The acoustic field is obtained in terms of the wave number integration for a horizontally stratified ocean. The Inverse Hankel Transform is obtained for shallow water over a Layered inhomogeneous elastic bottom using “Direct global Matrix approach” with Fast Field Approximation Technique. This paper presents the determination of total solution for the depth dependence of the field: the depth de...

We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the future light cone, which is then shown to be (essentially) the Hankel transform of order zero. We apply this to give a novel proof, solely based on the causality of this spatio-temporal wave propagation, of th...