基于修正伪Helmholtz分解算子的横向各向同性介质纵横波波场分离

纵横波波场分离是弹性波逆时偏移成像中的关键步骤，可以有效消除纵横波串扰和成像畸变，提高成像精度。在各向异性介质中，常用的波场分离法有非平稳滤波器或者低秩近似的方法，但由于使用多次傅里叶变换，导致波场分离计算成本较高。借鉴基于Helmhotz算子构建各向同性介质纵横波解耦方程的思路，提出消除振幅畸变的修正伪Helmholtz分解算子，通过待定系数方法求解横向各向同性介质中P波和S波2种模式的表达式，并将其变换为一阶解耦的伪弹性波方程，实现时空域纵横波波场解耦。通过简单模型的波场分离测试，得到分离后的P波与S波波场，验证了该方法的波场分离的有效性。此外，将解耦得到的矢量P波与矢量S波应用到弹性逆时偏移之中，利用矢量点积互相关成像条件得到清晰的弹性波逆时偏移成像结果，说明本方法在复杂介质中有着较好的适用性，同时可以有效地应用到VTI介质弹性逆时偏移之中。

Wavefield separation of P- and S-waves based on modified pseudo-Helmholtz decomposition operator in transverse isotropic media

The separation of P- and S-wave fields is a significant step in elastic reverse-time migration (ERTM), which can effectively eliminate the waveform crosstalk and image artifacts, thus improving the precision of imaging. In anisotropic media, nonstationary spatial filters or low-rank approximation methods are commonly used to separate the wavefields. However, the application of multiple Fourier transforms results in the high computation costs of the above wavefield separation methods. Based on the idea of constructing the isotropic decoupling equations of P- and S- waves with the Helmholtz operator, a modified pseudo-Helmholtz decomposition operator was proposed to eliminate the amplitude distortion. Then, the expressions of shear and dilatational waves in transverse isotropic media were solved with the method of undetermined coefficients. Meanwhile, these expressions were converted into the first-order decoupled pseudo-elastic wave equations, so as to realize the wavefield decoupling of P- and S-waves in time and space. Through the wavefield separation test of the simple model, the separated P and S-wave fields were obtained, which verified the effectiveness of the method for wavefield separation. Furthermore, the vector P- and S-waves obtained by decoupling were applied to the elastic reverse time migration, and the clear imaging results of elastic reverse-time migration were obtained with the vector dot product cross-correlation imaging conditions. Thereby, it is indicated that this method is well applicable to the complex media. Meanwhile, it could be effectively applied to the elastic reverse-time migration of VTI media.