waterstar2010 / fd_acoustic

Collection of Matlab and Python scripts for Finite-Difference seismic wave simulation in 1-D and 2-D

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.

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/ and Python/, respectively.

Higher spatial orders are achieved by a classical Taylor expansion.

For higher temporal orders there are two methods 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.

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.

Licence

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