322 



SHALLOW-WATER REVERBERATION 



inverse fourth power of the range, but that large 

 variations from this type of decay are observed. 

 Since the expected echo level also falls off at about 

 the inverse fourth power of the range,* the results of 

 reference 1 mean that the possibility of obtaining an 

 echo usually depends on the level of the reverbera- 

 tion peak relative to the expected echo level at the 

 range of the reverberation peak. If the reverberation 



-70 



100 



200 300 500 700 1000 



RANGE TO PEAK IN YARDS 



2000 



Figure 8. Expected level of peak of bottom reverbera- 

 tion as a function of range to peak and bottom type. 



peak is high enough to mask the echo at that range, 

 then the echo is not likely to be detected at any range 

 past the reverberation peak. Conversely, if the echo 

 level is well above the reverberation at the range of 

 the reverberation peak, bottom reverberation will 

 probably not limit echo ranging at any range. 



The above discussion is not by any means a com- 

 plete treatment of the problem of echo ranging in 

 shallow water. Many factors are involved in deter- 

 mining the echo-to-reverberation ratio at any range. 

 Also, no account has been taken of the fact that at- 

 tenuation at long range makes the echo level drop off 



much more rapidly than the inverse fourth power of 

 the range. However, attenuation also decreases the 

 received bottom reverberation levels, so that even at 

 long ranges the echo and reverberation levels should 

 decrease at roughly the same rate. In general, it can 

 be said that the problems involved in determining the 

 echo-to-reverberation ratio are so complicated that 

 no satisfactory quantitative treatment has ever been 

 given, although qualitative discussions have been 

 presented in a number of places.' It appears then from 

 the foregoing discussion that with present informa- 

 tion the best way to characterize bottom reverbera- 

 tion levels is in terms of the level at the principal rever- 

 beration peak ; this level is determined using equation 

 (54) of Chapter 12 and the known value of the bottom 

 scattering coefficient for 10 degrees grazing incidence. 



Figure 8 shows the expected average standard re- 

 verberation level at the reverberation peak, as a 

 function of the range to the peak and the bottom 

 type, for ordinary 24-kc echo-ranging gear sending 

 out a horizontal beam. In preparing this diagram it 

 was assumed that the range to the peak is six times 

 the depth of the bottom below the projector. The 

 absorption was taken to be 4 db per kyd, J^ was set 

 equal to —19 db for the 5- to 6-degree ray, 10 log m" 

 was taken from Table 7, and finally the reverberation 

 level for a 100-msec ping was calculated by the use of 

 equation (55) of Chapter 12. Although Figure 8 is the 

 best average curve which can be drawn with present 

 information, the likelihood of deviations in practice 

 from Figure 8 cannot be overstressed. In particular. 

 Figure 8 is not valid in isothermal or nearly isothermal 

 water, when the range to the reverberation peak will 

 usually be very different from six times the distance 

 between the projector and the bottom. It is also not 

 advisable to extend the results in Figure 8 to ranges 

 less than 100 yd because at such short ranges it is 

 again unlikely that the average assumed relationship 

 between range and depth will be valid. It should be 

 noted that the curves in Figure 8 incorporate the 6-db 

 correction for surface reflections discussed in Section 

 15.3.3. Thus, when the echo-ranging transducer is 

 deep, 6 db should be subtracted from the values in 

 Figure 8 to obtain the expected reverberation levels; 

 in such situations surface reflections will not be im- 

 portant in determining the bottom reverberation 

 level. 



In conclusion, we repeat that on the average the 

 reverberation in nonisothermal water seems to fall 

 off at about the inverse fourth power of the range, at 

 ranges past the reverberation peak, but that large 



