Elastic wave-mode separation for TTI media

Conclusions

Different wave-modes in elastic media can be separated by projecting the vector wavefields onto the polarization vectors of each mode. For heterogeneous models, it is necessary to separate wave-modes in the space domain by non-stationary filtering. I present a method for obtaining spatially-varying wave-mode separators for TI models, which can be used to separate elastic wave-modes in complex media. The method computes the components of the polarization vectors in the wavenumber domain and then transforms them to the space domain to obtain spatially-varying filters. In order for the operators to work in TI models with non-zero tilt angles, I incorporate one more parameter--the local tilt angle $\nu$ --in addition to the parameters needed for the VTI operators. This kind of spatial filters can be used to separate complicated wavefields in TI models with high heterogeneity and strong anisotropy. I test the separation with synthetic models that have realistic geologic complexity. The results support the effectiveness of wave-mode separation with non-stationary filtering.

I also extend the wave-mode separation to 3D TI models. The P-mode separators can be constructed by solving the Christoffel equation for the P-wave eigenvectors with local medium parameters. The SV and SH separators are constructed using the mutual orthogonality among P, SV, and SH modes. For the three modes, there are a total number of nine separators, with three components for each mode. The separators vary according to the medium parameters $V_{P0}$ , $V_{S0}$ , anisotropy parameters $\epsilon$ and $\delta$ and tilt $\nu$ and azimuth $\alpha$ of the symmetry axis. The P-wave separators are constructed under no kinematic assumptions, and amplitudes of P-mode correctly characterize the plane-wave solution. Shear wave separators are constructed under kinematic assumptions, and therefore the amplitudes of shear modes are inaccurate in the singular directions. Nevertheless, the proposed technique successfully separates fast and slow shear wavefields. The process of constructing 3D separators and separating wave-modes in 3D eliminates the step of decomposing the wavefields into symmetry planes, which only works for models with an invariant symmetry axis. Spatially-varying 3D separators have potential benefits for complex models and can be used to separate wave-modes in elastic reverse time migration (RTM) for TTI models. The spatially-varying 3D separators imply large computational and storage cost, and therefore, a more efficient separation method, such as the proposed table look-up alternative, is necessary for a successful implementation.

Elastic wave-mode separation for TTI media