Elastic Wavefield Decomposition for Reverse-Time Migration in 3D Transverse Isotropic Media

Elastic reverse-time migration (ERTM), which utilizes the advantages of both P- and S-wave modes, is a widely used application for imaging in 3D anisotropic media. However, crosstalk due to intrinsically coupled P- and S-wavefields may degrade the image quality. To solve this problem, this study presents an effective vector P- and S-wavefield decomposition scheme in ERTM that can improve the images of 3D transversely isotropic (TI) media. The proposed method consists of four steps: (1) rotating the observation coordinate system to align its vertical axis with the symmetry axis of 3D TI media; (2) deriving the formulations of the 3D TI decomposition operator by applying the VTI P/S wave-mode decomposition strategy based on eigenform analysis in the new coordinate system; (3) implementing vector P- and S-wavefield decomposition by constructing the 3D TI Poisson equation, and introducing a novel and efficient method based on the first-order Taylor expansion to accelerate the computational efficiency of the decomposition; and (4) applying a vector-based dot-product imaging condition to generate PP and PS images. Compared with previous studies, the algorithm of our proposed method in 3D TI media is both numerically stable and computationally efficient. The 3D TI decomposition operator generates vector P- and S-wavefields showing the correct amplitude/phase with the input ones. Several numerical examples illustrate the satisfactory performance of the proposed 3D TI decomposition operator and the effective image improvement.