HEWITT ET AL.; DEVELOPMENT AND USE OF SONAR MAPPING 



with increasing frequency above resonance. Using 

 this approach, the energy scattered by the bound- 

 ary of a fish school ensonified (irradiated acousti- 

 cally) with 30 kHz sound becomes negligible. 



Weston (1967) further suggested that an inco- 

 herent addition of reflected energy from indi- 

 vidual fish may be expected as sound is trans- 

 mitted across the boundary of a fish school. At 30 

 kHz, this component of target response becomes 

 dominant and is reduced (or enhanced) by multi- 

 ple scattering and absorption within the school. 



The target response due to sound scattering by 

 individual fish, assuming a mean wave phase in- 

 terference of zero, may be calculated by summing 

 the scattering cross sections of the fish comprising 

 the target. Expressed in target strength, TS: 



TS = TS, + 10 log n (decibels) 



where TS, = the average target strength of the 

 individual scatterer 

 n = the number of scatterers contribut- 

 ing to the total echo. 



The number of scatterers contributing to the 

 measured echo, n, may be estimated by applying 

 observed and theoretical school densities (fish per 

 cubic meter) to the ensonified volume. The enson- 

 ified volume may be estimated from: 



CT 



V = —{d)iD) (cubic meters) 



(1) 



CT 



where — 



the range extent of the volume 

 sampled by a sound pulse t sec- 

 onds long and moving at a speed 

 of c meters per second 



D = the vertical dimension of the school 

 in meters 



d = the horizontal dimension of the 

 school. 



School dimensions, D and d, are further limited 

 by beam geometry, i.e., a school may not be fully 

 ensonified if its dimensions exceed the effective 

 beam width at the range of detection. The effective 

 horizontal beam width may be estimated as that 

 between the half-power points or: 



2/?tani3 



where R = range of detection 



(B = 5° for the 30-kHz transducer used 

 in this study. 



Thus, d is the smaller of the measured horizontal 

 dimensions or 0.175i?. Vertical dimensions offish 

 schools are not readily measured with sonar. How- 

 ever, in studying echograms of thousands of 

 schools, Mais (1974) noted less variation in the 

 vertical school dimension than the horizontal di- 

 mension and reported a mean school thickness 

 of 12 m. The vertical effective beam width is esti- 

 mated to be 12° or 42 m at 200-m range. If D is 

 then assumed to be 12 m for all schools, there is 

 no limitation imposed by the vertical beam width 

 except that caused by vertical positioning of the 

 school. 



Using a 10 ms pulse length and estimating the 

 speed of sound in a seawater medium at 1,500 

 m/s, Equation (1) becomes: 



V = 90d 



where d is the smaller of the measured horizontal 

 dimensions or 0.175 R. 



Mais (1974) reported visual observations of an- 

 chovy schools and estimated average packing 

 density at 50 to 75 fish/m^. Graves^ analyzed in 

 situ photographs of three anchovy schools and re- 

 ported a mean density of 115 fish/m^ at a mean 

 spacing of 1.2 body lengths. Hewitt'' used an 

 idealized model of anchovy school compaction and 

 calculated school densities of 0.5, 1.4, 6.6, 217, 

 and 4,219 fish/m^ at interfish distances of 10, 7, 4, 

 1, and 0.2 body lengths, respectively. 



The target strength of an individual scatterer, 

 TS, may be estimated from considerations of 

 acoustic theory and extensions of empirical mea- 

 surements. Weston (1967) had shown the acoustic 

 response of an ideal gas bubble to be essentially 

 independent of frequency above resonance and 

 proportional to the surface area of the bubble. 

 When predicting the response of a fish swim 

 bladder, Weston suggested an enhancement of 



^Graves, J. 1974. A method for measuring the spacing and 

 density of pelagic fish schools at sea. SWFC Administrative 

 Report No. LJ-74-44. Southwest Fisheries Center, NMFS, 

 NOAA, La Jolla, CA 92038. 



Hewitt, R. 1975. Sonar mapping in the California Current 

 area: A review of recent developments. Unpubl. manuscr. 

 Southwest Fisheries Center, NMFS, NOAA, La Jolla, CA 

 92038. The compaction model cited here used an anchovy of 12 

 cm standard length and computed the space required for the 

 fish and a surrounding volume expressed in body lengths. The 

 inverse of the resulting volume yields compaction in fish per 

 cubic meter for a school of fish uniformly distributed in space. 



287 



