SECT. 4] 



SOUND SCATTERING BY MARINE ORGANISMS 



531 



ambiguity. Higher-frequency scattering layers, which clearly migrate both in 

 depth and frequency, may during their migrations occupy depths above, and 

 over-lapping with, the daytime depth of the low-frequency layer and further- 

 more may scatter sound over a frequency band including that of the low- 

 frequency layer (see Fig. 17). This phenomenon may produce an illusion of 

 migration in the low-frequency layer. 



B. Measurement of Volume Back-Scattering 



Some scattering-layer observations in the western North Atlantic have been 



analyzed by the method of Machlup and Hersey (1955) [see above, pages 522- 



524, especially equation (40)], by which the echo intensity (function of time) is 



translated into volume back-scattering coefficient (function of depth). The 



DEPTH (m) 

 300 400 



600 800 1000 



-70 



'e 



2 -80 



0.2 0.3 0.4 0.6 0.8 



TIME AFTER SHOCKWAVE (sec) 



Fig. 19. Volume back-scattering coeflficient versus time (depth), plotted on a logarithmic 

 scale, measured at 15 kc/s ; an example where m in the scattering layer is large 

 compared with surrounding volumes. 



computation was carried out for frequencies from 3.5 kc/s to 21.5 kc/s. The peak 

 values of m range from about 10"^ m-i to 10-^ m-i. Fig. 19 shows a graph of 

 m versus time after the shock wave, for a case where m in the layer is high 

 relative to surrounding volumes. These values of m vary over about the same 

 range as those reported by NDRC (1946a) except that smaller peak values of m 

 have been found in the more recent study. 



The problem remains to relate measurements of volume scattering to in- 

 formation about individual scatterers. When the individual scatterers are 

 distributed more or less at random and when their scattering cross-sections, 

 (t/477-, are a small fraction of the total area insonified, then the back-scattering 

 due to a number of scatterers may be calculated by adding independently 

 the scattering intensity due to each scatterer. Therefore, the total volume 



