Mean field of a sound wave propagating in an oceanic waveguide with random inhomogeneities

Abstract

The mean field is an important statistical characteristic of a sound wave propagating in an oceanic waveguide with random inhomogeneities such as internal gravity waves. A closed equation for the mean sound field propagating in a 3D random waveguide can be obtained with the use of the diagram technique. Using the Fourier transform, this equation is reduced to a one-dimensional integro-differential equation with respect to the vertical coordinate. The latter equation determines acoustic modes which are generally different from those in a regular waveguide. For low frequency sound waves, the integro-differential equation is solved approximately. This results in an explicit formula for the mean sound field as a sum of modes which attenuate exponentially with the propagation distance. The extinction coefficient of each mode is linearly related to the spectrum of random inhomogeneities. Therefore, measuring the extinction coefficients for different frequencies and different mode numbers, one can try to reconstruct this spectrum. The mean field of a sound wave propagating in a 2D random waveguide is also calculated. The result obtained is compared with that for a 3D random waveguide. This allows us to study the range of applicability of 2D approximation.