Indirect measurement of the mean acoustic backscattering cross section of fish

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Abstract
A technique is described for indirectly determining the average backscattering cross section of individual fish from the measured probability distribution function for the amplitudes of the envelopes of single fish echoes. The technique is based on the assumption that the on-axis echo envelope is Rayleigh distributed. The validity of the Rayleigh assumption was tested by making controlled measurements of the envelope amplitude statistics of single fish echoes for two acoustic frequencies and four different fish lengths. These tests showed that the echo envelope data most closely fit the Rayleigh model when the ratio of fish length to wavelength was large. The indirect measurement technique described has been used to analyze some single fish-echo amplitude data for Bering Sea walleye pollock. These results are compared with some measurements made using a dual beam, direct, target strength measurement system. Expressions for the bias and variance of the indirect estimation technique are derived in an Appendix.

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