An effective method to suppress numerical dispersion in 2D acoustic and elastic modelling using a high-order Padé approximation

Abstract

In this paper, we propose a method that can effectively reduce the numerical dispersion for solving the acoustic and elastic-wave equations. The method is a fourth-order Pade approximation scheme, in which the time difference operator is a rational function and a block tridiagonal system needs to be solved at each step. On the one hand, to efficiently solve a large linear system of equations we propose an explicit method for this implicit algrithom. On the other hand, to approximate the high-order spatial derivatives we use an eighth-order stereo-modelling method using wavefield displacements and their gradients simultaneously. For this new method, we investigate some mathematical properties including the stability, errors and the numerical dispersion relationship for 1D and 2D cases. We also present numerical results computed by the Pade approximation and compare them with the eighth-order Lax–Wendroff correction method and the eighth-order staggered-grid method. Numerical results show that the high-order Pade approximation scheme can effectively suppress the numerical dispersion caused by discretizing the wave equations when coarse spatial grids are used or models have strong velocity contrasts between adjacent grids. In contrast to other high-order finite-difference methods, the new method takes substantially less computational time and requires less memory because large spatial and time increments can be used. Thus the high-order Pade approximation method can potentially be used to solve large-scale wave propagation problems and seismic tomography based on the wave equations.