Mondaic
This tutorial is not for the latest stable Salvus version (viewing 2024.1.3).
import os
import numpy as np
import xarray as xr
import salvus.namespace as sn
from salvus.mesh.tools.transforms import interpolate_mesh_to_mesh

# Run simulations on this site.
SALVUS_FLOW_SITE_NAME = os.environ.get("SITE_NAME", "local")

Mesh-to-mesh interpolation

Micro-tutorial

Interpolating between two unstructured meshes is useful in several situations, such as

  • representing two models on the exact same mesh,
  • increasing the frequency band in an ongoing inversion, and
  • re-meshing a model when a decrease in the minimum velocity begins to result in under-resolved waveforms,

among others.

In this tutorial, we demonstrate how to perform mesh-to-mesh interpolation in 2-D (first) and 3-D (second).

2D

Build model

# Gaussian
x, y = np.linspace(0.0, 1.0, 100), np.linspace(0.0, 1.0, 100)
xx, yy = np.meshgrid(x, y, indexing="xy")
g = np.exp(-(((xx - 0.5) ** 2 + (yy - 0.5) ** 2) / (2 * 0.2**2)))

# Pars
vp = 2 * g + 1
rho = vp / 2

# Xarray dataset
ds = xr.Dataset(
    coords={"x": x, "y": y},
    data_vars={"vp": (["x", "y"], vp), "rho": (["x", "y"], rho)},
)

# Salvus wrapper.
m = sn.model.volume.cartesian.GenericModel(name="blob", data=ds)

# Plot
m.ds.vp.plot()
<matplotlib.collections.QuadMesh at 0x7340b3bf7a50>

Initialize project

p = sn.Project.from_volume_model("proj_2d", m, True)

Source and receiver

s = sn.simple_config.source.cartesian.ScalarPoint2D(x=0.25, y=0.25, f=1.0)
r = sn.simple_config.receiver.cartesian.Point2D(
    x=0.75, y=0.75, fields=["phi"], station_code="XX", network_code="XX"
)

p.add_to_project(sn.EventCollection.from_sources(sources=s, receivers=r))

Define two simulations

f_max = 10.0

# Common event configuration.
ec = sn.EventConfiguration(
    wavelet=sn.simple_config.stf.Ricker(center_frequency=f_max / 2),
    waveform_simulation_configuration=sn.WaveformSimulationConfiguration(
        end_time_in_seconds=1.0
    ),
)

# Heterogeneous - meshed at f_max.
s0 = sn.SimulationConfiguration(
    name="blob_fmax",
    max_frequency_in_hertz=f_max,
    event_configuration=ec,
    model_configuration=sn.ModelConfiguration(
        background_model=None, volume_models="blob"
    ),
    elements_per_wavelength=2.0,
)

# Homogeneous - meshed at 1.5 * f_max.
s1 = sn.SimulationConfiguration(
    name="homo_fmax_1.5",
    max_frequency_in_hertz=1.5 * f_max,
    event_configuration=ec,
    model_configuration=sn.ModelConfiguration(
        background_model=sn.model.background.homogeneous.IsotropicAcoustic(
            rho=rho.min(), vp=vp.min()
        ),
    ),
    elements_per_wavelength=2.0,
)

Add them to the project

for s in [s0, s1]:
    p.add_to_project(s, overwrite=True)

Perform mesh-to-mesh interpolation

Interpolate the blob mesh onto the homogeneous mesh

# Interpolate.
m2m = interpolate_mesh_to_mesh(
    p.simulations.get_mesh("blob_fmax"),
    p.simulations.get_mesh("homo_fmax_1.5"),
    use_layers=False,
    use_1d_vertical_coordinate=False,
)

# Visualize.
m2m
[2025-04-15 19:52:17,774] INFO: Creating mesh. Hang on.
[2025-04-15 19:52:17,858] INFO: Creating mesh. Hang on.
<salvus.mesh.data_structures.unstructured_mesh.unstructured_mesh.UnstructuredMesh object at 0x7340b2c3fcd0>

Add interpolated mesh to project

if "blob_fmax_1.5" not in p.simulations.list():
    p.add_to_project(
        sn.UnstructuredMeshSimulationConfiguration(
            name="blob_fmax_1.5", unstructured_mesh=m2m, event_configuration=ec
        )
    )

Simulate all 3

for name in ["blob_fmax", "blob_fmax_1.5", "homo_fmax_1.5"]:
    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)
[2025-04-15 19:52:18,640] INFO: Submitting job ...
Uploading 1 files...

🚀  Submitted job_2504151952813183_30b9e765bc@local
[2025-04-15 19:52:20,004] INFO: Submitting job ...
Uploading 1 files...

🚀  Submitted job_2504151952015440_395348d89e@local
[2025-04-15 19:52:22,531] INFO: Submitting job ...
Uploading 1 files...

🚀  Submitted job_2504151952536952_79f14b7bdb@local

Visualize results

Note that both blob_fmax runs are essentially identical, while the homogeneous run is very different. The small differences in the two blob runs are expected due to the different mesh resolutions and the broadband nature of the source wavelet.

p.viz.waveforms(
    event="event_0000",
    receiver_name="XX.XX",
    data=["blob_fmax", "blob_fmax_1.5", "homo_fmax_1.5"],
    receiver_field="phi",
)
[]

3-D

Build model

Add 3-D “plume” like structures. Add positive vp perturbations to the crust, negative vp perturbations to the mantle.

# Spherical coordinates
lat = np.linspace(-5.0, 5.0, 101)
lon = np.linspace(-5.0, 5.0, 101)
dep = np.linspace(0.0, 660e3, 101)

# Gaussian
xx, yy, zz = np.meshgrid(lat, lon, dep, indexing="xy")
g = np.zeros_like(xx)
for lats in lat[25:-25:25]:
    for lons in lon[::25]:
        g += np.exp(-(((xx - lats) ** 2 + (yy - lons) ** 2) / (2 * 0.5**2)))

# Xarray dataset
ds = xr.Dataset(
    coords={"latitude": lat, "longitude": lon, "depth": dep},
    data_vars={
        "vp": (["latitude", "longitude", "depth"], g * 20, {"units": "%"}),
    },
    attrs={
        "geospatial_lon_units": "degrees",
        "geospatial_lat_units": "degrees_north",
        "geospatial_vertical_units": "m",
    },
)

ds_mantle = ds.copy()
ds_mantle["vp"] *= -1

# Salvus wrapper.
mc = sn.model.volume.seismology.CrustalModel(name="crust", data=ds)
mm = sn.model.volume.seismology.MantleModel(name="mantle", data=ds)

# Plot depth slice.
mm.ds.vp.isel(depth=0).plot()
<matplotlib.collections.QuadMesh at 0x7340b196f390>

Initialize project

d = sn.domain.dim3.SphericalChunkDomain(
    lat_center=0.0,
    lon_center=0.0,
    lat_extent=5.0,
    lon_extent=5.0,
    radius_in_meter=6371e3,
)

# Add mantle and crustal model.
p = sn.Project.from_domain("proj_3d", d, True)
for m in [mc, mm]:
    p.add_to_project(m, overwrite=True)

Source and receiver

s = sn.simple_config.source.seismology.SideSetVectorPoint3D(
    fr=1e10,
    ft=0.0,
    fp=0.0,
    latitude=-2.5,
    longitude=-2.5,
    depth_in_m=0.0,
    side_set_name="r1",
)

r = sn.simple_config.receiver.seismology.SideSetPoint3D(
    latitude=2.5,
    longitude=2.5,
    fields=["velocity"],
    station_code="XX",
    network_code="XX",
    side_set_name="r1",
)

p.add_to_project(sn.EventCollection.from_sources(sources=s, receivers=r))

Define two simulations

p_min = 50.0

# Common event configuration.
ec = sn.EventConfiguration(
    wavelet=sn.simple_config.stf.Ricker(center_frequency=1 / (2 * p_min)),
    waveform_simulation_configuration=sn.WaveformSimulationConfiguration(
        end_time_in_seconds=600.0
    ),
)

# Heterogeneous - meshed at f_max.
s0 = sn.SimulationConfiguration(
    name="blobs",
    tensor_order=2,
    max_depth_in_meters=660e3,
    min_period_in_seconds=p_min,
    event_configuration=ec,
    model_configuration=sn.ModelConfiguration(
        background_model=sn.model.background.one_dimensional.BuiltIn(
            name="prem_iso_one_crust"
        ),
        volume_models=["mantle", "crust"],
    ),
    elements_per_wavelength=2.0,
)

# 1D only - meshed at a slightly lower resolution.
s1 = sn.SimulationConfiguration(
    name="1d",
    tensor_order=2,
    max_depth_in_meters=660e3,
    min_period_in_seconds=p_min,
    event_configuration=ec,
    model_configuration=sn.ModelConfiguration(
        background_model=sn.model.background.one_dimensional.BuiltIn(
            name="prem_iso_one_crust"
        ),
    ),
    elements_per_wavelength=1.5,
)

Add them to project

for s in [s0, s1]:
    p.add_to_project(s, overwrite=True)

Visualize mesh

p.viz.nb.simulation_setup("blobs")
[2025-04-15 19:52:25,359] INFO: Creating mesh. Hang on.
Interpolating model: mantle.
Interpolating model: crust.
<salvus.mesh.data_structures.unstructured_mesh.unstructured_mesh.UnstructuredMesh object at 0x7340b0966650>

Perform mesh-to-mesh interpolation

Interpolate the “plume” model from the “blobs” mesh to the “1d” mesh. Note that in this case we set use_layers and use_1d_vertical_coordinate to True. This ensures that the interpolation only happens between layers are consistent with each other (i.e. discontinuities are preserved) and that any topography and bathymetry will be flattened before the interpolation occurs.

# Interpolate.
m2m = interpolate_mesh_to_mesh(
    p.simulations.get_mesh("blobs"),
    p.simulations.get_mesh("1d"),
    use_layers=True,
    use_1d_vertical_coordinate=True,
)

# Assert mesh is different.
assert m2m.nelem != p.simulations.get_mesh("blobs").nelem

# Visualize.
m2m
[2025-04-15 19:52:30,450] INFO: Creating mesh. Hang on.
<salvus.mesh.data_structures.unstructured_mesh.unstructured_mesh.UnstructuredMesh object at 0x7340b2c1a6d0>

Add interpolated mesh to project

p.add_to_project(
    sn.UnstructuredMeshSimulationConfiguration(
        name="blobs_reinterp", unstructured_mesh=m2m, event_configuration=ec
    )
)

Simulate all 3

for name in ["blobs", "blobs_reinterp", "1d"]:
    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)
[2025-04-15 19:52:34,542] INFO: Submitting job ...
Uploading 1 files...

🚀  Submitted job_2504151952547205_5cd18dbd8c@local
[2025-04-15 19:53:05,057] INFO: Submitting job ...
Uploading 1 files...

🚀  Submitted job_2504151953062149_acb6c3e9c9@local
[2025-04-15 19:53:19,945] INFO: Submitting job ...
Uploading 1 files...

🚀  Submitted job_2504151953950851_3742f5cef3@local

Visualize results

Note that both runs with 3-D models are essentially identical, while the homogeneous run is very different. The small differences in the two 3-D runs are expected due to the different mesh resolutions, the broadband nature of the source wavelet, and the heterogeneity of the model.

p.viz.waveforms(
    event="event_0000",
    receiver_name="XX.XX",
    data=["blobs", "blobs_reinterp", "1d"],
    receiver_field="velocity",
)
[]