In this paper, we present dynamic equations of elastic wave propagations, the Galerkin variational equations, and the finite element equation in anisotropic porous media. We propose a finite element method based on solid displacements u and "relative fluid displacement" W to solve elastic equation which include both anisotropy of fluid micro-velocity field and Poiseuille macroscopic flow in two-phase anisotropic media. The artificial absorbing boundary conditions for porous VTI media (transversely isotropic medium with a vertical symmetry axis) are also given in this paper. Our numerical modeling results show that both the finite element method and the absorbing boundary conditions are effective and feasible. For the ideal (non-viscous fluid) phase boundary case, the slow quasi P-wave can be seen simultaneously from both solid/fluid wave-field snapshots, and for the viscous phase boundary case whether the slow quasi P-wave can be observed depends on the dissipative property of formations with fluids. The slow quasi P-wave is more easily observed from fluid displacement wave-fields than from the solid displacement wave-fields
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