MondaicThis 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")[2025-02-07 20:21:13,259] INFO: Creating mesh. Hang on.
<salvus.mesh.data_structures.unstructured_mesh.unstructured_mesh.UnstructuredMesh object at 0x7d6630362890>
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,
)
)[2025-02-07 20:21:13,842] 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)[2025-02-07 20:21:14,222] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2502072021398501_fe4effc91f@local
[2025-02-07 20:21:22,339] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2502072021350213_73924e7d55@local
[2025-02-07 20:21:31,002] INFO: Creating mesh. Hang on. [2025-02-07 20:21:31,148] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2502072021156900_d66f81e709@local
[2025-02-07 20:21:39,302] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2502072021309756_6a171e2236@local
[2025-02-07 20:21:47,984] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2502072021992079_d78c286a03@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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