Broadband modeling of the three-dimensional penetrable wedge

A ray method for finding the acoustic field due to a point source in a two-dimensional (2-D), penetrable-bottom wedge has been extended to the three-dimensional (3-D) wedge, where the receiver may lie cross slope as well as downslope or upslope from the source. The environment assumed is a simple model for a sand-bottom ocean near a shoreline: The wedge of water and the sand bottom are isovelocity, and the sound speed in the bottom is assumed to be greater than that in the water. The total field in the 3-D wedge is expressed as a sum of ray fields, each of which takes the form of a double integral over plane waves. As in the 2-D wedge method, the integrals are solved using the method of steepest descent, where the plane-wave reflection coefficients are placed in the ‘‘phase function’’ of the integrand and thus allowed to influence the location of the saddle points. The ray method is also extended to model broadband propagation: Eigenrays are found at coarsely spaced frequencies, and the eigenray characteristics are interpolated across frequency. The ray model is used to simulate the propagation of a pulse from a point source to a set of vertical arrays at various cross slope ranges. Mode extractions from the vertical array data demonstrate several interesting phenomena unique to 3-D wedge propagation: multiple mode arrivals, modal shadow zones, and the dependence of the shadow zones on mode number. An example illustrating mode wave-front curvature and mode capture is also given.