Acoustic Wave Propagation in Complicated Geometries and Heterogeneous Media

Abstract

We construct finite difference discretizations of the acoustic wave equation in complicated geometries and heterogeneous media. Particular emphasis is placed on the accurate treatment of interfaces at which the underlying media parameters have jump discontinuities. Discontinuous media is treated by subdividing the domain into blocks with continuous media. The equation on each block is then discretized with finite difference operators satisfying a summation-by-parts property and patched together via the simultaneous approximation term method. The energy method is used to estimate a semi-norm of the numerical solution in terms of data, showing that the discretization is stable. Numerical experiments in two and three spatial dimensions verifies the accuracy and stability properties of the schemes.