The probability distribution of a wave at a very large depth within an extended random medium

A plane wave is incident normally onto the boundary of a semi-infinite stationary random medium. The statistical moments of the field variable, both at one and at several points, are calculated when the refractive index of the medium at different points has a joint Gaussian probability distribution and Gaussian power spectrum, and the observer is at a very great depth within the medium. From these moments the probability distributions are calculated. The method uses a perturbation expansion. The limit of infinite distance and the limit of infinite depth are considered.