COHERENCE 



327 



SIGNAL 

 LENGTH 



i ff ^ jWH ii H i |. i ,g)i !l | >ri) !m i 

 REVERBERATION RECORDS 



l)i)(l»i)!,-^)m'liC<Mrip-(!()l!:.mtx<x<*>^>^^^ 



B -Z- 



C-^ 



•««-<x:><o<)B-«<;o-*<)C>*i-HH-<<^^ ^ <0: ■Xj>5C 





Figure 2. The coherence of reverberation. 



fluctuation of the transmission loss between the pro- 

 jector and the scattering centers. Transmission fluc- 

 tuations apparently do not obey a Rayleigh distribu- 

 tion; the standard deviation of the transmitted ampli- 

 tude is about 42 per cent of the mean transmitted 

 amplitude, in practice, as compared to the 52 per 

 cent predicted from the Rayleigh distribution.* Ship 

 roll is another factor, ignored in this sketchy treat- 

 ment, which is believed to produce significant fluctua- 

 tions in reverberation.' These neglected factors will 

 have to be taken into account before the theory of 

 reverberation fluctuation can be considered at all' 

 adequate. Also, the presence of these other sources of 

 fluctuation means that a determination of the average 

 number of scatterers giving rise to reverberation, by 

 a method such as that proposed in reference 6 would 

 not be too reliable even if the distribution function 

 for the number of scatterers were known. 



At the present time, average reverberation inten- 

 sities are determined by averaging between 5 and 12 

 pings. The validity of this procedure can be esti- 

 mated from the magnitude of the variance defined by 

 equation (1). It is easy to show that the standard 

 deviation of the average intensity of n pings is just 



'^ AP/n. If the distribution function is Rayleigh, 

 then from equation (6) we have 



Thus the average intensity / of 5 pings has a standard 

 deviation of +0.45/, or roughly 1.5 db. 



16.2 



COHERENCE 



The term coherence applied to reverberation refers 

 to a tendency of the received reverberation to occur 

 in the form of pulses of the approximate duration of 

 the ping length. The possession of coherence means 

 that if at any instant the reverberation level is high, 

 it is likely that the level will remain high for a little 

 while, and that if the reverberation level is low, it is 

 likely not to become large in a short time. 



An experimental study of reverberation coherence 

 has been made by UCDWR, and reported in Section 

 X of reference 2. Ten blobs of about equal amplitude 

 were chosen at random from two QB records of equal 

 ping length, in the time interval between 1.5 and 2.5 

 sec after midsignal. The amplitude was measured at 

 intervals of about 0.1 ping length from the middle of 

 each blob out to 2 ping lengths on either side. The 

 average amplitude at each of the measuring positions 

 on the ten blobs was then divided by the average 

 amplitude at the middle of the blob and was plotted. 

 The resulting graphs, one for each of several ping 

 lengths, are given in Figure 2, under the heading 

 Coherence Analysis. Time is plotted on the horizontal 

 axis; amplitude relative to the amplitude at the 



