Statistics of echoes from a directional sonar beam insonifying finite numbers of single scatterers and patches of scatterers.

Abstract

When a sonar beam sweeps across a field of scatterers, the echoes can fluctuate significantly from ping to ping. The fluctuations can be strongly non‐Rayleigh because: (1) there can be a small number of scatterers in the beam; (2) the distribution of scatterers can be inhomogeneous or “patchy;” and (3) the echoes are weighted by the nonuniform response of the sonar beam. In this paper, a general formulation combining equations derived by Ehrenberg [Proc. Conf. Eng. Ocean Environ. 1, 61–64, (1972)] and Barakat [Optica Acta 21, 903–921, (1974)] is developed to account for a directional sonar beam involving an arbitrary finite number of scatterers, each with an arbitrary echo probably density function (PDF) and randomly located in the beam. Theoretical predictions are made, along with numerical simulations for validation, for a range of conditions, including: (1) different number of scatterers arbitrarily located in the beam and (2) different echo PDFs of the scatterers. Here, a “scatterer” could be an individual or a patch of scatterers whose dimensions are much smaller than the footprint of the sonar beam. Although the application is intended for volumetric patches, the formulation could be applied to areal patches under appropriate conditions. [Work supported by ONR.]