三维TTI介质弹性波相、群速度的近似配方表征法

TTI介质弹性波相速度可以通过求解Christoffel方程得到，其精确式往往比较复杂，难以运用。为此，从Thomsen各向异性参数表征的TTI介质弹性波精确三维相速度表达式出发，利用近似配方法推导了TTI介质qP波和qSV波三维相速度的近似公式；将其代入Berryman的群速度表征中，得到了qP波和qSV波群速度的近似公式。理论分析和数值计算表明，基于近似配方法的相、群速度表达式在一定范围内与精确值吻合较好，能够适用于中强各向异性情况，且Thomsen参数ε与δ越接近，其精度越高；沿TTI介质对称轴方向和垂直对称轴方向的速度误差最小，而与对称轴呈45°方向误差相对较大；在相同各向异性强度下，qP波相、群速度误差一般要小于qSV波。

Approximate 3D phase and group velocities for elastic wave in TTI media based on an approximate match method

The phase velocities of elastic wave in TTI media can be obtained by solving the Christtoffel equation. But the exact equations are complicated and difficult to use. Starting from the 3D exact expression of phase velocities of elastic wave in TTI media characterized by Thomsen anisotropic parameters, the 3D approximation of qP- and qSV-wave phase velocities in TTI media is derived by an approximate match method. Substituting the approximation into the Berryman's group velocity equation, we can obtain the approximation of qP- and qSV-group velocity. Theoretical analysis and numerical calculations show that the approximation of phase and group velocities based on the approximate match method are in good agreement with the exact value within some ranges, and can be applied to the conditions of moderated and strong anisotropy. The closer the ε and δ are, the higher the approximation accuracy is. Meanwhile, the relative error along the symmetric axis and the vertical symmetric axis of the TTI media is the smallest, but increases near the direction at 45° to the symmetric axis. The relative error of approximate phase and group velocities of qP wave are smaller than qSV wave when the anisotropy is similar.