Multiple scattering with applications to fish-echo processing

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Abstract
A general expression was derived and evaluated for the backscattered echo energy of an acoustic pulse due to a collection of identical randomly distributed isotropic scatterers. Excess attenuation of the signal due to the extinction cross section of the scatterers as well as 2nd-order scattering were taken into account. Special attention is focused toward the numerical evaluation of 2nd-order cattering effects. The expression is evaluated for 3 scattering geometries. In each geometry, when the absorption cross section of the scatterers is small, 2nd-order scattering can be a factor in the backscattered energy. In this case, 2nd-order scattering at least partially offsets effects due to excess attenuation in the low-to-moderate attenuation region. When applied to fish-echo processing, it was shown that in most cases the results represent an upper bound for the processed signal from a school of fish. The directional characteristics, acoustic frequency of the pulse in relation to the resonance frequency of the swimbladder (if any), 1 and degree of randomness of the spatial distribution of the fish determine the degree to which 2nd-order scattering plays a role in this area.

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