FISHERY BULLETIN; VOL. 74, NO. 2 



75% due to shape distortion. Expressed in target 

 strength: 



TS, = 20 log L - 25 (decibels) 



(2) 



where L is the fish length in meters. Swim blad- 

 der volume is assumed to be 4.1% of total fish 

 volume and the radius of a sphere of equal vol- 

 ume equal to 0.043 L (after Haslett 1965). 



Using a standard length of 12 cm as typical of 

 anchovy school constituents detected by sonar 

 (Mais 1974), Equation (2) yields a TS, of -43.4 

 dB. It should be noted that Equation (2) makes no 

 provision for reflection, interference, or attenua- 

 tion of sound waves by fish tissue.® 



McCartney and Stubbs (1970) measured 

 maximum dorsal aspect target strengths of six 

 fish species at varying frequencies and lengths. 

 They fit Equation (3) to their data and further 

 showed that the swim bladder can account for 

 practically all of the scattering over a wide band 

 of frequencies: 



TS, = 24.5 logL - 4.5 log X - 26.4 



(3) 



where X = the wavelength of incident sound 

 defined as c(f)'^, where c is the speed of sound in a 

 saltwater medium = 1,500 m/s"^ and /"is the fre- 

 quency. For a 12 cm anchovy ensonified with 30 

 kHz sound. Equation (3) gives a TS, of -43.1 dB. 

 Love ( 197 1 ) reviewed maximum dorsal and side 

 aspect target strength measurements made by 

 several investigators. The data were obtained 

 using fish from eight different generic orders, 

 varying 100-fold in length, some with swim blad- 

 ders and some without, and ensonified over a fre- 

 quency range of 8 to 1,480 kHz. For dorsal aspect, 

 Love related maximum target strength, fish 

 length, and frequency by: 



TS, = 19.4 logL + 0.6 log A - 24.9. (4) 



For the anchovy described above, Equation (4) 

 predicts a TS, of -43.5 dB at dorsal aspect. 



Love described the side aspect data with the 

 following equation: 



TSi = 22.8 logL - 2.8 log \ - 22.9 (5) 



or -40.2 dB for the anchovy described at side 

 aspect. 



A similar regression on target strength mea- 



®Holliday (1972) reported an average swim bladder volume of 

 2.8% of the total fish volume for a sample of 239 anchovy. The 

 use of this value predicts an anchovy swim bladder response of 

 -44.3 dB. 



surements taken from dead fish in dorsal aspect 

 by six investigators and collated by Haslett 

 (1965) would describe a TS, of -49.8 dB for a 

 12-cm fish ensonified at 30 kHz (McCartney and 

 Stubbs 1970). An application of the equations 

 that Shibata (1970) used to describe his results 

 yielded values of -42.8 dB for maximum dorsal 

 aspect target strength and -40.0 dB for maxi- 

 mum side aspect target strength. 



Several authors have noted that acoustic 

 equipment commonly used by the biologist oper- 

 ates at frequencies (10 to 200 kHz) which gener- 

 ate sound at wavelengths comparable with the 

 size of fish under study. Interferences will occur 

 among the scattering components of a fish (swim 

 bladder, flesh, skeleton, and organs) and may be 

 expected to be a function of species and aspect. 

 Further, our measurements are of peak school 

 target strength taken from several transmissions 

 along one tangential to the school and may not be 

 the maximum value which would be obtained 

 from interrogation at several angles. 



Let us return now to the original calculations, 

 i.e., the incoherent summation of echoes from an 

 aggregation of fish which may now be expressed 



as: 



TS = TS, + 10 log [q (90 d)] 



(6) 



where TS, may vary from —50 to -40 dB, g is the 

 school density in fish per cubic meter and may 

 vary from 0.5 to 4,219, and d may vary from 5 m 

 (mean diameter of the minimum class size) to 79 

 m (0.175 R at R = 450 m, the maximum range 

 within the observation band). The expected range 

 of peak school target strengths (assuming inco- 

 herent addition and no interference or absorption 

 within the school) are listed below for foiu- as- 

 sumptions of fish target strength, TS,: 



where r = 10 ms, jS = 5°, and D = 12 m. 



Based on a framework of several assumptions, 

 we may expect a range of peak school target 

 strengths of about 50 dB whose position on the 

 decibel scale is determined from the value one 

 assumes to be the average target strength of the 

 individual scatterers comprising the school. 



288 



