Propagation modeling in a three-dimensional wedge using ray theory

Abstract

A useful model for shallow-water, sand-bottom coastal regions is the three-dimensional (3-D) wedge. Unlike the 2-D wedge, source and receiver may lie across the slope from each other, rather than directly upslope or downslope. Acoustic propagation in the 3-D wedge is modeled using an extension of the complex ray method developed for the flat waveguide and the 2-D wedge [E. K. Westwood, J. Acoust. Soc. Am. Suppl. 1 83, S79 (1988) and 84, S90 (1988)]. However, due to the phenomenon of horizontal refraction (the bending of multiply reflected rays when viewed from above), each ray field in the 3-D wedge must be expressed as a plane wave integral over two angular variables, rather than just one. Evaluation of the integrals involves finding complex saddle points, each of which consists of a pair of angles giving the eigenray direction. For rays that are reflected near the critical angle, numerical integration along the path of steepest descent must be performed; otherwise, a first-order saddle point approximation may be used. The nature of the field in the 3-D wedge will be discussed, and possible benchmark problems will be suggested. [Work supported by ONR contract N00014-87-K-0346.]