Maslov asymptotic extension of generalized Radon transform inversion in anisotropic elastic media: A least-squares approach

Abstract

Linearized asymptotic inversion of seismic data is carried out in general anisotropic media. In an anisotropic medium, even if it is homogeneous, the shear waves form (instantaneous) caustics. In the absence of caustics, we formulated the seismic inverse scattering problem via the generalized Radon transform. In the presence of caustics, which are associated with multi-pathing, we have to re-derive the inversion procedure which is now based on the weak formulation of the inverse problem. The key ingredients are the Maslov canonical operators describing the transmission from the image point to the sources and the receivers, and delicate high-dimensional stationary phase analyses. The importance of caustics in practical applications becomes apparent in the analysis of mode converted wave constituents in sedimentary basins.