Finite-Difference seismic wave simulation

This is a collection of Matlab and Python scripts to simulate seismic wave propagation in 1-D and 2-D.
The wave propagation is based on the first-order acoustic wave equation in stress-velocity formulation (e.g. Virieux (1986)), which is solved by Finite-Differences on a staggered-grid.

Content

In this repository 1-D and 2-D versions of Finite-Difference wave simulation codes are available in Matlab and Python.
The source code can be found in the directory Matlab/, Python/ and JupyterNotebook, respectively.

Higher spatial-orders are achieved by a classical Taylor expansion.

For higher temporal-orders there are two methods available:

Lax–Wendroff method (only in 1-D). Theory: Dablain (1986)
Adams-Bashforth method. Theory: Bohlen & Wittkamp (2016)

To explore the influence of different orders of accuracy you can run the script FD_1D_compare or FD_2D_compare.

Moreover, in 1-D there scripts to calculate and plot the numerical dispersion as well as the numerical dissipation (Adams-Bashforth method) are provided. Up to now, this scripts are Matlab only. The underlying theory is given in Bohlen & Wittkamp (2016).

Literature

Bohlen, T., & Wittkamp, F. (2016). Three-dimensional viscoelastic time-domain finite-difference seismic modeling using the staggered Adams–Bashforth time integrator. Geophysical Journal International, 204(3), 1781-1788.
Dablain, M. A. (1986). The application of high-order differencing to the scalar wave equation. Geophysics, 51(1), 54-66.
Virieux, J. (1986). P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method. Geophysics, 51(4), 889-901.