P-SV-wave propagation in heterogeneous media: grid method

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, th e grid method is flexible in incorporating surface topography and curved in terfaces. The grid method, in the same way as the staggered-grid finite-dif ference scheme, is developed from the first-order velocity-stress hyperboli c system of elastic wave equations. The free-surface conditions are satisfi ed naturally for the grid method. The method, with its small numerical disp ersion 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 triangul ar grid method is discussed in detail, and the numerical dispersion, stabil ity criterion and numerical simulations are presented. The grid method base d on triangular grids and quadrangular grids is also studied here.