Intensity moments by path integral techniques for wave propagation through random media, with application to sound in the ocean

Utilizing the formalism of path integrals, the intensity moments of waves propagated through anisotropic inhomogeneous random media in the presence of a deterministic wave speed variation can be formed. In the saturated scattering regime, intensity fluctuations are expected to be Rayleigh distributed to first order. A correction to Rayleigh statistics is calculated that results in a form for the intensity moments: 〈Iⁿ〉=n!〈I〉ⁿ[1+ 1/2 n(n−1)γ], where γ depends on the fluctuation spectrum of the medium. It is shown that the correction can be approximated by an integral along the ray of a spectrally weighted local contribution. This local contribution, called the micropath focusing function, depends both on the spectrum of the medium, and on a Green’s function which is shown to be related to the phase curvature. In the straight line horizontal ray approximation, the ‘‘micropath focusing parameter’’ γ can be approximated by 3/(2 ln Φ) in the partially saturated regime, and by [0.83/(ln Φ)^3/2](1/ΛΦ) in the saturated regime, where Φ and Λ are the strength and diffraction parameters for medium fluctuations along a ray. The internal wave spectrum is chosen as an example for fluctuations in oceanic sound transmission. Theoretical results are obtained for curved rays by numerical integration, and are compared with observations from three ocean acoustics experiments.