Acoustic estimates of fish density and scattering function

Abstract

The amplitude of a sonar echo from a fish depends upon the species and size of the fish, acoustic wavelength, aspect, position of the fish in the sonar beam, range and backscattering cross section. The problem is simplified to a single species and size of fish, vertically downward echo sounding, single aspect, and nonoverlapping echoes. After removal of attenuation due to range and absorption, 2 random functions remain. The position of the fish in the sonar beam is random and the scattering cross section for each trial is random. It is assumed that the fish have a uniform density (number/m3) and the probability density function (PDF) is calculated for insonification and reception. It is assumed that the PDF of the envelope of the echo (excluding the variability of insonification and reception) has a Rayleigh PDF. Assuming 2 PDF are independent, the PDF of the echo envelopes wE(e) is calculated. wE(e) depends upon the beamwidth of the sonar and the mean backscattering cross section. The theoretical PDF has the same shape as the measured PDF of echoes from alewife [Alosa pseudoharengus] in Lake Michigan [USA]. The fit of the PDF was used to estimate the backscattering cross section and fish density. This calibrates the echo-integration processing system. A profile of the density of alewife in Lake Michigan is shown.