摘要
波动方程分解是指从弹性波方程中分解出描述各种波场独立传播的波动方程。在各向异性介质中,由于纵波、横波是耦合在一起传播的,所以通常不具备解耦性质。本文从Thomsen弱各向异性近似和声学假设近似两个途径对三维TTI介质弹性波波动方程进行了分解。利用本征值方法求解三维TTI介质弹性波的Christoffel方程,得到描述SH波、qP波和qSV波的精确频散关系方程,通过Thomsen弱各向异性表征理论,推导出了弱各向异性条件下描述qP波和qSV波传播的时空域波动方程;由TTI介质qP波和qSV波耦合的频散关系方程出发,根据声学假设原理,推导出三维TTI介质描述qP波传播的波动方程。数值试算表明,通过波动方程分解获得的三维TTI介质qP波和qSV波波动方程具有较高的精度,为研究三维TTI介质qP波和qSV正演模拟和深度偏移算法奠定了理论基础。
Wave equation decomposition means wave equation decomposed from elastic wave equation to describe individual wavefield independent propagation. In anisotropic medium, P-wave and S-wave are coupling propagation and without decoupling nature generally. The paper carried out elastic wave equation decomposition in 3-D TTI medium from two ways: Thomsen weak anisotropic approximation and acoustic hypothesis approximation. Using eigenvalue method to solve the Christoffel equation of elastic wave equation in 3-D TTI medium and to get precious dispersion relation equation describing SH wave, qP-wave and qSV-wave, and the wave equation in time-space domain describing qP-wave and qSV-wave propagation in weak anisotropic condition was deduced by Thomsen weak anisotropic theory; the wave equation describing qP-wave propagation in 3-D TTI medium was deduced based on acoustic synthesis theory and starting from dispersion relation equation coupling qP-wave to qSV-wave in 3-D TTI medium. The numeric case showed the wave equation of qP-wave and qSV-wave in 3-D TTI medium by wave equation decomposition has higher precision, laid theoretical foundation for studying forward simulation and depth migration algorithm of qP-wave and qSV-wave in 3-D TTI medium.
出处
《石油地球物理勘探》
EI
CSCD
北大核心
2009年第1期19-27,共9页
Oil Geophysical Prospecting
基金
国家自然科学基金项目(40739908)资助
关键词
三维TTI介质
波动方程分解
弱各向异性
THOMSEN参数
近似
3-D TTI medium,wave equation decomposition,weak anisotropic approximation,acoustic synthesis approximation, Thomsen parameter
