Wavefronts and waveforms in deep-water sound propagation

Abstract

A new method of calculating waveforms in underwater sound propagation is presented. The method is based on a Hankel transform-generalized Wentzel-Kramers-Brillouin (WKB) solution of the wave equation. The resulting integral leads to a new form of ray theory which is valid at relatively low frequencies and allows evaluation of the acoustic field on both the illuminated and shadow sides of caustics and at cusps where two caustics meet to form a focus. The integral is evaluated by stationary phase methods for the appropriate number of stationary points. Rays of nearby launch angle which have a travel time difference less than a quarter period must be considered together. The description of all other ray arrivals corresponds to simple ray theory. The phase, amplitude, and travel time of broadband acoustic pulses are obtainable directly from a simple graph of ray travel time as a function of depth at a given range. The method can handle range dependence but is illustrated here in long-distance propagation in deep water where the ray paths do not pass close to surface or bottom. The method is fast and gives close agreement with normal-mode calculations. The field on the shadow side of a caustic is properly given in terms of rays with complex launch angles, but good approximations can be obtained without the need to find complex rays.