Modeling ‘acoustic color’ of fish at ultrasonic frequencies

Abstract

Acoustic color is a descriptor of the dual dependences of backscattering cross section or its logarithmic form, target strength, of an underwater object on sonar frequency and angle of incidence. Use of ‘color’ refers, in one sense, to the coding of backscattering cross section by color on a figure whose axes are frequency and angle. In a larger sense, ‘color’ refers to the frequency dependence of backscattering, in analogy with optics, recognizing that the spectral dependence can convey significantly more information about the scattering object than the angle dependence alone. Here, acoustic color is computed for 13 pollack (Pollachius pollachius) swimbladders for which high-resolution morphometric data are available. The represented total fish length range is 31.5–44.5 cm. Investigated frequencies span the range 35–125 kHz, and investigated angles for vertically downward ensonification span the range of tilt angles from 45 deg head down to 45 deg head up. Since high-frequency acoustic scattering by fish is dominated by the swimbladder when present, the backscattering cross section of the swimbladder is a very good approximation to that of the entire fish. The assumption of high frequencies also supports use of the Kirchhoff-approximation scattering model applied to the digital representation of the swimbladder wall as a pressure-release surface. Computational results are shown for a particular specimen, and for the entire set of specimens when averaged with respect to the backscattering cross section. Differences of individual dependences with respect to the mean are computed. Cross-correlation coefficients of the difference functions are then computed and further quantified in a covariance matrix.