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 is not satisfactory for anisotropic media and leaves the different wave modes only partially separated. The separation of anisotropic wavefields requires more sophisticated operators which depend on local material parameters. Wavefield separation operators for TI (transversely isotropic) models can be constructed 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 filters, which resemble conventional derivative operators. The spatially-variable “pseudo” derivative operators perform well in 2D heterogeneous TI media even at places of rapid variation. Wave separation for 3D TI media can be performed in a similar way. In 3D TI 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 only need to solve for the P wave polarization vectors from the Christoffel equation, and SV and SH wave polarizations can be constructed 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.