Improving the efficiency of elastic wave-mode separation for heterogeneous tilted transverse isotropic media

Wave-mode separation for TI (transversely isotropic) models can be carried out by nonstationary filtering the elastic wavefields with localized filters. These filters are constructed based on the polarization vectors obtained by solving the Christoffel equation using local medium parameters. This procedure, although accurate, is computationally expensive, especially in 3D. We develop an efficient method for wave-mode separation, which exploits the same general idea of projecting wavefields onto polarization vectors. The method consists of two steps: (1) separate wave modes in the wavenumber domain at a number of reference models to obtain the same number of partially separated wavefields; then transform all the wavefields to the space domain; (2) interpolate the wavefields (obtained in step 1) in the space domain using the spatially-variable model parameters. The new method resembles the phaseshift plus interpolation (PSPI) technique, which interpolates the wavefields that are reconstructed at several reference velocities. Synthetic examples indicate that the separation followed by interpolation is effective for models with complex geology. The new technique has the benefits of speed and accuracy.