基于旋转交错网格的双相各向异性介质二维三分量波场模拟

Study on 2D/3C wave propagation in two-phase anisotropic media using the rotated staggered-grid method

基于Biot双相介质模型,推导了双相TTI介质二维三分量一阶速度-应力弹性波方程,采用旋转交错网格(RSG)技术建立了各向异性孔隙介质波动方程的二维三分量高精度有限差分格式(FDTD),并引入不分裂卷积完全匹配层(CPML)作为吸收边界条件。为了验证算法可行性,对均匀双相TTI介质中的弹性波场进行了模拟。结果表明:使用旋转交错网格有限差分技术能够模拟出双相TTI介质中存在的快横波、慢横波、快纵波和慢纵波;双相各向异性介质中存在明显的横波分裂、波前面尖角和三分叉现象;不分裂卷积完全匹配层对边界反射的吸收效果较好。通过对比传统交错网格(SSG)和旋转交错网格有限差分技术,证明了旋转交错网格有限差分算法稳定性较强,精度较高,是一种实用的地震波场数值模拟方法。

Based on two-phase Biot model,the 2D/3C velocity-stress elastic wave equation of the two-phase TTI mediawas deduced. The solution of this equation using high accuracy rotated staggered-grid（RSG） finite difference time do-main（FDTD） method was presented. The unsplit convolutional perfectly matched layer（CPML） method was intro-duced into this method. To test this method,elastic waves propagation in two-phase homogeneous TTI media was simu-lated. The results obtained from RSG-FDTD simulation show that four types of wave,the fast S-wave,the low S-wave,thefast P-wave and the slow P-wave propagation in the two-phase TTI media can be clearly simulated. The shear wave split-ting,the wave fronts corners and the phenomena of trifurcation can be seen obviously. The CPML has a perfect absorptioneffect on the boundary reflection. Compared with the standard stagger-grid（SSG）,the RSG method is stable and canprovide accurate solutions. The RSG-FDTD method is a practical technique for seismic wave simulation.