3D elastic wave mode separation for TTI media

The separation of wave-modes for isotropic elastic wavefields is typically done using Helmholtz decomposition. However, Helmholtz decomposition using conventional divergence and curl operators in anisotropic media only partially separates the elastic wave-modes. The separation of anisotropic wavefields requires operators which depend on local material parameters. Wavefield separation operators for TI (transverse isotropic) models can be constructed based on the polarization vectors evaluated at each point of the medium by solving the Christoffel equation. These polarization vectors can be represented in the space domain as localized filters, which resemble conventional derivative operators. The spatially-variable pseudoderivative operators perform well in heterogeneous media even at places of rapid variation. In 3D TTI media, P and SV waves are polarized only in symmetry planes, and SH waves are polarized orthogonal to symmetry planes. Using the mutual orthogonality property between these modes, we need to solve only for the P wave polarization vectors from the Christoffel equation, and construct SV and SH wave polarizations using the relationship between these three modes. Synthetic results indicate that the operators can be used to separate wavefields for TI media with arbitrary strength of anisotropy.