各向异性双相介质弹性波场褶积算法数值模拟

Numerical Simulation of Elastic Wave Propagation in Heterogeneous Two-phase Media with Convolutional Differentiator Method

从各向同性介质中波场数值模拟的褶积微分算子法出发,推导出了各向异性双相介质中波场传播数值计算的褶积新算法。将常见的二阶微分Biot波动方程用等效的一阶速度-应力双曲方程表示,其中未知的波场向量包括固相和流体的速度分量和应力分量,由此对方程的时间项使用交错网格差分方法计算,而对空间项则采用褶积微分算法进行求解。对各向异性双相介质在单层介质模型和双层介质模型中的波场特征进行了研究。研究的结果显示,在两层介质分界面上当地震波产生反射时能观测到两类纵波和横波,并且在衰减系数大的介质里慢纵波很难见到。

A new numerical simulation method with convolutional algorithm for elastic waves propagation in heterogeneous two-phase media is derived from the convolutional differential simulation for the propagation in homogeneous media,and the second-order Biot wave equation is expressed as first-order velocity-stress hyperbolic equations,in which the unknown wavefield vectors are velocity and stress components in both fluid and solid phases.The temporal term in the wave equation is computed by stager-grid finite difference method and the spatial term is computed by the new convolutional differentiator.The wavefield characters of heterogeneous two-phase media are studied in both single and two-layered models.The results show that on the subsurface in the two-layered model,two types of fast P-wave and one type of S-wave can be observed when seismic wave is reflected,meanwhile in the media with large attenuation coefficient the slow P-wave is hard to be observed.