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This documentation is not for the latest stable Salvus version.

Custom Source Time Functions

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%matplotlib inline
%config Completer.use_jedi = False
# Standard Python packages
import os
import pathlib

# Third-party imports.
import numpy as np
import matplotlib.pyplot as plt
import pyasdf

# Salvus packages
import salvus.flow.api
import salvus.flow.simple_config as sc
from salvus.mesh.simple_mesh import basic_mesh

SALVUS_FLOW_SITE_NAME = os.environ.get("SITE_NAME", "local")

Main message

Salvus offers a number of parameterized source time functions (STFs) - if that is not sufficient one can construct a custom one from a numpy array as illustrated in the following cell. Several rules apply:
  • The array has to have the shape [npts, N] where npts the number of samples and N is the number of source components. The order can also be reversed in which case the array will automatically be transposed by SalvusFlow before the simulations are run.
  • The spatial weights (f[_x, ...], m_[xx, yy, ...]) are always multiplied on top of the given STFs. Thus either normalize these or set the weights all to 1.0.
  • For sources that have multiple components, e.g. vectorial or moment tensor sources, N is either equal to the number of independent source components (xy[z] in the vectorial case, m_xx, m_yy, ... in the tensor case) or equal to 1 in which case a copy of that array will be created before the weights are applied.
  • The order of the given components must either be xy[z] in the vectorial case or adhering to the Voigt notation in the tensor case.
  • Potentially specified rotation matrizes for the sources are applied after the weights and original STFs have been multiplied.
# A single array.
stf = sc.stf.Custom.from_array(
    np.sin(np.linspace(0, 4 * np.pi, 100)),
    sampling_rate_in_hertz=2.0,
    start_time_in_seconds=0.0,
)
stf.plot()

# Combine with a source object to create a complete source object.
# Note the different weights will define the final source together
# with the STF.
src = sc.source.cartesian.VectorPoint2D(
    x=10.0, y=0.0, fx=1e-2, fy=-2e-2, source_time_function=stf
)
# It is also possible to specify a separate array for every components.
array = np.array(
    [
        1.5 * np.sin(np.linspace(0, 4 * np.pi, 100)),
        -3.0 * np.sin(np.linspace(0, 4 * np.pi, 100)),
    ]
)

stf = sc.stf.Custom.from_array(
    array, sampling_rate_in_hertz=2.0, start_time_in_seconds=-10.0
)
stf.plot()

# Note that in this case the weights should be set to 1.0
src = sc.source.cartesian.VectorPoint2D(
    x=10.0, y=0.0, fx=1.0, fy=1.0, source_time_function=stf
)

Introduction

Salvus comes with a few wavelets that can readily be used as source time functions. However, sometimes it is necessary to define a custom source time function. This tutorial shows how to do that.
The Ricker wavelet is the second derivative of a Gaussian, and defined as
s(t)=(1−2 t2 π2 ω2) exp⁡(−t2 π2 ω2),s(t) = \left(1 - 2\,t^2\,\pi^2\,\omega^2\right) \, \exp\left(-t^2\,\pi^2\,\omega^2\right),