Some statistical properties of lake surface reverberation

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Abstract
This report describes the results of an experimental study of the properties of the outputs of a multielement sonar receiving array operating in a reverberant environment. The objective of the study is to obtain additional insight into the (statistical) properties of the receiver outputs through the application of statistical tests to the measured receiver outputs. The experimental data for the study are measurements of surface reverberation resulting from the scattering of 100-μs cw acoustic pulses by the wind driven surface of a freshwater lake. Simultaneous measurements were obtained of the outputs of six different elements of a horizontal, linear receiving array. The statistical validity of these experimental data was examined with statistical tests for independence and homogeneity. The statistical distribution of each receiver output was examined by testing for normality; each receiver output was tested at 900 different observation times. The results of these tests indicated that, when surface reverberation only was present, each output exhibited a Gaussian distribution. Tests of the mean receiver outputs were also conducted and resulted in the conclusion that the mean receiver outputs were negligibly small.

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