project or create a new one.
p = sn.Project.from_domain(
path="project",
# Should match the volume model.
domain=sn.domain.dim2.BoxDomain(x0=0, x1=3000, y0=-1000, y1=0),
load_if_exists=True,
)
We start with an isotropic acoustic model with 3 layers using a custom
bm model file.%%writefile layered_model.bm
NAME radial_model
ACOUSTIC true
UNITS m
COLUMNS depth rho vp
0.0 1000.0 1500.0
200.0 1000.0 1500.0
200.0 1300.0 1900.0
500.0 1300.0 1900.0
500.0 2200.0 3200.0
4000.0 2200.0 3200.0Writing layered_model.bm
Similarly, we introduce a VTI layered model, where the second and third layer have a higher wave speed in horizontal direction.
%%writefile layered_model_ani.bm
NAME radial_model
ACOUSTIC true
ANISOTROPIC true
UNITS m
COLUMNS depth rho vpv vph
0.0 1000.0 1500.0 1500.0
200.0 1000.0 1500.0 1500.0
200.0 1300.0 1900.0 2100.0
500.0 1300.0 1900.0 2100.0
500.0 2200.0 3200.0 3500.0
4000.0 2200.0 3200.0 3500.0Writing layered_model_ani.bm
The anisotropic parameters for vertical and horizontal P-wave velocities cam also
represent an isotropic medium equivalent to the first example when using the same value for
VPV and VPH.%%writefile layered_model_fake_ani.bm
NAME radial_model
ACOUSTIC true
ANISOTROPIC true
UNITS m
COLUMNS depth rho vpv vph
0.0 1000.0 1500.0 1500.0
200.0 1000.0 1500.0 1500.0
200.0 1300.0 1900.0 1900.0
500.0 1300.0 1900.0 1900.0
500.0 2200.0 3200.0 3200.0
4000.0 2200.0 3200.0 3200.0Writing layered_model_fake_ani.bm
Now, we create simulation configurations for all three 1D models. Obviously, the fake anisotropic model will result in the same waveforms as the isotropic model.
for name, bm in zip(
["isotropic", "anisotropic", "fake-anisotropic"],
["layered_model.bm", "layered_model_ani.bm", "layered_model_fake_ani.bm"],
):
p.add_to_project(
sn.SimulationConfiguration(
name=name,
max_frequency_in_hertz=20.0,
elements_per_wavelength=1.5,
model_configuration=sn.ModelConfiguration(
background_model=sn.model.background.one_dimensional.FromBm(
filename=bm, reference_datum=0.0
),
),
event_configuration=sn.EventConfiguration(
wavelet=sn.simple_config.stf.Ricker(center_frequency=10.0),
waveform_simulation_configuration=sn.WaveformSimulationConfiguration(
end_time_in_seconds=1.5,
),
),
absorbing_boundaries=sn.AbsorbingBoundaryParameters(
reference_velocity=2200.0,
reference_frequency=10.0,
number_of_wavelengths=7,
),
),
)
p.viz.nb.simulation_setup("anisotropic")[2026-06-03 00:05:55,156] INFO: Creating mesh. Hang on.
<unstructured_mesh.unstructured_mesh.UnstructuredMesh object at 0x73ed67e4dc10>
Finally, we highlight two more model parameterizations for anisotropic acoustic material using the Thomsen parameters and a second-order tensor, which can be seen as a reduced form of the 4th-order elastic tensor.
We add two more meshes representing the equivalent isotropic and anisotropic media in this parameterization as
UnstructuredMeshSimulationConfiguration.def convert_thomsen_params_to_vti_tensor(
dim: int,
rho: np.ndarray,
vp: np.ndarray,
delta: np.ndarray,
epsilon: np.ndarray,
):
if dim == 2:
model = {
"M0": 1 / (vp**2 * rho),
"D11": (1 + 2 * epsilon) / rho,
"D12": (delta - epsilon) / rho,
"D22": 1 / rho,
}
elif dim == 3:
model = {
"M0": 1 / (vp**2 * rho),
"D11": (1 + 2 * epsilon) / rho,
"D12": np.zeros_like(rho),
"D13": (delta - epsilon) / rho,
"D22": (1 + 2 * epsilon) / rho,
"D23": (delta - epsilon) / rho,
"D33": 1 / rho,
}
return model
def interpolate_vti_model_onto_mesh(mesh: sn.UnstructuredMesh):
if "VPV" in mesh.elemental_fields.keys():
vti_model = convert_thomsen_params_to_vti_tensor(
dim=2,
rho=mesh.elemental_fields["RHO"],
vp=mesh.elemental_fields["VPV"],
delta=0.5
* (
mesh.elemental_fields["VPH"] ** 2
/ mesh.elemental_fields["VPV"] ** 2
- 1.0
),
epsilon=0.5
* (
mesh.elemental_fields["VPH"] ** 2
/ mesh.elemental_fields["VPV"] ** 2
- 1.0
),
)
for k, v in vti_model.items():
mesh.elemental_fields[k] = v
del mesh.elemental_fields["VPV"]
del mesh.elemental_fields["VPH"]
del mesh.elemental_fields["RHO"]
else:
vti_model = convert_thomsen_params_to_vti_tensor(
dim=2,
rho=mesh.elemental_fields["RHO"],
vp=mesh.elemental_fields["VP"],
delta=np.zeros_like(mesh.elemental_fields["VP"]),
epsilon=np.zeros_like(mesh.elemental_fields["VP"]),
)
for k, v in vti_model.items():
mesh.elemental_fields[k] = v
del mesh.elemental_fields["VP"]
del mesh.elemental_fields["RHO"]
return mesh
mesh = p.simulations.get_mesh("isotropic")
mesh = interpolate_vti_model_onto_mesh(mesh)
p.add_to_project(
sn.UnstructuredMeshSimulationConfiguration(
unstructured_mesh=mesh,
name="thomsen-isotropic",
event_configuration=p.entities.get(
"simulation_configuration", "anisotropic"
).event_configuration,
)
)
mesh = p.simulations.get_mesh("anisotropic")
mesh = interpolate_vti_model_onto_mesh(mesh)
p.add_to_project(
sn.UnstructuredMeshSimulationConfiguration(
unstructured_mesh=mesh,
name="thomsen-anisotropic",
event_configuration=p.entities.get(
"simulation_configuration", "anisotropic"
).event_configuration,
)
)[2026-06-03 00:05:55,595] INFO: Creating mesh. Hang on.
At the surface of the domain, we consider a single point source at the center of the horizontal extent and model a linear array of receivers with a spacing of 20 m.
src = sn.simple_config.source.cartesian.ScalarPoint2D(x=1500, y=0, f=1.0)
recs = sn.simple_config.receiver.cartesian.collections.ArrayPoint2D(
x=np.linspace(100, 2900, 141), y=np.zeros(141), fields=["phi"]
)
p += sn.Event(event_name="event", sources=src, receivers=recs)
p.viz.nb.domain()
It is time to actually run the simulations for all 5 scenarios.
for name in [
"isotropic",
"anisotropic",
"fake-anisotropic",
"thomsen-anisotropic",
"thomsen-isotropic",
]:
p.simulations.launch(
simulation_configuration=name,
events=p.events.list(),
site_name=SALVUS_FLOW_SITE_NAME,
ranks_per_job=1,
)
p.simulations.query(block=True)[2026-06-03 00:05:55,862] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2606030005941279_a723cfcbaa@local
[2026-06-03 00:05:57,331] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2606030005335300_1dab45e67a@local
[2026-06-03 00:05:58,806] INFO: Creating mesh. Hang on. [2026-06-03 00:05:58,873] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2606030005877851_3958daa590@local
[2026-06-03 00:06:00,358] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2606030006362420_a2271d52c9@local
[2026-06-03 00:06:01,919] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2606030006924221_f564e245a3@local
Of course, regardless of the parameterization of the medium, the waveforms of all isotropic simulations coincide. The same is true for both anisotropic parameterizations. Note, however, the difference between isotropic and anisotropic material.
p.viz.nb.waveforms(
data=["isotropic", "fake-anisotropic", "thomsen-isotropic"],
receiver_field="phi",
)
p.viz.nb.waveforms(
data=["anisotropic", "thomsen-anisotropic"],
receiver_field="phi",
)
p.viz.nb.waveforms(
data=["isotropic", "anisotropic"],
receiver_field="phi",
)
p.waveforms.get(data_name="isotropic", events=p.events.list())[0].plot(
component="A",
receiver_field="phi",
plot_types=["shotgather"],
)
p.waveforms.get(data_name="anisotropic", events=p.events.list())[0].plot(
component="A",
receiver_field="phi",
plot_types=["shotgather"],
)
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