CONTINUOUS AND DISCRETE INVERSE-SCATTERING PROBLEMS IN A STRATIFIED ELASTIC MEDIUM .I. PLANE WAVES AT NORMAL INCIDENCE

This paper investigates the problem of obtaining an analytic solution and practical computational procedures for recovering the properties of an unknown elastic medium from waves that have been reflected by or transmitted through the medium. The medium consists of two homogeneous half spaces in contact with a heterogeneous region. The analytic solution is obtained by transforming the equation of motion for the propagation of plane waves at normal incidence in a stratified elastic medium into a one dimensional Schrädinger equation for which the inverse scattering problem has already been solved. The practical computational procedures are obtained by solving the corresponding discrete inverse scattering problem resulting from approximating the heterogeneous region with a sequence of homogeneous layers such that the travel time through each layer is the same. In both the continuous and discrete inverse scattering problems, the impedance of the medium as a function of travel time is recovered from the impulse response of the medium. A discrete analogy of the continuous solution is also developed. Similar results are obtained for a stratified elastic half space bounded by a free surface. © 1969, Acoustical Society of America. All rights reserved.