Abstract
In this paper, we first present the Birkhoffian system corresponding to the elastic wave equations in fluidsaturated porous medium, and then develop a symplectic stereomodelling (SSM) algorithm for solving the Birkhoffian system. The SSM method uses the secondorder symplectic geometric algorithm for time advancing and the fourth-order stereomodelling method to approximate the high-order spatial derivatives. Based on such a structure, it can not only preserve the symplectic geometry structure of the Birkhofffian system, but also suppress effectively the numerical dispersion caused by discretization of the wave equations when coarse grids are used or models have large velocity contrasts between layers. And the SSM method has second-order accuracy in time and fourth-order accuracy in space. We apply the SSM method to simulate waves propagating in porous media, and compare the numerical results with the analytical solutions and the numerical results by the conventional symplectic method (CSM) and the Lax-Wendroff correction (LWC) method.
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