306 



DEEP-WATER REVERBERATION 



have shown that the main beam from standard 24-kc 

 gear will usually reach a depth of 1,000 ft at a range 

 of about 2,000 yd. The median curve for volume re- 

 verberation in Figure 31 does not show any evidence 

 of an increase in the volume-scattering coefficient at 

 long ranges; it will be recalled that the value of 

 10 log m in these deep layers frequently exceeded the 

 mean value of 10 log m in the ocean by 15 db or more. 

 However, it appears that this failure to observe the 

 deep layer must have been due to sampling. More 

 recent studies by UCDWR, still unpublished, show 

 that the deep layer is frequently discernible as a very 

 definite bulge on the reverberation curve. These new 

 data also show that the maximum value of 10 log m 

 is —50 db or perhaps even slightly higher rather than 

 the —60 db value indicated by Figure 31. 



From Figure 31 and from equation (26) of Chap- 

 ter 12, we may conclude that the backward volume- 

 scattering coefficient m for horizontally projected 

 24-kc beams varies between 10~* and 10~' per yd 

 with 10~* the typical value. It will be noted that the 

 dimensions of m in equation (26) of Chapter 12 are 

 per yard; values of m expressed per foot will be one- 

 third or 5 db less. Also, from Chapter 12, we recall 

 that this value of m is about 3 db greater than the 

 "true" value of the backward-scattering coefficient 

 of the ocean. Since equation (45) of Chapter 12 does 

 not describe the range dependence of surface rever- 

 beration very well, determination of the surface 

 scattering coefficient m' from comparison of that 

 equation with Figure 31 is not very meaningful. 

 However, if we make the comparison, with A set 

 equal to 4 db per kyd and /, set equal to — 16 db, '* 

 the median values of 10 log m' at ranges of 100 and 

 1,000 yd for wind speeds greater than 20 mph are 

 respectively —22 db and —31 db. (Note that m' is a 

 dimensionless quantitj\) 



It will be recalled that at the beginning of this 

 chapter we assumed that surface reverberation could 

 be eUminated by pointing the transducer downward. 

 Off the main lobe, the response 6(9,0) of standard 

 24-kc transducers is usually assumed to average 

 about 30 db less than the peak response on the main 

 lobe,'' but this is only an approximate average value. 

 Using this 30-db estimate, we see from Figure 31 that 

 at ranges of 100 yd, in high sea states, surface rever- 

 beration may exceed volume reverberation even with 

 the transducer directed downward, but only if the 

 volume reverberation level is close to the minimum 

 values observed. At ranges greater than about 500 

 yd, or with wind speeds less than about 15 mph, 



pointing the transducer downward should usually 

 eliminate .surface reverberation (see Figure 20). This 

 estimate of the wind speeds and ranges at which sur- 

 face reverberation can be eliminated by pointing the 

 transducer downward assumes, however, that the 

 volume reverberation with the transducer pointed 

 downward is the same as when the transducer is hori- 

 zontal. Measurements reported in reference 2 sug- 

 gest that the volume scatterers are anisotropic and, 

 specifically, have a smaller backward-scattering 

 coefficient when the sound arrives from a vertical 

 direction than when the sound arrives from a hori- 

 zontal direction. However, the observed difference in 

 10 log m was only about 6 db and thus hardly affects 

 the conclusion stated previously that surface rever- 

 beration can almost always be eliminated by pointing 

 the transducers downward. 



14.2.5 Scattering Coefficient of a 

 Layer of Bubbles 



It is of interest to compare the median values of 

 10 log m' obtained from Figure 31 with the values ex- 

 pected if the surface consisted of a dense layer of 

 resonant bubbles. The theory of air bubbles in water 

 is given in Chapter 28; the geometry of scattering by 



Figure 32. Scattering from surface layer of bubbles. 



such a layer is illustrated in Figure 32. By definition, 

 a densely populated layer of bubbles is one in which 

 the attenuation is so high that there is essentially 

 infinite transmission loss through the layer. For this 

 reason, in Figure 32, energy reaches the scatterer at 

 X and returns to the scatterer at along the direct 

 path OAX only; scattering along a path reflected 

 from the air-water interface, such as OBX, can be 

 neglected since almost no energy reaches B. It fol- 

 lows from bubble theory that multiple scattering can 

 be neglected as well. Neglecting refraction, the 

 expected reverberation intensity can now be calcu- 

 lated directly from equation (29) of Chapter 12, 

 using 



h = '— e-^-« (11) 



m 



No 



(12) 



