A Functional-Analytical Solution to the Ocean Tomography Problem Taking the Interaction of Modes into Account

Abstract—A scheme of mode tomography of sound inhomogeneities and currents in the ocean, based on a mathematically rigorous functional-analytical algorithm, is considered. A distinctive feature of the proposed approach is the possibility of taking nonadiabatic mode propagation into account without involving iterative procedures. To simulate the scattering data, the solution of the coupled Lippmann–Schwinger equations is numerically implemented to describe the effects of multichannel mode scattering on inhomogeneities of sound sped and currents. Karhunen–Loeve functions are used to reconstruct three-dimensional scatterers, which allows one to reduce the number of unknowns when solving the inverse problem. The model results illustrate the high spatial resolution and the ability to achieve acceptable noise immunity of the discussed tomographic scheme when using a broadband sensing mode.