Linearity of fisheries acoustics, with addition theorems

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Abstract
An experiment to verify the basic linearity of fisheries acoustics is described. Herring (C l u p e a h a r e n g u s L.) was the subject fish. Acoustic measurements consisted of the echo energy from aggregations of encaged but otherwise free‐swimming fish, and the target strength functions of similar, anesthetized specimens. Periodic photographic observation of the encaged fish allowed characterization of their behavior through associated spatial and orientation distributions. The fish biology and hydrography were also measured. Computations of the echo energy from encaged aggregations, derived by exercising the linear theory with the target strength functions of anesthetized fish and gross behavioral characteristics of encaged fish, agreed well with observation. This success was obtained for each of four independent echosounders operating at frequencies from 38 to 120 kHz and at power levels from 35 W to nearly 1 kW. In addition to demonstrating the basic linearity of fisheries acoustics, the experiment verified both conventional acoustic measurements on anesthetized fish, at least for averaging purposes, and the echo integration method. Two simple theorems summarizing the meaning of linearity for use with the echo integration method are stated.

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