Multidimensional Born velocity inversion: Single wideband point source

Abstract

The inverse scattering problem for an acoustic medium is considered within the approximate direct inversion framework. As opposed to iterative methods, the direct inversion approach gives an estimate of the medium velocities by operating on the observed scattered field without repeated solutions of the forward problem. Previous solutions to the multidimensional Born velocity inversion problem require either coincident source and receiver arrays or plane-wave sources. In both cases an array of point sources is required to collect the proper data for inversion. In this paper, the solution to the single point source problem is derived. It is shown that by extrapolating and imaging the observed scattered field appropriately, the projections of the velocity function at all angles can be obtained. The velocities are, then, reconstructed by the inverse Radon transform method of tomography.