332 



VARIABILITY AND FREQUENCY CHARACTERISTICS 



16.4 REVERBERATION FROM WIDE- 

 BAND PINGS 



Up until now, this volume has been concerned 

 almost completely with reverberation from narrow- 

 band CW pings (in a CW ping the nominal trans- 

 mitting frequency is fixed during the interval of 

 transmission). However, other types of pings have 

 been used, as in FM sonar. In this section we shall 

 examine the reverberation resulting from the use of 

 wide-band pings. 



Strictly speaking, no ping which has a finite dura- 

 tion can possibly be single-frequency; other fre- 

 quencies than the nominal one must be present in 

 order that the signal can build up and die off. How- 

 ever, 100-msec CW pings at 24 kchave band widths of 

 the order of 10 c, while wide-band pings often have 

 band widths of 1,000 c or more (for example, a 

 1-msec CW ping has a band width of 1,000 c). It may 

 be expected that this very real difference in the order 

 of frequency spread will be reflected in a difference 

 in the nature of the returning reverberation. 



According to Section 12.5, widening the frequency 

 band in the ping should not seriously affect average 

 reverberation levels, if the frequency response of the 

 gear is sufficiently flat. In other words, the theoretical 

 formulas in Chapter 12 giving the average time decay 

 of reverberation fronra single ping should be just as 

 valid (or invalid) for wide-band pings as for narrow- 

 band pings. It is true that many of the parameters 

 in the formulas of Chapter 12 are frequency-de- 

 pendent, such as the transmission loss, transducer 

 directivity, and the scattering coefficients. However, 

 these quantities vary smoothly and relatively slowly 

 with frequency and can be replaced by their averages 

 over even a 10-kc wide band without introducing 

 much error. Thus the resultant theoretical average 

 reverberation levels for wide-band pings are simply 

 an average, over the frequency band included in the 

 ping, of the levels predicted for the narrow-band 

 pings. A more quantitative discussion of the qualita- 

 tive ideas in this paragraph can be found in a report 

 by CUDWR.22 



The average fluctuation, as defined by equation 

 (1), cannot be written simply as the average of the 

 fluctuations of the individual frequency components. 

 Thus, there is reason to expect that the fluctuation 

 of wide-band pings may be different from that of CW 

 pings. The expected magnitude of the fluctuation of 

 wide-band pings will depend on the mechanism 

 hypothesized as responsible for the fluctuation. Con- 



fining our attention for the moment to those wide- 

 band pings resulting from the use of very short ping 

 lengths, then, if the Rayleigh distribution is valid, it 

 is apparent from the form of equation (2) that the 

 magnitude of the fluctuation as defined by equation 

 (1) does not depend on the ping length. In other 

 words, with square-topped CW pings the magnitude 

 of the fluctuation will be the same for wide-band 

 pings as for narrow-band pings. 



However, the decrease of the ping length required 

 to widen the frequency band of a CW ping will in- 

 crease the rapidity of the fluctuation, since it de- 

 creases the blob width. This decrease in blob width 

 does not necessarily improve the recognizability of a 

 returning echo since the echo length is decreased 

 correspondingly. Studies of echoes resulting from CW 

 pings (see Chapters 21 and 23) indicate that echoes 

 look very much like reverberation blobs, of width 

 about equal to the ping length. This similarity be- 

 tween echoes and reverberation blobs makes it very 

 difficult to devise means for improving the detectabil- 

 ity of echoes from CW pings against a reverberation 

 background, other than the obvious but not always 

 feasible procedure of reducing the average reverbera- 

 tion intensity. It is true that a time average over a 

 relatively short interval will include a large number 

 of reverberation blobs and this time average wifl 

 fluctuate much less rapidly than the unaveraged re- 

 verberation. However, because of the similarity of the 

 echo to the reverberation blobs, any averaging pro- 

 cedure applied to the sound returning from a short 

 CW ping is likely to eliminate the echo. 



Nevertheless, by adjusting the time interval over 

 which the average is taken, some beneficial effect 

 may be hoped for, especially when the echo intensity 

 is much larger than the average reverberation in- 

 tensity. Some studies made with very short (0.3 

 msec) unmodulated pings support this hope. It was 

 found that the use of these very short pings signifi- 

 cantly reduced the number of false contacts reported 

 and that the maximum range at which a target could 

 be identified was not affected. 



When frequency-modulated pings are used, the 

 signal sent into the water has a continuously varying 

 frequency. With such pings, the received reverbera- 

 tion at any instant may include a wide band of 

 frequencies, depending on the band included in the 

 original ping and on the receiving pass band of the 

 equipment. Theoretical analysis of the expected fluc- 

 tuation of the reverberation from such pings is diffi- 

 cult, but it has been shown^' that the envelope of the 



