Normal-Mode and Ray Theory Applied to Underwater Acoustic Conditions of Extreme Downward Refraction

Abstract

This theoretical article investigates the acoustic field in the image-interference and shadow-zone regions for a model in which the sound velocity decreases with increasing depth from the surface. Near the surface the shadow-zone boundary is the surface-grazing ray, while in deeper regions this boundary is a caustic. The field near the caustic is investigated by modified ray theory based on Airy functions. A comparison of mode theory results with those of ray theory indicates that there is a −π/2 jump in the ray theory phase when the ray touches a caustic. There is, however, no such jump when the ray becomes horizontal. The normal-mode series is absolutely convergent for ranges greater than 1.732 times the sum of the source and receiver depths. When the shadow zone is bounded by a well-developed caustic, the series converges so slowly as to be impractical except at ranges well into the shadow-zone region.