Mondaic
This tutorial is presented as Python code running inside a Jupyter Notebook, the recommended way to use Salvus. To run it yourself you can copy/type each individual cell or directly download the full notebook, including all required files.
This notebook shows how to interpolate a given model defined on a regular grid to a Salvus mesh using the Marmousi model as an example.
# initialize notebook
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import obspy
import salvus.namespace as sn
plt.rcParams["figure.figsize"] = (10, 8)The Marmousi model is provided in a segy file, which we open with obspy and map to numpy arrays.
def get_marmousi():
nx, ny = 2301, 751
dx, dy = 4.0, 4.0
rho = np.empty((ny, nx))
st = obspy.read("data/marmousi_density.segy.gz")
for _i, tr in enumerate(st):
rho[_i, :] = tr.data
vp = np.empty((ny, nx))
st = obspy.read("data/marmousi_velocity.segy.gz")
for _i, tr in enumerate(st):
vp[_i, :] = tr.data
x = np.arange(nx) * dx
y = np.arange(ny) * dy
return x, y, vp, rhoPlot the model to verify we got it in correctly:
x, y, vp, rho = get_marmousi()
fig, axes = plt.subplots(2, 1)
axes[0].imshow(vp)
axes[1].imshow(rho)
plt.show()
Build a rectilinear mesh for a subregion of the model. While this might be simplistic, note that the model interpolation afterwards would be the same for any unstructured mesh.
fmax = 10.0 # maximum frequency in Hz
elements_per_wavelength = 2.0 # resolution criterion
# region in the marmousi model to mesh
mesh_min_x = x.max() * 0.2
mesh_max_x = x.max() * 0.7
mesh_min_y = y.min()
mesh_max_y = y.max()
diff_x = mesh_max_x - mesh_min_x
diff_y = mesh_max_y - mesh_min_y
m = sn.simple_mesh.basic_mesh.CartesianHomogeneousAcoustic2D(
vp=vp.min(),
rho=rho.min(),
x_max=float(diff_x),
y_max=float(diff_y),
elements_per_wavelength=elements_per_wavelength,
max_frequency=fmax,
tensor_order=4,
).create_mesh()
m.points[:, 0] += mesh_min_x
m.points[:, 1] += mesh_min_yInterpolate the model to the mesh's element nodes using a scipy function and attach it to the mesh for plotting:
from scipy.interpolate import RectBivariateSpline
f_vp = RectBivariateSpline(x, y, vp.T[:, ::-1])
f_rho = RectBivariateSpline(x, y, rho.T[:, ::-1])
nodes = m.get_element_nodes()
nodes_x = nodes[:, :, 0]
nodes_y = nodes[:, :, 1]
vp_nodes = f_vp(nodes_x, nodes_y, grid=False)
rho_nodes = f_rho(nodes_x, nodes_y, grid=False)
m.attach_field("VP", vp_nodes)
m.attach_field("RHO", rho_nodes)
m.attach_field("fluid", np.ones(m.nelem))
m
<salvus.mesh.unstructured_mesh.UnstructuredMesh at 0x7f55f4066650>
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