The Inverse Scattering Problem in a Nonstationary Medium

Abstract

We consider the inverse scattering problem in a homogeneous nonstationary one-dimensional medium for a system of acoustic equations. A class of boundary sources is identified for which the problem of determining the time-dependent density is uniquely solvable. A method using integro-functional Volterra equations of first and third kind is proposed for the inverse problem. A regularized iterative algorithm is developed for the inverse problem in the framework of finite-difference theory. The results of a computational experiment are reported, applying the algorithm to various nonstationary media and boundary sources.