Propagation through an anisotropic random medium

An expression is derived, Eq. (59), for the mutual coherence of an initial plane wave signal that has propagated a distance, z, into an anisotropic random medium. This expression is valid for cases in which the characteristic radiation wavelength divided by 2π $\text{.λ̄/2π}$ is roughly speaking of the same order as, or greater than, all characteristic correlation lengths in the direction perpendicular to the mean propagation direction, which is taken to lie in a horizontal plane. The exact condition is given in Eq. (48). We require $\text{λ̄/2π}$ to be much smaller than all characteristic correlation lengths in the horizontal plane. Two derivation procedures are used. One follows that introduced by Beran (J. Opt. Soc. Am. 56, 1475 (1966)] for cases in which $\text{λ̄/2π}$ is much smaller than all characteristic correlation lengths and one is based on introducing simplifications in a Bethe‐Salpeter equation. We discuss the problem of the loss of spatial coherence of an acoustic signal due to scattering by the ocean temperature microstructure in the light of the theory presented.