High-frequency wave propagation in random media - A unified approach

High-frequency wave propagation in a random medium over long propagation distances, where the fluctuations in the wave field are not small and caustic formation is likely, is studied. Techniques based on the geometrical optics approximation or ray theory as well as those based on the parabolic wave equation are examined. It is shown that for small fluctuations in the refractive index of order $\sigma ( {\sigma \ll 1} )$ and long propagation distances of order $\sigma ^{ - 2/3} $, that both these methods are equivalent at high frequencies, at least away from caustics. Since previous theories have identified this $\sigma ( \sigma ^{ - 2/3} )$ distance scale as that on which random caustics first appear, we also derive a regularization of the ray approximation, which is called the beam method, and which is uniformly valid in the vicinity of caustics.On the $\sigma ^{ - 2/3} $ scale, the random ray process converges to a diffusion Markov process, and equations can be derived for the joint distribution of an a...