A combined compact finite difference scheme for solving the acoustic wave equation in heterogeneous media

Abstract

In this paper, we consider the development and analysis of a new explicit compact high‐order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation through a heterogeneous media with variable media density and acoustic velocity. The new scheme is compact and of fourth‐order accuracy in space and second‐order accuracy in time. The compactness of the scheme is obtained by the so‐called combined finite difference method, which utilizes the boundary values of the spatial derivatives and those boundary values are obtained by one‐sided finite difference approximation. An empirical stability analysis has been conducted to obtain the Courant‐Friedrichs‐Levy (CFL) condition, which confirmed the conditional stability of the new scheme. Four numerical examples have been conducted to validate the convergence and effectiveness of the new scheme. The application of the new scheme to a realistic wave propagation problem with a Perfect Matched Layer is validated in this paper as well.