基于改进声波方程和MCPML边界的频率域高精度正演模拟

数值频散和边界反射是频率域模拟时需要解决的两个重要问题.然而,受计算效率和分解阻抗矩阵时的内存占用量的制约,提高有限差分算子长度或增加有限差分网格数目均不是提高频率域模拟精度的最优解决方案.本文首先分析了数值频散产生的理论机制,在此基础上,推导了一种“波数补偿”的声波方程表达式来压制数值频散,并给出其物理意义,有效地改善了数值频散问题,提高了模拟精度;在边界问题上,本文采用多轴卷积完全匹配层(MCPML)边界条件代替传统的完全匹配层(PML)边界条件,快速吸收边界内的残余能量,压制边界反射.结合改进声波方程和MCPML边界条件,给出了一种高精度的频率域声波方程有限差分格式.数值模拟结果表明,在不增加计算量和内存占用量的前提下,本文研究的方法、正演精度高、波场模拟清晰、无干扰反射,是一种可靠高效的频率域模拟方法.

High precision simulation in frequency domain based on improved acoustic equation and MCPML boundary

Numerical dispersion and boundary reflection are two important problems affecting the simulation results in frequency domain. However, restricted by the computational efficiency and memory consumption of impedance matrix decomposition, increasing the length of finite-difference operators or the number of finite-difference grids are not the optimal solution to improve the simulation accuracy. Firstly, the theoretical mechanism of numerical dispersion is analyzed. On this basis, an improved acoustic equation expression with "wave number compensation" is derived and its physical significance is elaborated, which could effectively suppress numerical dispersion and improve simulation accuracy; On the boundary reflection problem, instead of perfectly matched layer (PML) boundary, the multi-axial convolution perfectly matched layer (MCPML) boundary is used to rapidly absorb the residual energy and eliminate the boundary reflection. Combined with the improved acoustic equation and MCPML boundary, a high-precision expression of acoustic equation in frequency domain is studied. The numerical simulations demonstrate that the proposed method in this paper is a high-precision simulation method in frequency domain, with high simulated accuracy and efficiency, clear simulated wave fields and without increasing the calculation amount and memory consumption.