Dispersion Equations for a Shallow-Water Waveguide With Two-Layer Bottom and Their Application in Geoacoustic Inversion

In this study, the dispersion of acoustic waves in a shallow-water environment with a two-layer bottom (gradient layer over a uniform basement) is investigated. This model leads to an analytical solution for eigenfunctions, and its versatility allows many different sound-speed profiles to be considered. Ordinary differential equations describing the dependence of horizontal wave numbers of normal modes on the geoacoustic parameters of both layers are derived. It is shown that integration of these equations allows one to model dispersion curves for every point of a gridded multidimensional parameter space for a shallow-water waveguide model at very low computational cost. This advancement has many potential applications, including new ways to perform Bayesian geoacoustic inversion by highly efficient maximization of the posterior probability density over the corresponding space of geoacoustic parameters. This approach is demonstrated by performing geoacoustic inversion of measured modal-dispersion data collected on the New England Mud Patch.