The probability distribution of intensity for acoustic propagation in a randomly varying ocean

Probability distributions of intensity fluctuations from the MATE, AFAR, and S. W. Bermuda underwater acoustics experiments are compared with recently derived theoretical expressions. The limitations and strengths of these expressions are discussed. In particular, it is found that the work of Furutsu [J. Math. Phys. 17, 1252–1263 (1976)] gives a good description of the probability distribution function of intensity or log intensity, requiring only a knowledge of the second‐ and third‐order intensity moments. Furutsu’s description is not asymptotically correct at large range, so a modified form is proposed for the moments of intensity that reduce analytically to the log‐normal distribution at short range and to the exponential distribution at large range. This new form also predicts the higher moments well but cannot be inverted analytically. A numerical inversion is used, and the ensuing distribution agrees well with the analytical result of Furutsu. It is expected that the new expression will be applicable at all ranges.