310 



SHALLOW-WATER REVERBERATION 



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-40 

 -5 

 -6 

 -70 

 -80 

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 -80 

 -60 

 -100 



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-90 

 -100 



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-12 

 -130 



40 



80 



120 



240 



280 



160 200 



RANGE IN YARDS 



O MEASURED LEVELS 



Figure 4. Observed and predicted bottom reverberation levels. 



320 360 



— PREDICTED LEVELS 



0.01 sec; then there is a rather rapid growth in the 

 reverberation intensity when the main beam reaches 

 the bottom. Further illustrations of the reverbera- 

 tion measured with the beam down 30 degrees are 

 shown in Figure 5. The ocean depth was 48 ft and 

 the projector depth 10 ft so that the peak of the 

 reverberation is observed to come in at a time cor- 

 responding to a range of about 25 yd. The ensuing 

 lesser maxima are the result of successive multiple 

 reflections from surface and bottom. These observa- 

 tions were taken over a bottom thickly covered with 

 boulders of the order of one foot in diameter. An 

 interesting feature of these curves is the change in 

 the duration of the main reverberation pulse as the 

 frequency changes. The duration of the pulse de- 

 creases progressively with increasing frequency; this 

 effect is due to decrease in beam width. In the case of 

 the projector directed upward at an angle of 30 de- 

 grees, it is seen from Figure 5 that the surface rever- 

 beration peaks predicted in Figure 1 are lacking. This 

 absence is due to the fact that the reverberation was 



measured under conditions which combined very 

 shallow water with a smooth sea surface and a rough 

 sea bottom, so that bottom reverberation masked 

 surface reverberation at practically all ranges. Under 

 other circumstances, with a smooth bottom and a 

 rough sea, or deeper water, the peak of surface rever- 

 beration can usually be observed before the crash of 

 bottom reverberation comes in. 



These remarks indicate that bottom reverberation, 

 under at least some circumstances, behaves quali- 

 tatively as would be expected from a siriiple geomet- 

 rical analysis of the time required for the sound to 

 reach the bottom. The next step in the analysis is to 

 attempt to make a quantitative prediction of the 

 expected reverberation levels, and then to compare 

 these theoretical predictions with experiments. 



From formula (54) of Chapter 12, it is clear that 

 the received reverberation depends on the transmis- 

 sion loss to and from the bottom, on the transducer 

 directivity, and on the scattering strength of the 

 bottom. It can be assumed that the transducer 



