An novel finite difference dispersion error elimination mechanism in the Lax–Wendroff high-order time discretization

Abstract

Time domain finite difference methods have been widely used for wave-equation modelling in exploration geophysics over many decades. When using time domain finite difference methods, it is desirable to use a larger time step so as to save numerical simulation time. The Lax–Wendroff method is one of the well-known methods to allow larger time step without increasing the time grid dispersion. However, the Lax–Wendroff method suffers from more time consumption because there are more spatial derivatives required to be approximated by the finite difference operators. We propose a new finite difference scheme for the Lax–Wendroff method so as to reduce the numerical simulation time. Then we determine the finite difference operator coefficients and analyse the dispersion error of the proposed finite difference scheme for the Lax–Wendroff method. At last, we apply the proposed finite difference scheme for the Lax–Wendroff method to different velocity models. The numerical simulation results indicate that the proposed finite difference scheme for the Lax–Wendroff method can effectively suppress time grid dispersion and is more efficient compared to the traditional finite difference scheme for the Lax–Wendroff method.