Propagation of radiation from a finite beam or source through an anisotropic random medium

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Abstract
In a previous paper, we solved the problem of propagation of a plane wave in an anisotropic random medium. The characteristic correlation distances in the horizontal propagation direction were assumed to be large compared to the radiation wavelength divided by 2π, (λ̄/2π), while in the vertical direction, these distances were, roughly speaking, assumed to be of the same order or smaller than λ̄/2π. For this medium, we derive here the equation governing the propagation of the coherence function for a finite beam or source of characteristic dimension a. This equation is then averaged over the vertical direction and solved. The solution is given in terms of a definite integral over the horizontal spectrum of the index-of-refraction field. The point source solution (a → 0) and the plane-wave case (a → ∞) are given as special cases. Explicit solutions are given for the propagation of an acoustic field in the ocean under conditions for which the spectrum satisfies a minus two power law.

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