Normal modes in the ocean-sediment acoustic waveguide system at the New England Mud Patch

The sediment at the New England Mud Patch (NEMP) consists of a near-homogeneous mud layer overlying a sand-mud basement in which the sound speed follows closely an inverse-square law. In combination, the ocean and sediment form a three-layer acoustic waveguide. With a sound source located in the ocean, an analysis of the acoustic field in each of the layers is presented, based on spatial Fourier transforms taken over depth and horizontal range, taking account of the boundary conditions at the sea surface, the seabed, and the top of the basement. A familiar mapping leads to modal solutions for the field in each of the layers involving MacDonald's function. A component of these solutions is a transcendental characteristic equation, which is solved for the eigenvalues using an iterative procedure, the graphical bisection method. Under the conditions of site SC2 at the NEMP, only eleven eigenvalues exist, each associated with a propagating normal mode. When the density of the basement and the depth of the ocean, respectively, are allowed to go to zero and infinity, the NEMP waveguide takes the form of an inverted Pekeris waveguide and, in this limit, the NEMP characteristic equation reduces identically to that of the Pekeris channel.