Chapter 16 

 VARIABILITY AND FREQUENCY CHARACTERISTICS 



IN PRECEDING CHAPTERS, we havc derived theoreti- 

 cal formulas for the average reverberation inten- 

 sity, and have compared these formulas with average 

 reverberation intensities observed in practice. By 

 means of this comparison, we have obtained average 

 values of the backward scattering coefficient for 

 volume, surface, and bottom reverberation. In this 

 chapter we shall attempt to analyze the differences 

 between reverberations from successive pings sent 

 out under apparently the same circumstances. These 

 differences may be deviations in amplitude, or devia- 

 tions in the frequency spectrum of the received re- 

 verberation. 



There are several reasons for such an analysis. 

 First, it is desirable to know just how well the average 

 curve may be expected to represent individual rever- 

 beration curves. Secondly, the deviations from the 

 average depend on the type of mechanism giving rise 

 to the reverberation; thus, analysis of the deviations 

 can give valuable information on the sources of re- 

 verberation. Finally, such an analysis may easily re- 

 veal significant differences between the behavior of 

 echo fluctuation and reverberation fluctuation since 

 the mechanisms producing these two types of fluctua- 

 tion are undoubtedly somewhat different. These dif- 

 ferences in behavior, if well understood, may be 

 utilized in methods for improving the recognition 

 differential for the echo against a reverberation back- 

 ground. 



16.1 



FLUCTUATION 



In analyzing the amplitude deviations of individual 

 reverberation curves from the average, it is con- 

 venient to distinguish between fluctuation and co- 

 herence. Fluctuation refers to the deviation from the 

 average of the intensity received at a definite time 

 following the initial ping. This fluctuation is usually 

 measured by the variance 



A/2 = {I - If = P - (ly (1) 



where 7 is the average intensity at a time t seconds 



after midsignal, and P is the average of the square 

 of this intensity. Average values will be designated 

 by a bar throughout the remainder of this chapter. 

 As discussed in Chapter 12, the average intensity at 

 the time t is to be determined by the following proc- 

 ess. A large number of reverberation records are 

 taken under circumstances as nearly identical as 

 possible, and the intensity of the reverberation at a 

 time t seconds after midsignal is read off each record. 

 The average of these intensities is the value referred 

 to by the bar. 



Evidently, if all the pings were sent out under 

 exactly the same circimistances, the received inten- 

 sity at time t should be constant, and AP in equation 

 (1) would be zero. However, no two pings occur 

 under precisely the same circumstances. There are 

 variations in the power output of the projector; varia- 

 tions in the orientation of the receiver because of ship 

 roll; variations in such oceanographic factors as wave 

 height, wind force, temperature-depth distribution, 

 water depth, and type of bottom material; and over- 

 all variations in transmission anomaly. Some of these 

 sources of reverberation fluctuation can be mini- 

 mized. The power output of the projector can be 

 stabilized to a fraction of a decibel; the ship will not 

 roll on a calm day; and the effects of changing wind 

 force and bottom character can be eliminated by 

 studying only volume reverberation. However, large 

 fluctuations remain no matter how much control is 

 exercised. These remaining fluctuations in volume 

 reverberation are regarded as an inherent property 

 of reverberation. 



In the derivation of equation (13) of Chapter 12, 

 expressing the time variation of volume reverbera- 

 tion from a single ping, it was assumed that the re- 

 verberation is due to the scattering of sound by a 

 large number of scatterers in the ocean. Fluctuation 

 in the received reverberation is caused by the fact 

 that the total reverberation amplitude is the sum of 

 the amplitudes received from all the individual 

 sources. These individual amplitudes have random 



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