A hybrid scheme for seismic modelling based on Galerkin method

作者：Liu, Tao^*; Hu, Tianyue; Sen, Mrinal K.; Yang, Jinhua; Wang, Runqiu; Wei, Jianxin; Wang, Shangxu

来源：Geophysical Journal International, 2011, 186(3): 1165-1178.

DOI：10.1111/j.1365-246X.2011.05094.x

• Numerical solutions
• Instability analysis
• Numerical approximations and analysis
• Computational seismology
• Wave propagation

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.

• 出版日期2011-9
• 单位北京大学; 中国石油大学（北京）