Multiple scattering with applications to fish-echo processing

A general expression has been 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 second-order scattering have been taken into account. Special attention is focused toward the numerical evaluation of second-order scattering effects. The expression is evaluated for three scattering geometries. It is shown in each geometry that when the absorption cross section of the scatterers is small, second-order scattering can be a factor in the backscattered energy. In this case, second-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), and degree of randomness of the spatial distribution of the fish determine the degree to which second-order scattering plays a role in this area.