起伏地表下基于改进BISQ模型双相介质中曲线网格有限差分法波场模拟

Wavefield modeling in two-phase media including undulated topography based on reformulated BISQ model by Curvilinear Grid FD method

本文以基于改进BISQ模型的二维双相各向同性介质一阶速度-应力方程为基础,推导出了曲线坐标系下对应的方程,然后采用低频散、低耗散的同位网格MacCormack有限差分法来离散方程,并采用紧致的单边MacCormack差分格式结合牵引力镜像法来施加自由地表边界条件,实现了地震波场数值模拟.曲线网格有限差分法采用贴体网格来描述自由表面,地表的网格线紧贴地形,避免了台阶近似造成的数值散射.数值模拟结果表明,在双相介质起伏自由地表和分界面处,各类波型复杂的反射透射规律可以清晰展现,曲线网格有限差分法可以精确地解决地震波在含起伏地表的双相各向同性介质中的传播问题.

In this article,the corresponding equations in curvilinear coordinate system based on the first-order velocity stress equation of two-phase isotropic media based on the improved BISQ model are derived,then the equations are numerically solved by an optimized high-order nonstaggered finite difference scheme,that is,DRP/opt MacCormack scheme.To implement the undulating free-surface topography,we derive the analytical relationship between derivatives of velocity components and use the compact finite-difference scheme and traction-image method.The curvilinear grid finite difference method uses body-conforming grid to describe the free surface,thus avoids the numerical approximation caused by scattering.In the undulating free surface andthe undulating interface of two-phase medium,the complex reflection wave and transmission wave can be clearly demonstrated by the numerical simulation results.The simulation results show that the curvilinear grid finite-difference method can accurately solve the propagation problem of seismic waves in a two-phase isotropic medium with undulating surface.