qS-wave decoupling equation for wavefield separation in transversely isotropic media

Abstract

Considering the anisotropy of the earth media is helpful in reducing the depth error between seismic and drilling and providing reliable imaging data for seismic interpretation and inversion. Transversely isotropic media with a vertical axis of symmetry are the most common type of anisotropic media and have been under constant study. The separation of the P- and S-wavefields, which affects the accuracy of elastic wave imaging and the inversion in transversely isotropic media with a vertical axis of symmetry, is a hot research topic. Among the commonly used wavefield decoupling methods, the S-wave is typically obtained by subtracting the P-wave from the total wavefield. However, this kind of wavefield decoupling method often leads to severe P-wave crosstalk in the separated S-wavefield; thus, it needs further development. In this paper, the principle that the divergence of the S-wave is zero is employed to solve the unresolved S-wave elastic parameters of the S-wave stiffness matrix by utilizing the modified zero-order pseudo-Helmholtz decomposition operator. The obtained S-wave elastic parameters are employed to construct the qS-wave stress and facilitate the derivation of the relationship between the qS-wave particle velocity and the qS-wave stress. Furthermore, a qS-wave decoupling first-order velocity–stress equation, which matches the qP-wave decoupling first-order velocity–stress equation, is derived. By jointly using the decoupling equations of qS- and qP-wave, the separation of the P- and S-wavefields in transversely isotropic media with a vertical axis of symmetry is realized. The efficiency of the proposed method is demonstrated via numerical tests conducted to assess the wavefield separation. Moreover, a complex model is employed to perform elastic reverse-time migration, resulting in the acquisition of accurate imaging results for PP, PS, SP, and SS waves, without the presence of significant artefacts. The correctness of the qS-wave decoupling equation in transversely isotropic media with a vertical axis of symmetry is confirmed by the comparative tests using decoupling methods in isotropic media.