VTI介质修正声学近似qP波波动方程与模拟

Wave equation and numerical simulation for qP wave in VTI media with modified acoustic approximation

各向异性介质中纵横波通常耦合在一起传播,纵横波解耦是地震波传播理论研究的重要内容。经典的声学近似通过设置垂向qSV波速度V_(S0)为0来解耦qP波场,但是存在退化qSV波等问题。本研究将垂向qSV波速度V_(S0)考虑成波数k_(x)、k_(z)和各向异性参数ε、δ的函数,对声学近似进行修正,推导了VTI介质修正声学近似qP波频散关系和波动方程。VTI介质修正声学近似qP波波动方程包含椭圆项和非椭圆项两部分,因此采用混合有限差分/伪谱算法进行求解,即采用有限差分法求解椭圆项、伪谱法求解非椭圆项。频散关系分析和数值示例表明,基于修正声学近似的qP波波动方程不包含退化qSV波,是纯qP波方程,与弹性波方程模拟结果吻合较好,且具有较高精度;该方程在ε≥δ和ε<δ的VTI介质中均是稳定的,并且精度高于声学近似模拟结果。

In anisotropic media,qP and qS waves are usually coupled to propagate together.The decoupling of qP and qS waves is an important part of the theoretical study of seismic wave propagation.The classic acoustic approximation decouples the qP wavefield by setting the vertical velocity V_(S0) of qSV wave as zero,but there are problems such as degraded qSV waves.In this paper,the acoustic approximation was modified by considering the V_(S0) as a function of the wave numbers k_x,k_(z) and the anisotropy parameters ε,δ,and the dispersion relation and wave equation for qP wave in VTI media with the modified acoustic approximation were then derived.This wave equation for qP wave,containing elliptic terms and non-elliptic terms,was solved by using the hybrid finite difference/pseudo spectral method:the finite difference method for solving the elliptic terms and the pseudo spectral method for solving the non-elliptic terms.The dispersion analysis and numerical examples show that the qP wave equation with the modified acoustic approximation as a pure qP wave equation without any degenerate qSV wave is in good agreement with the simulation results of the elastic wave equation and has high accuracy.It is stable in VTI media with both ε≥δ and ε<δ,and more accurate than the simulated results with the acoustic approximation.