Sound scattering from a few scatterers: Application to swimbladder fish

Abstract

This paper presents a general method for describing sound scattering by an ensemble of a few scatterers. A scheme is developed for calculating the effective scattering function of such an ensemble, including all orders of multiple scattering between targets. The method is then applied to low-frequency sound scattering by small fish schools. It is shown that in the backscattering, certain regular patterns in scattering appear as a result of interference rather than multiple scattering, when the fish form an ordered structure. The interference peaks are due to in-phase scattering, and can be explained by the Bragg reflection mechanism. Such regular interference patterns are gradually degraded, as the random deviation in each individual fish location from its mean position increases. For a completely random distribution of fish, the model recovers the results from the random-phase approximation. For the forward-scattering case, it lacks either the regular or the noisy interference. The scattering strength seems rather smooth, and may be well approximated by the incoherent summation of forward-scattering function of each individual fish. The scattering by partially or perfectly ordered fish schools is hardly distinguishable from that by totally random distributions of fish in the forward direction. [Work supported by the National Science Council and the Spanish Ministry of Education.]