THE 3-DIMENSIONAL INVERSE SCATTERING PROBLEM IN RANDOM-MEDIA

The three-dimensional inverse scattering problem (ISP) in random media with Gauss' delta correlated density is considered. It is assumed tha t the scattering field satisfies the nonstationary Schrodinger equatio n and the unknown density depends on three spatial variables. The nons tationary Schrodinger equation is often used by physicists in applicat ions related to ocean acoustics, optics, and other fields. Using heuri stic arguments of statistical physics we obtain a deterministic ISP in which the density ensemble average and the dispersion are incorporate d in the unknown coefficient. A version of the quasi-Newton method is developed for the latter ISP. The main mathematical result is the conv ergence theorem for this method. The results of this paper are a basis for future computations, which will be discussed elsewhere. (C) 1995 Academic Press, Inc.