Scattering pattern analysis and true‐amplitude generalized Radon transform migration for acoustic transversely isotropic media with a vertical axis of symmetry

ABSTRACT In multi‐parameter ray‐based anisotropic migration/inversion, it is essential that we have an understanding of the scattering mechanism corresponding to parameter perturbations. Because the complex nonlinearity in the anisotropic inversion problem is intractable, the construction of true‐amplitude linearized migration/inversion procedures is needed and important. By using the acoustic medium assumption for transversely isotropic media with a vertical axis of symmetry and representing the anisotropy with P‐wave normal moveout velocity, Thomsen parameter δ and anelliptic parameter η, we formalize the linearized inverse scattering problem for three‐dimensional pseudo‐acoustic equations. Deploying the single‐scattering approximation and an elliptically anisotropic background introduces a new linear integral operator that connects the discontinuous perturbation parameters with the multi‐shot/multi‐offset P‐wave scattered data. We further apply the high‐frequency asymptotic Green's function and its derivatives to the integral operator, and then the scattering pattern of each perturbation parameter can be explicitly presented. By naturally establishing a connection to generalized Radon transform, the pseudo‐inverse of the integral operator can be solved by the generalized Radon transform inversion. In consideration of the structure of this pseudo‐inverse operator, the computational implementation is done pointwise by shooting a fan of rays from the target imaging area towards the acquisition system. Results from two‐dimensional numerical tests show amplitude‐preserving images with high quality.