椭球各向异性介质弹性波完全解耦波动方程

波动方程解耦是指从弹性波方程中解耦出描述各种波型独立传播的波动方程，在地震波数值模拟、地震偏移成像和多分量地震学理论研究中具有非常重要的作用。在大多数各向异性介质中，纵波、横波是耦合在一起传播，通常不具备精确解耦性质，但椭球各向异性（EA）介质却是一个例外。首先从均匀EA介质弹性波精确频散关系方程出发，利用因式分解方法将其分解为三个解耦的频散方程；然后利用傅里叶反变换得到了均匀EA介质完全精确解耦的qP波、qSV波和SH波的波动方程。理论公式和数值模拟均表明：在均匀EA介质中，qP波、qSV波和SH波可以完全精确解耦，三种波可通过解耦的波动方程独立传播；qP波和SH波的波前面为椭球状，qSV波的波前面为球状且与各向异性参数无关；三个完全解耦的波动方程不仅适用于弱各向异性EA介质，也同样适合强各向异性EA介质。

The complete decoupled wave equations for ellipsoidal anisotropic media

The decoupling of the wave equation refers to the decoupling of an elastic wave equation into wave equations that can describe the independent propagation of various wave patterns, which plays an important role in numerical simulation of seismic waves, seismic migration, and multi-component seismology. In most anisotropic media, the qP wave and qS wave are generally coupled for propagation without exact decoupling nature, but it is found that the ellipsoidal anisotropic (EA) media are an exception. First, on the basis of the exact dispersion relation equation of the elastic wave in homogeneous EA media, three decoupled dispersion equations are decomposed from this equation by the factorization method and then transformed into the completely and exactly decoupled wave equations of the qP wave, qSV wave, and SH wave in homogeneous EA media by inverse Fourier transform. The theoretical formulas and numerical examples indicate that the qP wave, qSV wave, and SH wave can be completely and exactly decoupled and propagate independently in homogeneous EA media by decoupled wave equations. The wavefront of the qP wave and SH wave is ellipsoidal, and the wavefront of the qSV wave is spherical, independent of anisotropic parameters. The three complete decoupled wave equations are suitable not only for weak anisotropic EA media but also for strong anisotropic EA media.