P–SV‐wave propagation in heterogeneous media: grid method - Jianfeng, Zhang; Tielin, Liu (Geophysical journal international, 1999)
SUMMARY We present a new numerical modelling algorithm for P–SV‐wave propagation in heterogeneous media, which is named the grid method in this paper. Similar to the finite‐element method in the discretization of a numerical mesh, the grid method is flexible in incorporating surface topography and curved interfaces. The grid method, in the same way as the staggered‐grid finite‐difference scheme, is developed from the first‐order velocity–stress hyperbolic system of elastic wave equations. The free‐surface conditions are satisfied naturally for the grid method. The method, with its small numerical dispersion and good stability, is of high accuracy and low computational cost. Each time step needs 34M+N multiplication operations and 26M+N addition operations for N nodes and M triangular grids. In this paper, the triangular grid method is discussed in detail, and the numerical dispersion, stability criterion and numerical simulations are presented. The grid method based on triangular grids and quadrangular grids is also studied here.