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The echo-integration (EI) method is the primary method for fisheries resource surveys by acoustics. Application of the EI results to estimation of individual school abundance and/or to school descriptors for species identification, however, has not been well developed. This paper first considers, based on the basic theory of the EI method, the raw volume backscattering strength of an individual school and the school section scattering strength, both of which are observed by the beam of an echo sounder. Next, approximation methods to estimate the total school scattering strength of an individual school are proposed. The methods are verified by an exact computer simulation of school echoes. The methods are applied to actual echo data obtained by a quantitative echo sounder to confirm the applicability. The section scattering strength is appropriate as an index of school abundance, but the school scattering strength, especially the strength approximated by combining echo sounder data with sonar 3D distribution data, is most appropriate for the abundance index of an individual school. Classification: Fisheries acoustics Keyword: Section scattering strength, Total scattering strength, Volume backscattering strength J. Marine Acoust. Soc. Jpn. Vol. 38 No. 4 Oct. 2011 178 In this study, first, the scattering strengths of individual schools are theoretically considered, new or clear definitions of scattering indexes are proposed, and they are evaluated using an exact computer simulation. Next, as applications, the abundance measurement methods of a school are proposed and school features for species identification are discussed. The scattering features of an individual school are usually evaluated as the “average volume backscattering strength” or the “scattering energy,” which are obtained, respectively, by averaging and by cumulating raw volume backscattering strength (SV) values processed under the assumption that the volume scattering theory holds. However, the raw SV values become smaller than the actual values at the periphery of the school, while the range of echoes is expanded beyond the actual range of fish distribution. This phenomenon is called the “border effect”. This effect should be corrected to make the average volume backscattering strength and the scattering energy good features for describing schools, but the correction is not easy. In this paper, we examined the two-dimensional “(school) section scattering strength” or “scattering energy” which involves less border effect, and newly propose a three-dimensional “(total) school scattering strength” which corresponds to the target strength of the school. For the purpose of species identification, the section scattering strength is useful, but for a more quantitative purpose the school scattering strength is preferred. However, the latter generally needs beam scanning over a whole school and alternative approximation methods using rotation or lamination of the section are proposed here. Furthermore, a combination method with data from an echo sounder beam and from vertical scanning of sonar beams is proposed. Since verification using actual fish echoes is difficult, an exact computer simulation is employed to evaluate the above indexes. Additionally, the scattering indexes of actual fish schools are obtained to confirm the effectiveness of the indexes. 2. Theoretical consideration 2.1 Volume scattering theory and echo-

Section and Total Scattering Strengths of Individual Fish Schools