Theoretical study of echo energy scattered by a random distribution of air-filled fluid spherical shells: Application to fish stock assessment by the echo integration method

Abstract

This work is intended to give a preliminary examination of the influence that the swimbladder may have on the linearity principle of the echo integration method. In doing this, the fish school is modeled as a random distribution of air-filled fluid spherical shells immersed in water. The wall of the shell represents the fish body whereas the inside of the shell represents the swimbladder. The mean echo energy scattered by such a distribution has been calculated as a function of the ratio b/a of inner to outer radius of the shell, with the interference of direct echoes, the shadowing effect, and the second-order scattering being taken into account. The numerical simulations show that at a given fractional volume number of targets, the mean echo energy scattered by the distribution is a bit larger than that predicted by the linearity assumption when b/a is less than a certain value κ, and it may be much smaller than the predicted value when b/a is greater than κ. Consequently, the swimbladder may be the major cause of the energy attenuation, due to the shadowing effect, and its influence on the linearity principle depends on its relative size.