【摘要】 将基于计算数学中F0rsyte广义正交多项式的迭积微分算子引入到地震波动方程的一阶速度——应力方程的空间微分运算中去,并采用时间错格有限差分算子替代传统的差分算子以匹配高精度的空间迭积微分算子,从而发展一种全新的地震波场正演模拟方法,来解决复杂非均匀介质模型中的波场传播问题.为了大幅衰减人工边界引起的反射,本文将完全匹配层(Perfectly Matched Layer,PML)吸收边界条件引入到所构建的方法中,以解决迭积微分算子法的边界问题.以二维波动方程为例,用迭积微分算子法实现了双相介质的地震波场正演模拟,模拟结果表明,双相介质模型较好地解释了合流体孔隙特性.同时也表明迭积微分算子法是一种非常实用、有效的数值模拟方法.更多还原

【Abstract】 The key issue in this paper is to introduce the convolutional differentiator based on Forsyte generalized orthogonal polynomial in mathematics into the spatial differentiation of the first velocity-stress equation.To match the high accuracy of the spatial differentiator, this method in the time coordinate adopts staggered grid finite difference instead of conventional finite difference to model seismic wave propagation in heterogeneous media.To attenuate the reflection artifacts caused by the artificial boundary, the Perfectly Matched Layer (PML) absorbing boundary is also considered in the method to deal with the boundary problem due to its advantage of automatically handling large-angle emission.This paper constructs the constitutive relationship for two-phase media, and further derives the first-order velocity-stress equation for 2D two-phase media.Numerical modeling using the CFPD method is carried out in the above-mentioned media.The results modeled in Biot two-phase media can better explain the liquid pore characteristics and can also prove that CFPD is a useful numerical tool to study the wave propagation in complex media.更多还原