双相各向异性介质中弹性波方程的有限元解法及波场模拟

FINITE ELEMENT METHOD OF THE ELASTIC WAVE EQUATION AND WAVEFIELD SIMULATION IN TWO-PHASE ANISOTROPIC MEDIA

基于双相各向异性介质模型 ,首先推导了双相各向异性介质中弹性波传播的动力学方程及其Galerkin变分方程和有限元运动方程 ,然后给出了孔隙弹性波方程的有限元数值解法以及二维双相PTL介质中波场模拟的人为吸收边界条件 .最后 ,利用本文给出的有限元方法对双相PTL介质和双相各向同性介质中的弹性波传播进行了数值模拟 .结果表明 :有限元方法和吸收边界条件有效、可行 ,在理想相界条件下 ,不论是从固体位移 ,还是从流体位移的波场快照都能看到明显的慢速拟P波 ;在黏滞相界情况下 ,能否观察到慢速拟P波 ,与含流体地层介质的耗散性质有关。对实际含流体介质 ,从流体位移分量的波场快照比从固体位移波场快照更容易观察到慢速拟P波 .

Based on the two phase anisotropic model 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. The finite element method is used for solving the porous elastic wave equations under artificial absorbing boundary conditions. The numerical simulation of the elastic wave propagation in the two phase PTL and the two phase isotropic media is carried out by using the finite element method. The results show that both the finite element method and the absorbing boundary conditions are effective and feasible. In the ideal phase boundary case, a slow quasi P wave can be seen in both solid and fluid wave field snapshots; in 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.