Coupled-mode modeling of sound propagation in range-dependent fluid–solid media

This paper develops a discrete coupled-mode method for wave propagation in a cylindrically symmetric fluid–solid medium with a symmetric point source on the vertical symmetry axis. Range dependence is handled by a discretization of the medium into laterally homogeneous ring regions. Modal reflection (or scattering) matrices, recursively computed by an initial inward propagation step using mode orthogonality, relate the expansion coefficients for outgoing and incoming (back-scattered) normal modes. Incorporation of the source condition yields the field in the innermost ring region. A subsequent outward propagation step, stabilized by the stored reflection matrices to satisfy the outer boundary condition, yields the modal expansion coefficients of the field in each ring region. With fluid overlying a solid bottom, upsloping and downsloping parts of the medium require different propagation equations to satisfy the continuity conditions at the vertical ring-region interfaces. An approximate solution appears by replacing the involved Hankel functions by their asymptotic expressions for large arguments. Compared to the solution for a symmetric horizontal line source in a corresponding medium, invariant in the line-source direction, the approximate solution involves a back-scattering term as well as a mode-dependent and phase-changing source-correction factor in addition to the correction factor for the different geometrical spreading.