The coherent Green’s function for acoustic propagation in a random ocean

Abstract

We have derived an algorithm for calculating the coherent Green’s function of an acoustic wave propagating in an ocean possessing index‐of‐refraction fluctuations. This function is related to the so‐called strength parameter which can be used to characterize the statistics obeyed by the acoustic field. Since we are interested in a wave solution we do not make the geometric optics approximation. Consequently, it is necessary to generalize the usual form of the Markov approximation. This is done in analogy with Dashen’s investigations. Our analysis accounts for the ocean boundaries and the depth dependence of the mean index of refraction. It is, however, restricted to convergence zone propagation. The phenomenological model of internal waves introduced by Garrett and Munk is used to describe the random fluctuations in the index of refraction. The analysis is based on the use of a Feynman path integral. The path integral formalism is particulary well suited to the approximations we consider. The algorithm co...