Critical angle effects and their treatment using ray theory and mode theory

Abstract

The interaction of the acoustic field from a point source with a fluid half-space is examined in terms of ray theory and mode theory. For ray theory, a complex ray approach [E. K. Westwood, J. Acoust. Soc. Am. 85, 1872–1884 (1989)] is used to find the reflected and transmitted fields as the sum of one or two eigenrays. The approach uses the method of steepest descent to solve the plane-wave integral for the fields, where the reflection and transmission coefficients are allowed to influence the locations of the saddle points and their steepest descent paths. As a consequence, saddle points are complex, and complicated processes such as the reflected lateral wave, beam displacement, and the transmitted evanescent field are included. For mode theory, the ORCA normal mode model [Westwood et al., J. Acoust. Soc. Am. 100, 3631–3645 (1996)] is used to illustrate the effects of the critical angle on the mode structure in a Pekeris waveguide. The Pekeris branch cut is shown to correspond to the lateral wave, and a method for replacing its branch line integral with a series of modes is described.