The Three-Dimensional Inverse Scattering Problem in Random Media

Abstract

The three-dimensional inverse scattering problem (ISP) in random media with Gauss′ delta correlated density is considered. It is assumed that the scattering field satisfies the nonstationary Schrodinger equation and the unknown density depends on three spatial variables. The nonstationary Schrodinger equation is often used by physicists in applications related to ocean acoustics, optics, and other fields. Using heuristic arguments of statistical physics we obtain a deterministic ISP in which the density ensemble average and the dispersion are incorporated in the unknown coefficient. A version of the quasi-Newton method is developed for the latter ISP. The main mathematical result is the convergence theorem for this method. The results of this paper are a basis for future computations, which will be discussed elsewhere.