Solution to the inverse problem of the 1-D wave equation

Abstract

A general solution for the determination of a variable coefficient in the 1-D wave equation from an additional boundary condition is presented. The Gopinath–Sondhi equation is shown to be a special case of this general solution. One application of this inversion method is to determine the structure of vertically inhomogeneous media from the backscattered waves generated by arbitrary incident waves. When a priori information about the unknown structure is available, a method is presented for the incorporation of this information to stabilize the inversion algorithm.