On the Modeling of Acoustic Fields in a Marine Waveguide with Refined Boundary Conditions at the Surface and Bottom

The problem of the sound field of a point sound source placed in a nonideal marine waveguide is considered. The boundaries of the waveguide are assumed to be plane-parallel, and three layers are distinguished: a water layer with an inhomogeneous refractive component of the sound speed, a layer of liquid sediments, and an elastic bottom layer on a rigid base. At the top, the water layer adjoins a homogeneous air half-space. For the given waveguide model, analytical expressions for the impedance functions at the boundaries of the water layer are obtained for the first time, which makes it possible to construct the Green’s function of the vertical boundary-value problem. Moreover, exact values for the residues of the Green’s function are found, which allows for writing down an exact analytical representation for the acoustic pressure potential in the form of a sum of normal modes. It is shown that, in this model, the influence of the continuous spectrum (integrals along the branch cuts) is small even at short distances from the source. As the thickness of the elastic layer decreases, the discrete spectrum of the problem tends to the values for the classical waveguide; with sufficiently large thickness and attenuation, it resembles the discrete spectrum of the Pekeris elastic waveguide. Examples of numerical implementation for waveguide parameters typical for the Black Sea region are given.