Ray displacements and time delays in the ray-mode analogy

Abstract

The “ray-mode” analogy is useful for qualitatively anticipating the gross features of underwater acoustic modal propagation. With each acoustical mode, it associates a cycle distance and cycle time (related to modal group velocity) along the analogous “ray-paths.” In this paper, it is demonstrated that the phenomenon of ray displacements as proposed in modified ray theory and a corresponding cycle travel time modification can account for quantitative discrepancies between ray and modal cycle distances and group velocities [see, K.M. Guthrie, J. Sound Vib. 32, 289–293 (1974)]. The purpose of this demonstration is twofold. On one hand, the cycle distance and travel time modifications, as a physical explanation for the discrepancies, are shown to be local, near-boundary phenomena. On the other hand, the quantitative success of beam and time displacements as a correction to bring modified cycle distance and travel times into agreement with the more exact modal results, serves as a test of the approximations used to develop modified ray theory.