The average three-dimensional target strength of fish by spheroid model for sonar surveys

Tang, Y., Nishimori, Y., and Furusawa, M. 2009. The average three-dimensional target strength of fish by spheroid model for sonar surveys. – ICES Journal of Marine Science, 66: 1176–1183. When surveying fish schools by sonar, the fish are insonified from various directions. Because the fish target strength (TS) has three-dimensional directivity, according to its orientation relative to the sonar beam, the TS must be appropriately averaged. By connecting the geometries of the sonar beam and the fish body, the relationship between the apparent orientation of fish, as viewed by the sonar, and the actual orientation in space is derived. Using this relationship, equations for calculating the three-dimensional-averaged TS ( 3D) are presented. A prolate-spheroid, modal-series, scattering model is then used to determine the characteristics of 3D against various parameters, such as fish attitudes, fish length, sonar frequency, and method of beam scanning. The model is evaluated with two boundary conditions at the spheroid surface: a gas-fluid boundary relevant to fish with a swimbladder, and a fluid-fluid boundary relevant to fish without a swimbladder. The results reveal that 3D varies greatly with the horizontal aspect (yaw angle), but only slightly with the vertical aspect (pitch angle) of the fish. The difference in 3D between the side-on aspect and the end-on (head or tail) aspect increases with the ratio of the fish length to the acoustic wavelength.