Horizontal and vertical covariance of surface reverberation

Abstract

Lake surface reverberation was measured simultaneously on four horizontally separated and nine vertically separated staves in two linear arrays. The vertical array was found to maintain a significant level of coherence at much larger separations than the horizontal array. The normalized horizontal covariance was constant with time, while the normalized vertical covariance oscillated slowly with a period that depended on the separation of the vertical staves. The measurements were compared to a theoretical model of reverberation by D. Middleton. The model was implemented with a uniform planar distribution of surface scatterers and adequately predicted the horizontal spatial covariance and the time dependence of both the horizontal and vertical covariance. However the simple planar surface model was unable to model the vertical spatial covariance, indicating a need for a more detailed description of the surface.