Non-Rayleigh Distributions in Underwater Acoustic Reverberation in a Patchy Environment

In this communication, two main causes for the probability distribution function (pdf) of reverberation amplitude to deviate from the Rayleigh model are identified: (1) sonar configuration and (2) environmental variability. If the total environment may be considered as a patchwork of local environments that are resolvable by the sonar system, but not reliably distinguishable due to positional inaccuracies and overlap in the range of reverberation amplitude values, then the resulting ensemble may have a pdf that is a mixture of the pdfs of the local components. The number of components in a mixture of Rayleigh models is examined, using the measurements and results of Abraham and Lyons [J. Acoust. Soc. Amer., vol. 106, pp. 1307-1315, 1999]. The patchiness of the environment determines the number of components and their proportions in the mixture, while the sonar configuration determines the kernel of the pdf. Finally, the issue of stationarity is discussed as it applies to a patchy environment. It is concluded that although the reverberation from a patchy environment is, strictly speaking, nonstationary, the perception of stationarity may be achieved if the components in the mixture recur with some regularity, and if the sampling window is wide enough in space and/or time to include a sufficient number of recurrences of all components.