Finite-Difference Seismic Wave Simulation

This is a collection of Matlab and Python scripts for simulating 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.

Contents

This repository contains 1-D and 2-D versions of Finite-Difference wave simulation codes in both Matlab and Python. The source code can be found in the Matlab/, Python/, and JupyterNotebook directories, respectively.

Higher spatial orders are achieved through a classical Taylor expansion.

For higher temporal orders, two methods are available:

1. Lax–Wendroff method (only in 1-D). Theory: Dablain (1986)

2. 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.

Additionally, in 1-D, scripts are provided for calculating and plotting numerical dispersion, as well as numerical dissipation (Adams-Bashforth method). Currently, these scripts are only available in Matlab. The underlying theory is presented 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 (https://doi.org/10.1093/gji/ggv546).

• Dablain, M. A. (1986). The application of high-order differencing to the scalar wave equation. Geophysics, 51(1), 54-66 (https://doi.org/10.1190/1.1442040).

• Virieux, J. (1986). P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method. Geophysics, 51(4), 889-901 (https://doi.org/10.1190/1.1442147).

Licence

This collection is available under the GNU General Public License v3.0. See the LICENCE file for more information.