DEEP-WATER REVERBERATION LEVELS 



337 



ducer between the sound returning at time t and the 

 horizontal plane; J, (6) is the surface-reverberation 

 index corresponding to the angle of elevation 6; and 

 the other cjuan titles have the meanings given in the 

 section entitled "Theoretical Formula for Volume 

 Reverberation Level" with the further specification 

 that A is the transmission anomaly along the actual 

 ray path to the surface. 



Because of reflections from the air-water interface, 

 not taken into account in equation (7), measured 

 surface reverberation levels with horizontal beams 

 will usually be about 6 db higher than the levels 

 predicted by that equation. 



Dependence on Range 



According to equation (7), the surface reverbera- 

 tion intensity at short ranges, where the transmission 

 anomaly 2 A can be neglected, should be proportional 

 to the inverse cube of the range, provided m' and 

 Js{ff) also change negligibly with increasing range. 

 This simple inverse cube dependence is observed only 

 rarely. When refraction near the surface is sharply 

 downward, surface reverberation drops abruptly be- 

 low volume reverberation at the range where the 

 limiting ray dips beneath the surface scattering layer. 

 Moreover, the decay of surface reverberation inten- 

 sity is usually faster than inverse cube even when 

 downward refraction is weak or absent. For high wind 

 speeds (and therefore high sea states) the decay is 

 especially rapid; for wind speeds greater than 20 mph, 

 the surface reverberation levels usually drop off 

 nearly as the fifth power of the range, and rates of 

 decay as high as the seventh power have sometimes 

 been observed. Factors which may contribute to this 

 unexpectedly high decay rate are: (1) a decrease in 

 the surface scattering coefficient m' as the incident 

 sound ray becomes more nearly horizontal; (2) at- 

 tenuation ; (3) the sound-shadowing effect of surface 

 water waves; and (4) image interference, that is, the 

 interference between direct and surface-reflected 

 waves. 



Dependence on Wind Force 



The wind-speed dependence of surface reverbera- 

 tion is most marked at short ranges. At ranges of 

 1,500 yd or more, with horizontal beams, the received 

 reverberation does not depend on wind speed, and for 

 this reason is ascribed to scattering from the volume 

 of the sea. At a range of 100 yd, as the wind speed 

 increases from 8 to 20 mph, the median reverberation 

 level rises steeply in a manner roughly described by 



equation (6) of Chapter 14. With horizontal beams, 

 little increase in level has been observed as the wind 

 speed increases from zero to 8 mph, or as it increases 

 beyond 20 mph. 



Dependence on Frequency 



The frequencj'-dependent terms in equation (7) 

 are the surface-reverberation index Js{9), the trans- 

 mission anomaly term 2.4, and possibly the surface- 

 scattering coeflSciert m'. The value of Js(,B) can be 

 determined from the pattern function of the trans- 

 ducer, by equations (40), (41), and (42) of Chapter 

 12. The transmission anomaly can be estimated by 

 the methods described in Chapter 5 of Part I. Un- 

 fortunately, there are no experimental data on the 

 variation of surface scattering coefficients with fre- 

 quency. 



Magnitude of the Surface-Scattering 

 Coefficient 



The magnitude of 10 log m' can be obtained from 

 comparison of equation (7) with the measured rever- 

 beration at any range. Although this process is open 

 to criticism, since equation (7) does not describe the 

 range dependence of surface reverberation very well, 

 it furnishes us with the only information we now 

 have on the magnitude of the surface scattering 

 coefficient. 



By using equation (7), it appears that the increase 

 in surface reverberation at 100 yd as the wind speed 

 increases, noted in the preceding subsection, is due to 

 increases in the surface scattering coefficient m' as 

 the sea becomes rougher. Thus, at a range of 100 yd 

 the median values of 10 log m' obtained by comparing 

 equation (7) with measured levels are —57 db at 

 wind speeds less than or equal to 8 mph, and —22 db 

 at wind speeds greater than 20 mph. At 1,000 yd, for 

 wind speeds greater than 20 mph, 10 log m' averages 

 — 31 db. It does not seem possible according to 

 Section 14.2.5 to interpret the reverberation meas- 

 ured at high wind speeds as a result of scattering from 

 a dense layer of bubbles. 



17.2.3 Deep- Water Levels with 

 Horizontal 24-kc Beams 



For prediction of deep-water, 24-kc reverberation 

 levels with horizontal beams, Figure 31 of Chapter 14 

 can be used. This figure shows the highest reported 

 reverberation levels, the lowest reported levels, and 

 the median levels, for various ranges and wind speeds. 



