The qP-and qSV-wave separation in 2D vertically transversely isotropic media and their applications in elastic reverse time migration

Compressional and shear wave separation is an important step in anisotropic elastic reverse time migration (ERTM). With separated wavefields, we can generate images between different wave types and reveal more subsurface physical properties, as well as remove unwanted crosstalk and improve image quality. Traditional Helmholtz decomposition based on divergence and curl operations for isotropic media cannot be directly extended to vertically transversely isotropic (VTI) media. Wave-mode separation methods, similar to the nonstationary spatial filter and Poynting vector, cannot preserve the phase and amplitude information of the original coupled wavefield, thus limiting their application in ERTM. Currently, the anisotropic wavefield decomposition methods include the wavenumber-domain approach, the low-rank approximation, and other separation approaches based on different approximations, e.g., weak or elliptical anisotropy. These methods are either computationally intensive or involve large separation errors, especially in models with strong heterogeneities and anisotropy. The VTI wavefield separation operator is essentially defined in a mixed space-wavenumber domain. We introduce scalar operators to transfer operations from this mixed space-wavenumber domain to the space domain. The local wave propagation direction in the scalar operators is estimated using the Poynting vector, which is highly computationally efficient in the space domain. When we apply the wave separation method to ERTM, we not only obtain the vectorized qP and qSV waves but also retrieve the scalar qP wavefield. The scalar and vector wavefields preserve the amplitude and phase information in the original coupled wavefield. For anisotropic ERTM, we suggest using the scalar imaging condition to generate the PP image and the magnitude-and sign-based vector imaging condition to produce the PS image, both having higher image accuracy than the dot-product imaging condition. Numerical examples are used to validate our anisotropic wavefield separation method and the related ERTM workflow.