横向各向同性介质拟声波一阶速度—应力方程

基于弹性波的基本理论,首先推导了VTI介质拟声波一阶速度—应力方程,通过坐标变换,还得到了TTI介质拟声波一阶速度—应力方程,并从能量守恒的角度证明了上述方程比基于频散关系推导出的拟声波方程更加稳定。针对各向异性参数ε<δ的模型,对新推导的方程引入横波项,消除了残留的横波产生的数值模拟不稳定现象。通过对均匀二维模型和逆冲模型的正演模拟表明:新推导的方程不仅能很好地维持qP波的运动学特征,而且能够很好地适应任意旋转角度的TTI模型,并且在旋转角变化的TTI介质中数值稳定性要好于基于频散关系推导出的拟声波方程。

First order velocity-stress equation in TI media

Based on the elastic wave theory, we first derive in this paper a quasi-acoustic equation in VTI medium which expressed by velocity and stress. Then we popularize it into TTI media with coordinate transformation. The energy conservation proves that the velocity-stress equations derived from elastic theory are more stable than equations derived from the dispersion relation. For model with anisotropic parameters , the issue about residual shear instability can be solved by introducing a shear correction. Numerical simulation shows that the new equation can not only describe the kinematic characteristics of qP wave, and also adapt well to TTI media. Furthermore, the numerical examples verify the stability of the equations.