Comparison of numerical dispersion in acoustic finite-difference algorithms

Abstract

Numerical simulation of the acoustic wave equation is widely used to synthesise seismograms theoretically, and is also the basis of the reverse time migration. With some stability conditions, grid dispersion often exists because of the discretisation of the time and the spatial derivatives in the wave equation. How to suppress the grid dispersion is therefore a key problem for finite-difference approaches. Different methods are proposed to address the problem. The commonly used methods are the high order Taylor expansion methods and the optimised methods. In this paper, we compare the performance of these methods in the space and time–space domains. We demonstrate by dispersion analysis and numerical simulation that a linear method without iteration performs comparably to the optimised methods, but with reduced computational effort.