Asymptotic Solution for the Sound Field in Shallow Water with a Negative Velocity Gradient

Abstract

A solution, valid at high frequencies, for the sound field in shallow water having a negative velocity gradient is obtained by normal-mode theory. Using this solution, relatively simple expressions for the decay of intensity over intermediate and long ranges can be obtained if it is assumed that propagation is basically governed by the mode with phase velocity equal to the surface sound velocity. The transmission loss as a function of range follows a three-halves-power law at intermediate ranges and a cylindrical spreading law at long ranges. In both regions, attenuation due to bottom losses is assumed to be present, and it is shown that the value of this attenuation is approximately the same as that derived by a ray-theory model. In addition, the results of this analysis are in accord with other semiempirical predictions for the transmission loss in shallow water.