A 3D fast decoupled operator for anisotropic P/S wavefield decomposition for elastic reverse time migration

The existing 3D anisotropic P/S wavefield decomposition methods is usually difficult to be applied in the production due to their large-scale computation. To solve this problem, we develop a fast decoupled operator to decompose the P/S waves in 3D vertical transverse isotropic (VTI) media and apply this operator to elastic reverse time migration (ERTM) and associated angle-domain common-image gathers (ADCIGs). To start with, we solve the 3D VTI Christoffel equation and obtain the three eigenvectors that represent P-, SV- and SH-wave polarization directions. We then project the original elastic wavefields to those polarizations and derive the decomposed P/S formulations. To improve the efficiency and model adaptability, we further eliminate the phase angle terms from decomposed formulations and converted the decomposed formulations to the space domain. A fast 3D decoupled operator is thusly developed and produce the approximate P-, SV- and SH-waves components that can calculate the accurate phase angles as those of exact P-, SV- and SH-waves. The calculated phase angles and separated P/S waves are finally used for ERTM imaging and ADCIGs extraction. The synthetic examples demonstrate the effectiveness of our proposed method.