Elastic wave-mode separation for VTI media

Elastic wave propagation in anisotropic media is well represented by elastic wave equations. Modeling based on elastic wave equations characterizes both kinematics and dynamics correctly. However, because P and S modes are both propagated using elastic wave equations, there is a need to separate P and S modes to obtain clean elastic images. The separation of wave modes to P and S from isotropic elastic wavefields is typically done using Helmholtz decomposition. However, Helmholtz decomposition using conventional divergence and curl operators in anisotropic media does not give satisfactory results and leaves the different wave modes only partially separated. The separation of anisotropic wavefields requires the use of more sophisticated operators which depend on local material parameters. Anisotropic wavefield separation operators are constructed using the polarization vectors evaluated by solving the Christoffel equation at each point of the medium. These polarization vectors can be represented in the space domain as localized filtering operators, which resemble conventional derivative operators. The spatially-variable “pseudo” derivative operators perform well in heterogeneous VTI media even at places of rapid velocity/density variation. Synthetic results indicate that the operators can be used to separate wavefields for VTI media with an arbitrary degree of anisotropy.