新声学近似波动方程纯qP波有限差分正演

Finite-difference forward modeling of pure qP wave based on new acoustic approximation

新声学近似将qSV波各个方向的波速设为0,消除了传统声学近似在模拟过程中出现的残余qSV波,理论上能够模拟纯qP波。利用传播方向矢量代替波数矢量的空间近似方法,虽然可以在时间—空间域中对基于新声学近似的qP波频散进行有限差分法求解,但理论上会存在一定误差。为了提高纯qP波的模拟精度,通过引入中间变量,将基于新声学近似的qP波频散中分数形式的空间—波数域混合算子转化成一个求解中间变量的线性方程,将复杂的qP波频散关系转化为形式上更简单的时间—空间域纯qP波波动方程组,且推导过程未采用任何近似,因此该方程能够精确模拟基于新声学近似的qP波传播规律,理论上具有更高的精度,并通过有限差分法实现了二维VTI介质中纯qP波正演模拟。数值结果也证明,新的纯qP波波动方程具有更高的精度。

For the new acoustic approximation,the velocity of qSV wave in all directions is set to 0,which eliminating residual qSV waves present in traditional acoustic approximations during the simulation process,so it is naturally able to simulate pure qP wave.The spatial approximation method using propagation direction vectors instead of wave number vectors can be used to solve the qP wave dispersion based on the new acoustic approximation in the time-space domain by using finite difference methods,but there may be some theoretical errors.In order to improve the simulation accuracy of pure qP wave,this paper by introducing intermediate variable,the fractional spatial wavenumber domain mixed operator in qP wave dispersion relationship based on the new acoustic approximation is transformed into a linear equation for solving intermediate variables.This converts the complex qP wave dispersion relationship into a simpler form of time-space domain pure qP wave equation group,and the derivation process does not adopt any approximations.Therefore,this equation can accurately simulate the propagation law of qP waves based on the new acoustic approximation,theoretically with higher accuracy,and achieve pure qP wave forward simulation in two-dimensional VTI media through finite difference method.The numerical results also demonstrate that the new pure qP wave equation has higher accuracy.