Limited‐view diffraction tomography in a nonuniform background

Abstract

The main problems in geophysical diffraction tomography are (1) complicated media and (2) rather limited acquisition geometries. Existing algorithms solve the limited‐view problem in an iterative manner, but are valid only for line sources and 2-D homogeneous background models. In this paper, we derive an iterative algorithm based on asymptotic wave theory that can compensate for a limited acquisition geometry. The method is valid for a 2-D nonuniform background model and point‐source illumination (i.e., a 2.5-D geometry). Paraxial ray tracing is employed to model the arbitrary background wave response, and the general structure of the algorithm has a strong resemblance to the iterative ART‐algorithm used in straight ray tomography. Our method is shown to be stable in the presence of moderate white noise and gives reasonable results, both geometrically and quantitatively, when applied to synthetic crosshole data involving a nonhomogeneous background model and limited view.