Approximate Inversion of a Class of Generalized Radon Transforms

Abstract

Generalized Radon transforms (GRT) serve, for instance, as linear models for seismic imaging in the acoustic regime. They occur when the corresponding inverse problem is linearized about a known background compression wave speed (Born approximation). The resulting GRT is completely determined by this background velocity. In this work, we present an implementation of approximate inversion formulas for this class of GRTs proposed and analyzed in [Grathwohl et al., Inverse Problems, 34 (2018), 014002] and [Grathwohl et al., Inverse Problems, 34 (2018), 114001], where we restrict ourselves to layered background velocities in two dimensions. In a series of numerical experiments, we intensively test our implementation, reproducing theoretical predictions. Further, we drive the validity of the linearization to its limits.