Efficient Elastic Wave-mode Separation in TTI Media

Wave mode separation is an indispensable step in elastic wave equation imaging. For isotropic media, the separation is typically done using Helmholtz decomposition. However, Helmholtz decomposition does not completely separate wave modes for anisotropic media. Wavefield separation operators for TI (transverse isotropic) models are 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 wave mode separation for TI media is usually implemented as non-stationary filtering with local filters. However, the accurate separation in the space domain is computationally expensive especially in 3D. In this paper, we show an efficient method for wave-mode separation, which exploits the same general idea of projection on polarization vectors. The method consists of two steps: first separate wave modes in the wavenumber domain for a number of reference models, and second interpolate the wavefields in the space domain using the spatially-variable model parameters. An example shows that the separation by interpolation works well for models with complex geology.