FISHERY BULLETIN: VOL. 69. NO. 4 



r 



TARGET STRENGTHS 



or AN 

 INDIVIDUAL FISH 



FOR DORSAL ASPECT* 

 I00< Lf £14000 



FOR SIDE ASPECT- 



150 < LI < 20000 



Figure 6. — Nomogram for calculating the dorsal-aspect 

 and maximum side-aspect target strengths of an indi- 

 vidual fish. 



QUANTIFICATION AND 

 IDENTIFICATION OF SCHOOLS 



Since estimates for the maximum side-aspect 

 and dorsal-aspect targret strengrths of individual 

 fish are available, the determination of the 

 target strengths of fish schools at these aspects 

 will depend on the detei-mination of the efl^ects 

 of the number of fish in the school and their 

 distribution. If the fish are widely spaced, or 

 in a plane perpendicular to the sonar beam, so 

 that there is no acoustic interaction among the 

 individuals, the target strength of the school is 

 equal to the average tai'get strength of an indi- 

 vidual ])lus 10 times the logarithm of the number 

 of fish. The probability of finding a school that 

 meets these qualifications is quite small and 

 therefore the effects of interactions among the 

 fish must be taken into account. 



Little exjierimental work on the acoustic inter- 

 actions of fish in a school has been done, although 

 some measurements of the target strengths of 

 groups of fi.sh have been made, usually with 

 little concern for the distribution of the indi- 

 viduals (e.g., Thorpe and Ogata, 1967; Shishko- 

 va, 19(50). Some theoretical work on distribu- 

 tions of scatterers has been done, the scatterers 

 usually being point scatterers or small bubbles 

 (e.g., Foldy, 191."); Weston, 196(5). Weston 

 ( 1967) has applied the results for bubbles to fish 



schools and has estimated reflection coefiicients 

 for regions well-below and well-above resonance. 

 Since there is no interference region for a bubble, 

 he does not concern himself with interference 

 efl'ects, and his results are of limited value in the 

 interference region. Boyles (1969) has dis- 

 cussed the mathematical theory of multiple scat- 

 tering from fish schools, but to obtain results 

 in the interference region the complete spatial 

 scattering and absorption pattern of an individ- 

 ual fish must be known. 



The identification of a school of fish utilizing 

 target strength information is obviously much 

 more difficult than its quantification, and since 

 it is not yet possible to quantify fish schools with 

 this information, it is surely not yet possible 

 to identify them. 



Figure 3, which summarized Haslett's work, 

 seems to indicate that no reasonable pattern of 

 target strength vs. frequency can be found for 

 any s]iecies due to the rapid fluctuations of target 

 strength. Haslett's measurements were made 

 at three widely spaced frequencies. Measure- 

 ments made by the author at a larger number 

 of more closely spaced frequencies indicate that 

 for individual fish these fluctuations are not so 

 rapid and that possibly individual fish may be 

 identified through the use of target strength vs. 

 frequency (a L-vs. L X) curves. Dorsal aspect 

 target strength measurements made on six bay 

 anchovies, Anchoa mitchilU, one Atlantic men- 

 haden, Brevoortia tyraymus, five goldfish, Caras- 

 shcs auvatiis, and six Atlantic silversides, Menid- 

 ia meniditt, revealed that all of these fish had 

 similar or/Lr vs. L \ curves (Love, 1971). The 

 most notable feature of these curves is a deep 

 minimum in the neighborhood of L/\ = 10. This 

 minimum is easily seen in the average curves 

 for each species shown in Figure 7. Similar 

 measurements on three mummichogs, Fundulns 

 heterocUtiis, five striped killifish, Funduhts 

 majiilis. six black crappies, Pomoxis n'niromacu- 

 latiis. and four si)otted seatrout, Cynscion nehn- 

 losus, revealed that the cr/L^ vs. L/k curve for 

 any individual of these species bears no easily 

 discernible relation to that of most, or all, of 

 the other individuals of that species, or to the 

 average curve for that species. 



The anchovies, goldfish, and menhaden are 



712 



