各向异性介质地震波场数值模拟及特征分析

由于各向异性广泛存在于地下岩石中,随着勘探精度的不断提高,对地下介质的各向同性假设越来越不能够满足于现状,因此对各向异性介质的数值模拟显得更为重要。本文推导了各向异性介质的弹性波动方程,总结了震源类型,通过PML方法处理了人工边界问题,通过快照分析验证了数值频散、稳定性条件。研究结果表明:① PML完全匹配层,可较好地解决人工边界问题;②减小空间采样间隔压制数值频散比减小时间采样间隔效果要好得多,盲目减小时间采样间隔会大大降低数值模拟的运算效率;③各向异性介质中弹性波场中除含有准纵波外,还含有速度较慢的准横波;④准纵波波前能量要比由各向异性引起的准横波能量强,准纵波和准横波的波前随着各向异性介质参数的变化而变化。

The Seismic Wave Numerical Simulation and Characteristics Analysis in Anisotropic Medium

Due to the anisotropy widely exists in underground rocks, and with the increasing of exploration precision, isotropic hypothesis of underground media can't be gradually content with the status quo, so the numerical simulation of the anisotropic medium is more important. This paper derived the elastic wave equation of anisotropic medium, summarized the source type, tackled the problem of the artificial boundary by PML method, and verified the numerical dispersion and stability conditions by snapshots. The results show that: 1) PML based on staggered grid can solve the problem of the artificial boundary; 2) reduce the spatial sampling interval is much better than reduce time sampling interval to suppress numerical dispersion and blindly reduce time sampling interval can reduce the operational efficiency of the numerical simulation; 3)there is quasi p-wave and slow quasi s-wave in the elastic wave field of anisotropic medium; 4) quasi p-wave front energy is stronger than quasi s-wave energy, quasi p- wave and quasi s-wave front are changed as parameters of anisotropic medium.