Symplectic stereomodelling method for solving elastic wave equations in porous media

Abstract

In this paper, we propose a new symplectic stereomodelling (SSM) method to solve lowfrequency poroelastic wave equations in fluid-saturated porous media, which is proved to be symplectic for time advancing. First, we change the two-phase system without the dissipative mechanism into the generalized Birkhoffian system for the two-phase medium case, and then suggest a symplectic scheme to numerically discretize the Birkhoffian system via the two-stage partitioned Runge-Kutta method. In the SSM method, we use the symplectic algorithm for time advancing and employ the stereomodelling method to discretize the high-order spatial derivatives. In addition, the SSM method relies on the spatial operator-split technique to effectively reduce numerical dispersion and achieve better numerical stability. Based on this structure, the SSM method can (1) effectively suppress the numerical dispersion caused by the discretization of wave equations when coarse grids are used or when the porous medium has discontinuous interfaces, and (2) preserve the Birkhoffian structure of the two-phase system without the dissipative mechanism for the long-time computation of modelling wave propagating in two-phase media. Our numerical experiments show that the SSM method can provide clear seismic wavefields including fast P, slow P and S waves on coarser grids for porous media saturated with fluid. This is in contrast with other numerical methods, such as the fourth-order Lax-Wendroff correction and the conventional symplectic method, which suffers from serious numerical dispersion for the same case. © The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.