Acoustic waves in a shallow inhomogeneous ocean with a layer of sediment

This paper deals with the direct underwater acoustics problem for a heterogeneous ocean of uniform depth with an acoustically interacting uniform layer of sediment. The acoustic properties of the ocean column are assumed to vary only with depth. Using the standard boundary conditions, i.e. a pressure release surface, continuity of normal stress and displacement across the ocean-seabed interface, and Sommerfeld type radiation conditions, we are able to determine the acoustic far-field using normal modal expansions. The nonhomogeneous character of the ocean is conveniently handled using transmutation theory. Transmutation theory yields an explicit form for the characteristic equation, and in addition, an appropriate inner product for the composite Sturm-Liouville system. The Fourier coefficients for the expansion of the propagating fundamental solution is also obtained. A numerical scheme is presented and several examples are given.