TTI介质声波方程分裂式PML吸收边界条件研究

摘要

We study split perfectly matched layer (SPML) absorbing boundary conditions for TTI media based on the characteristics of TTI media acoustic wave equation.We firstly summarize several common TTI media acoustic wave equations and compare these wave equations in detail from the perspective of wavefield propagation stability for TTI media.We conclude that the TTI acoustic approximation equation introduced SV-wave component is applicable for TTI media.Then we derive the TTI media first-order acoustic wave equation based on the SPML boundary condition from the TTI P-wave and SV-wave coupled second-order wave equation.Afterwards we give the concrete implementation method for high-order staggered-grid finite-difference algorithm.The numerical modeling examples show that the SPML boundary condition can absorb the artificial boundary reflection very well.The boundary reflection absorbing effect of the proposed SPML algorithm is much better compared with the optimal sponge boundary condition.%针对倾斜横向各向同性(TTI)介质声波波动方程的特点,研究了TTI介质分裂式完全匹配层(Split perfectly matched layer,SPML)吸收边界条件.首先对常见的几种TTI介质声波波动方程进行了归纳,并从TTI介质波场传播稳定性的角度进行对比分析,结果表明,引入横波分量的TTI介质纵横波耦合方程适用于TTI介质.然后从TTI介质纵横波耦合二阶波动方程出发,推导得到其一阶波动方程的形式,进而推导出一阶波动方程形式的SPML波动方程,并给出了高阶交错网格有限差分算法的具体实现过程.数值模拟结果表明,SPML吸收边界条件能达到很好的人工边界反射吸收效果,相比优化海绵吸收边界条件,其人工边界反射吸收效果更好.