Target structure dependence of the linearity principle in the estimation of underwater target abundance by the echo integration method

The estimation of fish abundance by the echo integration method is based on the assumption that the total integrated echo intensity returned from randomly distributed targets is proportional to the quantity of those targets. The validity of this assumption depends not only on the number density of targets under investigation, but also on their physical structure. This is evidenced by a study of the echo energy scattered by a random distribution of underwater spherical targets. Numerical results show that under same conditions (measuring system, signal frequency, target size, etc.), the linearity principle may hold for spheres made of one material (a fluid, for example), but fail for spheres made of other materials (soft, rigid, and steel spheres in our case). The interference of direct echoes, the shadowing effect, and the multiple scattering of second order are taken into account in the calculation