LOVE: MEASUREMENTS OF FISH TARGET STRENGTH 



is reflected and some is transmitted. After this 

 ti-ansmitted portion reaches the second boundary, 

 some of the energy is transmitted into the third 

 medium and some is reflected back into the sec- 

 ond medium, where it is again partially reflected 

 from the first boundary. This process continues 

 until a steady state is reached. The solution of 

 this problem is relatively easy, but it is inter- 

 esting because the resultant am])litudes of the 

 transmitted and reflected waves depend on the 

 phases of the component waves. The component 

 waves add vectorially and whether the amplitude 

 of the initially reflected wave is increased or de- 

 creased depends on the thickness of the second 

 medium and the wavelength of the incident wave. 



The reflection of sound from an infinite plate 

 poorly approximates the reflection from a fish, 

 and it is useful to examine the reflection from a 

 finite object such as a sphere. When the sphei-e 

 is large compared to the acoustic wavelength, 

 the echo originates from specular reflection, in 

 which the part of the sphere near the point 

 where the sound wave is normally incident pro- 

 duces a coherent reflected wave. When the size 

 of the sphere is comijarable to a wavelength, in- 

 terfei-ence effects similar to those mentioned for 

 the plate with finite thickness will cause the 

 acoustic cross-section to vary. When the sphere 

 is small compared to a wavelength, scattering 

 takes place and the acoustic cross-section of a 

 sphere of radius o is proportional to a'^/X* where 

 X is the wavelength. This solution was obtained 

 by Lord Rayleigh and hence this region is called 

 the region of Rayleigh scattering. 



For objects other than spheres, analysis be- 

 comes difficult, if not impossible. However, as 

 long as the object is not highly compressible, 

 the concept of the regions of Rayleigh scattering, 

 interference effects, and geometric reflection is 

 valid. For a fish, the distinctions between these 

 regions becomes unclear because of the fish's 

 internal structure. When the fish is very small 

 compared to the acoustic wavelength, Rayleigh 

 scattering can be expected. However, if the fish 

 has a gas-filled swim bladder the gas bubble will 

 resonate at some wavelength in this region, 

 greatly increasing the target strength over that 

 predicted by Rayleigh scattering. When the size 

 of the fish is comparable to the wavelength, in- 



terferences will occur among the fish flesh and 

 organs, the skeleton, the gas in the swim bladder, 

 and the boundaries of the fish. When the fish 

 is larger than the wavelength, the dimensions of 

 many of these parts will be comparable to the 

 wavelength and the region of interference effects 

 will be greatly extended into what would be the 

 region of geometric reflection for a homogeneous 

 body. 



Gushing et al. (1963) have assumed that the 

 region of interference effects extends from L/\ 

 = 8 to L/\ = 100, where L is the fish length, 

 and \ is the acoustic wavelength, and they sug- 

 gest that for quantitative results this region 

 should be avoided. Neglecting the fact that they 

 have ignored the effects of swim bladder reso- 

 nance, the limits they have jilaced on the inter- 

 ference region will now be examined. For a rigid 

 sphere of radius a the limits of the interference 

 region are approximately 1 ^ 27ra/\ ^ 10, and 

 for any other object these limits will probably 

 be farther apart. Measurements on individual 

 fish indicate that interference effects occur at 

 values of L'k -- 0.7 (Love, 1971) and this can 

 be taken as a lower limit. (This is not to say 

 that it is the lower limit, only that this is as low 

 as measurements have been made.) Haslett 

 (1962a) examined a small number of whiting to 

 determine their "standard dimensions." He 

 found that the diameter of the backbone was 

 about 0.01 the length of the fish. Assuming that 

 the backbone of a fish is the smallest part of a 

 fish which contributes to its echo, this m.eans 

 that if interference effects occur in the back- 

 bone until its circumference is something near 

 10 times as large as the wavelength, as in the 

 case for the sphere, then the upiier limit of the 

 interference zone for a fish will be at least Lk 

 — 200. Again, measurements have been made 

 which indicate that the upper limit will be at 

 least this high (Haslett, 1969). Therefore, it 

 may be assumed that the limits of the interfer- 

 ence region are at least 0.7 ^ L/K ^ 200. 



If it is assumed that fish of interest to com- 

 mercial fishermen range from 10 cm to 150 cm, 

 and that fish-finding sonars have frequencies 

 ranging from 10 kHz to 200 kHz, then the range 

 of interest for fisheries applications will be 0.7 ^ 

 L/k < 200, the limits set for the interference 



705 



