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.