结合泊松算法和波场分解成像条件的各向异性优化纯声波方程逆时偏移

常规各向异性逆时偏移主要采用伪声波方程，该类方程容易引起成像剖面上的伪横波干扰及数值不稳定，发展各向异性纯声波方程能够较好地解决上述问题。为此，首先回顾了TTI介质中两种常用的伪声波方程；再采用最小二乘方法获得了优化的纯声波频散关系；在此基础上，结合泊松算法和有限差分求解高精度纯声波方程。在传统互相关成像条件中，全波场信息均参与其中，容易引起较强的低频噪声干扰。鉴于此，将基于Hilbert变换的复数波场分解成像条件推广至各向异性介质，对获得的TTI纯声波沿不同方向分解，选取传播方向相反的波场分量参与最终成像。理论和模型算例表明，将优化纯声波和波场分解成像条件结合能够有效压制各向异性逆时偏移中的伪横波干扰及低频噪声，获得高质量的成像剖面。

Reverse-time migration of optimized pure acoustic equation in anisotropic media by combining Poisson algorithm and wavefield decomposition imaging condition

The traditional anisotropic reverse-time migration mainly adopts pseudo-acoustic wave equations (PWEs), which can easily lead to pseudo-shear wave interference on imaging profiles and numerical instability. Developing anisotropic pure acoustic wave equations (PAWEs) can solve the aforementioned problems. Therefore, this paper first reviews two commonly used PWEs in TTI media, and then an optimized pure acoustic wave dispersion relation based on least squares is obtained. On this basis, the high-accuracy PAWE is solved by the Poisson algorithm and finite-difference. In the conventional cross-correlation imaging condition, the full wavefield information is involved, which is prone to cause strong low-frequency noise. Given this issue and anisotropy, the isotropic imaging condition based on complex wavefield decomposition is further extended to anisotropic media. The wavefield can be decomposed to the different directional components, and the components with opposite propagation directions are selected for the final imaging. The basic theory and model examples verify that the combination of the optimized pure acoustic waves and the imaging condition for wavefield decomposition can effectively suppress pseudo-shear wave interference and low-frequency noise in anisotropic reverse-time migration, and high-quality imaging profiles can be produced.