High-frequency coherence functions propagated along ray paths in the inhomogeneous background of a weakly random medium: II—Higher moments

Abstract

In a previous article [R. Mazar and L. B. Felsen, J. Acoust. Soc. Am. 81, 925–937 (1987)], it has been shown how the ray trajectories in the refracting background of a weakly fluctuating medium with large scale inhomogeneities can form the basis for propagating and evaluating the high-frequency two-point coherence function. Approximate results there, derived by a multiscale expansion technique, account for multiple isolated ray arrivals at observation points far from caustics, and blend smoothly into the transitional behavior due to closely adjacent rays near caustics. In the absence of fluctuations, this assertion has been verified by recovery of the isolated ordinary and uniform deterministic ray theory intensities, respectively, and it is therefore believed that our spectral construction properly describes the high-frequency two-point coherence function when randomness is included. The ray-based approach is now extended to multifrequency higher-order coherence functions. The new results are shown to recover the predictions from nonuniform and uniform ray theory when the fluctuations are removed, and they are also shown to yield previously obtained results for the special case of the two-frequency fourth moment in a homogeneous background. These checks lend confidence in the validity of the extended theory presented here.