2 1/2-D elastic ray-Born migration/inversion theory for transversely isotropic media

David W. S. Eaton, Robert R. Stewart

Linearized (ray-Born) scattering formulae are derived that relate the observed seismic wavefield to perturbations in qP- and qS-wave velocities, density and the three Thomsen anisotropy parameters (, and ) for transversely isotropic media. These formulae form the basis for a 2.5 dimensional migration/inversion algorithm that accounts for anisotropic effects in both wave propagation and scattering. The technique is applicable to seismic data acquired across geologic strike over a 2-D inhomogeneous medium. The l2-norm inversion is carried out by minimization of an objective function that incorporates a priori data and model covariances, so that the problem is always well-posed and can accommodate insufficient and inaccurate data. Anisotropic model parameters that are obtained in the inversion may be useful for sand/shale discrimination, characterization of thinly laminated rock layers or analysis of fracturing.