Using the Rytov approximation, an expression is derived for the log-amplitude correlation function of weak fluctuations induced in a plane wave propagating in a forward-scattering medium. The expression is valid at any range where weak fluctuations exist, including ranges which are shorter than the correlation length. For ranges well in excess of the correlation length, we derive a general expression for the scintillation index, which applies also in nonisotropic media, for moderate and high frequencies. The behavior of the scintillation index at very short ranges in isotropic media characterized by one or two scales is examined, and its dependence on frequency (k) and range (z) is listed for several regimes. Propagation is also studied in a nonisotropic medium, where the refractivity fluctuations are governed by the Garrett–Munk internal-wave spectrum. Here, the frequency–range dependence of the scintillation index changes from k3/2z5/2 at near ranges to kz2 at more distant ones.
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Shimshon Frankenthal (1985) studied this question.