Ray methods for flat and sloping shallow-water waveguides

A ray method for finding the acoustic field due to a point source in the presence of a plane, penetrable interface is extended to two simple models for shallow-water ocean environments: the flat, isovelocity waveguide (the Pekeris model) and the sloping, isovelocity waveguide (the penetrable wedge). In both cases, the sound speed in the bottom is assumed larger than that in the water. The total field is expressed as a sum of ray fields, each of which takes the form of a plane wave integral. The integrals are solved using the method of steepest descent, where the plane wave reflection and transmission coefficients are allowed to influence the location of the saddle points. For a Pekeris waveguide in which three modes are trapped, agreement between the ray model and the SAFARI model is nearly perfect at all ranges, while the discrete normal mode solution is in error when a mode is near cutoff. The ray model is accurate even when the water depth is half of the acoustic wavelength. For the penetrable wedge problem, the plane wave integral for the ray field is developed, and the origin of the multiple lateral wave fields is examined. Excellent agreement between the ray model and a two-way coupled mode model is demonstrated. Examples of the eigenray structure in both the flat and sloping waveguides are given.