A hybrid scheme for seismic modelling based on Galerkin method

Abstract

Purely numerical methods for modelling seismic wave propagation are now fairly popular. In this paper, we report on the development of a hybrid finite element-finite difference method. Our method first employs semi-discretization of the finite element method in a part of the spatial domain (in the z-direction for 2-D situation) to obtain a wave equation in weak form, and then uses the finite difference method to solve it. This offers significant advantages in applying non-uniform grids with improved accuracy. To improve the computational efficiency, we introduce the spectral element method to replace the traditional finite element method, which leads to a diagonal mass matrix with sufficient accuracy. After that, we carry out detailed analyses of the dispersion behaviours for both uniform and non-uniform cases; the dispersion curves demonstrate high precision of our method in numerical modelling, especially in dealing with non-uniform grids. Some examples are presented to demonstrate performance of this method and confirm the analytic results. © 2011 The Authors Geophysical Journal International © 2011 RAS.