Elastic wavefield separation for VTI media

The separation of wave modes 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. We construct operators for anisotropic wavefield separation based on the polarization vectors evaluated at each point of the medium by solving the Christoffel equation using local medium parameters. These polarization vectors can be represented in the space domain as localized convolutional operators, which resemble conventional derivative operators. The spatially-variable “pseudo ” derivative operators perform well in heterogeneous VTI media even at places where the media are changing rapidly. Synthetic results indicate that the operators can be used to separate wavefields for VTI media with arbitrary degree of anisotropy. This methodology is applicable for elastic reverse time migration (RTM) in heterogeneous anisotropic media.