Finite Element Method of the Elastic Wave Equation and Wave‐Fields Simulation in Two‐Phase Anisotropic Media

Abstract

AbstractBased on the two‐phase anisotropic model, firstly, this paper analyses and presents the dynamic equations of elastic wave propagation, the Galerkin variational equation, and the finite element equation in two‐phase anisotropic media. Secondly, the finite element method for solving the porous elastic wave equations and the artificial absorbing boundary conditions are given. Finally, the numerical simulation of the elastic wave propagation in the two‐phase PTL and the two‐phase isotropic media is implemented by using the finite element method. The results show that both the finite element method and the absorbing boundary conditions are effective and feasible. For the ideal 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 seen depends on the dissipative property of the formation with fluids. And the slow quasi P‐wave is more easily observed from the fluid displacement wave‐fields than from the solid displacement wave‐fields for the practical formation with fluids.