Inverse problem for a stratified ocean and bottom

In this paper it is shown how to use the methods of one-dimensional inverse scattering theory, in particular the new approach of Deift and Trubowitz [Comm. Pure Appl. Math. 32, 121–251 (1979)], to recover the sound speed for the case of a stratified ocean with a pressure release surface driven by a harmonic point source at a finite depth from a measurement of the normal derivative at the pressure release surface. The method is not a perturbation technique. For comparison, this same problem is examined when the sound speed is slightly perturbed from unity using a technique of Cohen and Bleistein [SIAM J. Appl. Math. 32, 784–799 (1977) and Geophysics 44, 1077–1087 (1979)].