Forward scattered waves in random media—The probability distribution of intensity

Abstract

An acoustic wave propagating in a medium with an index of refraction that is random in space and time acquires intensity modulations that can be modeled in terms of a space–time autocorrelation function, a scattering strength parameter γ, and a scaled range X. Over a wide range of γ, X, and medium autocorrelation functions, the probability distributions of intensity vary from lognormal at small X to exponential at large X. The generalized gamma distribution [E. W. Stacy, Ann. Math. Stat. 33, 1187–1192 (1962)] is characterized by three parameters, and reduces to many well-known distributions. It varies smoothly from lognormal to exponential as the parameters change. It is proposed that this distribution is a general analytic form that represents the probability distribution of intensity as a function of range, depth, and time in forward scattering. This proposition is tested with the measured temporal intensity fluctuations from the Mid-Ocean Acoustic Transmission Experiment, MATE. It is also tested wtih depth-range results from Monte Carlo simulations of wave propagation in a random medium with a power law autocorrelation function. The fitted generalized gamma distributions for the data sets chosen lie within the 95% Kolmogorov confidence bands for the true unknown probability distributions. In past treatments of this subject, the intensity moments have been used almost exclusively in modeling the probability distributions. The benefits of using distribution modeling rather than moment methods are described. Also discussed are the anomalies encountered for a medium with Gaussian autocorrelation.