Lebedev网格改进差分系数TTI介质正演模拟方法研究

The study on numerical simulation method of Lebedev Grid with dispersion improvement coefficients in TTI media

本文采用一种新的交错网格-Lebedev网格(LG)进行TTI介质的正演模拟研究,避免了Virieux标准交错网格(SSG)算法在处理TTI、单斜等各向异性介质时波场插值引入的数值误差,提高了模拟精度.在方法实现过程中,本文针对有限差分正演模拟面临的网格频散与边界反射两个关键性问题分别做了优化,并通过模型试算验证了它们的有效性与可行性:(1)结合最小二乘思想推导出新的频散改进差分系数(DIC),该系数比Taylor系数更能有效地压制粗网格引起的数值频散,可以节约内存,提高计算效率;(2)将分裂的多轴完全匹配层(M-PML)吸收边界条件引入到LG算法中,解决了传统PML边界条件在某些各向异性介质中的不稳定现象并且具有较好的边界吸收效果.

This paper adopted a Lebedev Grid （LG） as the new kind of staggered grid scheme for finite-difference（FD） modeling in TTI media. Compared to Virieux＇s Standard Staggered Grid （SSG）, this scheme can avoid the numerical dispersion from the interpolate wavefield. In process of implementation, we also do some improvements for both the grid dispersion and boundary reflection which are the two key aspects for FD numerical simulation. Numerical experiments testified the validity and feasibility of the optimized algorithm as follows. （1） we derived a new dispersion improvement coefficients （DIC） combining the least square method, which can reduce the numerical dispersion caused by coarse grid, and more effectively than Taylor coefficients with lower storage and higher computational efficiency （2） we also apply the split Multiaxial PML （M-PML） absorbing boundary condition to LG scheme which can solve the instability in certain anisotropic media caused by the traditional PML method without losing its boundary absorbing effect.