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 0x7fb49266b610>
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[2024-03-15 09:14:32,773] INFO: Creating mesh. Hang on. [2024-03-15 09:14:33,217] INFO: Creating mesh. Hang on.
<salvus.mesh.unstructured_mesh.UnstructuredMesh at 0x7fb483d51750>
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)[2024-03-15 09:14:33,537] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2403150914652257_b3cd507a04@local
[2024-03-15 09:14:34,411] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2403150914415123_d78c50d0e7@local
[2024-03-15 09:14:35,428] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2403150914431648_2f84ab32e6@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 0x7fb47be43210>
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")[2024-03-15 09:14:36,793] INFO: Creating mesh. Hang on.
Interpolating model: mantle.
Interpolating model: crust.
<salvus.mesh.unstructured_mesh.UnstructuredMesh at 0x7fb47bbd4fd0>
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[2024-03-15 09:14:38,338] INFO: Creating mesh. Hang on.
<salvus.mesh.unstructured_mesh.UnstructuredMesh at 0x7fb47c0135d0>
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)[2024-03-15 09:14:39,032] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2403150914035673_9929eb2455@local
[2024-03-15 09:15:02,680] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2403150915684986_117c991edc@local
[2024-03-15 09:15:15,929] INFO: Submitting job ... Uploading 1 files... 🚀 Submitted job_2403150915932553_ce6281f9b4@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",
)[]