A fast 3D decoupled operator for P/S wave-mode decomposition in TI media and its application in elastic reverse time migration

With the development of multi-component acquisition technology, elastic reverse-time migration (ERTM) is widely used for seismic imaging in 3D anisotropic media. However, crosstalk artifacts degrade the image quality due to intrinsically coupled P- and S-wavefields. To solve this problem, this study presents an effective vector P- and S-wavefield decomposition approach that can improve the ERTM image of 3D Transverse Isotropy (TI) media. Firstly, we rotate the observation coordinate system to align its vertical axis with the tilted symmetry axis. Secondly, based on the 3D VTI decoupled operator, we derive the formulations of the 3D TI decomposing operator in the new coordinate system. Thirdly, we implement the vector P- and S-wavefield decomposition on the space domain by introducing a novel and efficient formula, which accelerates the computational efficiency of the decomposition. Finally, we introduce P/S wave-mode decomposition method into ERTM via a dot-product imaging condition to generate high-quality PP and PS images. Compared with previous studies, our proposed method in 3D TI media is both numerically stable and computationally efficient. Several numerical examples illustrate the good performance of our approach on image improvement in 3D TI media.