FISHERY BULLETIN: VOL. 69, NO. 4 



(5) 



01- in logarithmic form, 



10 log /, = 10 log (-2L\ + 10 log h — 40 log r. 



(6) 



Defining the echo level (E) as 10 log Ir and the 

 source level (S) as 10 log /,„ and rearranging, 



T r= E — S 



40 log r. 



(7) 



Equation (7) can be used to compute target 

 strength in an ideal medium. In a real medium, 

 however, the actual transmission loss will in- 

 clude effects due to absorption, scattering, re- 

 fraction, and the boundaries. Hence, in a real 

 medium 



E — S 



2H 



(8) 



where H is the one way transmission loss. H 

 takes into account spreading loss, absorption, 

 and any anomalies. In actual practice H cannot 

 always be reliably predicted and must be mea- 

 sured unless the ranges involved are small. 

 Equation (8) is known as the active sonar equa- 

 tion and is always used in the computation of 

 target strength since it involves only directly 

 measurable quantities — echo level, source level, 

 and transmission loss. 



It is impossible for more sound to be reflected 

 from a target than is incident upon it, and it is 

 therefore seemingly impossible for any object 

 to have a positive target strength, yet many large 

 targets do. This is a consequence of the refei-- 

 ence distance being 1 m, and the measurements 

 being made at greater distances, with spherical 

 spreading assumed in order to calculate the 

 target .strength. However, the spreading loss 

 very close to a target is less than the spherical 

 spreading loss which is assumed, and hence pos- 

 itive target strengths can be obtained for large 

 targets. 



The imiwrtance of the target strength of a po- 

 tential target is obvious from the sonar equation 

 (equation (8)). The maximum range at which 

 a target can be detected in any given environ- 

 ment depends on its target strength and the 

 characteristics of the transmitting and receiving 



systems. Therefore, an estimate of target 

 strength is essential to the effective design and 

 operation of any active sonar system. 



The quantification of a fish school, knowing its 

 target strength, is possible because the target 

 strength of a school depends on the average size, 

 number, distribution, and aspect of the individ- 

 uals in the school. In order to quantify fish 

 schools using target strenglh information, it is 

 first necessary to determine the size and number 

 of individuals required to produce a given target 

 strength. The initial step in this process is the 

 determination of the target strenglh of an in- 

 dividual fish. The application of this knowledge 

 to studies on the acoustic intei'actions of arrays 

 of scatterers will eventually produce accurate 

 predictions of school target strength. The great 

 majority of work done up to this time has been 

 on individual fish, and quite a bit more must be 

 done before this initial step is completed. De- 

 finitive work on the quantification and identifi- 

 cation of fish schools utilizing target strenglh 

 information awaits completion of this step. 



Reflection of sound from an object in water 

 occurs when the oliject has an acoustic impedance 

 which differs from that of the water. Acoustic 

 impedance is defined as the product of the den- 

 sity (p) of a substance and the velocity of sound 

 (c) in that substance. The proportion of sound 

 reflected from or transmitted into an object in 

 water depends on the magnitude of the imped- 

 ance mismatch between the object and the water. 

 The simplest case of reflection occurs when a 

 plane wave is normally incident upon a plane 

 boundary between two semi-infinite media. The 

 pressure amplitude reflection coeflicient is de- 

 fined as the ratio of the reflected pressure ampli- 

 tude to the incident pressure amplitude, and for 



this case it is found to be P-^- P'^', where 



p2C2 + PlCl 



piCi is the impedance of the medium in which 

 the incident wave is traveling and pjC; is the 

 impedance of the medium upon which the wave 

 is incident. If the second medium is reduced to 

 finite thickness and a third medium is i)laced 

 behind it (the third medium may or may not be 

 the same as the first), the jiroblem l)ecomes 

 slightly more complicated. When the incident 

 \vave arrives at the first boundary, some energy 



704 



