Comparison of the measured covariance of surface reverberation for horizontal and vertical arrays

Abstract

An experimental study of the scattering of sound from the surface of a freshwater lake was performed. The study utilized nine staves in a vertical receiving array and four staves in a horizontal receiving array to examine the spatial and temporal covariance of the reverberation for both orientations simultaneously. The reverberation returns were generated by repetitively projecting a 100-μs cw pulse centered at 80 kHz at the wind-roughened surface of the freshwater lake at a 10.5° grazing angle. The returns were digitized and the covariance was estimated on a general purpose computer by ensemble averaging over 500 pings. Significant differences were observed between the covariances of the vertical and horizontal arrays. The envelope of the covariance between the vertical staves maintained a significant level at much larger separations than the horizontal array. The normalized covariance of the horizontal array was constant with time, while the normalized covariance of the vertical array slowly oscillated with time because the phase of the vertical covariance changed linearly with time. Thus the joint reverberation process measured by the horizontal staves was reducible to joint wide-sense stationarity while the joint reverberation process measured by the vertical staves was not. The vertical covariance was also found to depend on the location of the staves on the array for a fixed separation.