Acoustic mode decoupling via environmentally adaptive coordinates

Abstract

A normal mode expansion is used to relate the coupling of energy between modes to horizontal derivatives of the eigenfunctions. A curvilinear coordinate system is constructed using a WKB approximation for a reference eigenfunction such that horizontal derivatives causing coupling vanish. The curvilinear coordinate system is defined such that constant surfaces of the vertical wave number integral coincide with surfaces of constant curvilinear depth. Thus any particular zero of an eigenfunction lies on a constant depth surface in the curvilinear system. The horizontal derivatives of all other modes depend on a ratio of vertical wave numbers with the reference mode. Nearly constant horizontal behavior of this wave number ratio supports the decoupling of all modes in the curvilinear system. Such coordinate systems naturally adapt to the environment even with realistic sound-speed profiles that include discontinuities as well as sloping bottom bathymetry. They provide an adiabatic normal-mode basis for constructing acoustic models in the fully three-dimensional environments of continental shelf regions. Environmentally adaptive coordinate systems also provide a rational basis for interpolating three-dimensional environmental data.