TRANSDUCER HORIZONTAL 



301 



layer and is difficult to estimate. If the attenuation 

 is as large as 1 db per yd, a value which is observed 

 in wake measurements (see Chapter 35), equation (9) 

 would be satisfied even with very large values of h. 

 In fact, it is obvious that the relation (9) will always 

 be satisfied if 



(Cor)a»l. 



(10) 



If (8) is not satisfied, it is easy to see that (9) will not 

 be satisfied if (10) is violated. 



We may summarize this discussion of the validity 

 of the argument that m' should decrease at least as 

 rapidly as sin d by stating that the argument may be 

 correct, but requires further quantitative informa- 

 tion on the thickness of the scattering layer and the 

 attenuation to be expected in the layer. Until this 

 information is forthcoming, the hypothesis that m' 

 decreases with decreasing angle of incidence on the 

 surface is not a wholly acceptable explanation of the 

 variation of surface reverberation with range. 



At small grazing angles, the peaks of the water 

 waves are sometimes hidden from the sound source 

 by the troughs. This shadowing effect of waves also 

 causes a reduction of the irradiation of the surface. 

 If the scatterers are largely concentrated in a layer 

 whose depth is small compared with the wave height, 

 a reduction in reverberation might be expected at 

 small grazing angles. Since the grazing angle decreases 

 with increasing range, this effect could account for 

 the rapid decrease of surface reverberation. This 

 hypothesis of the shadowing effects of waves has the 

 added virtue that it explains the increasing rate of 

 decay with increasing sea state, since the larger the 

 waves the more important this effect would be. How- 

 ever, this hypothesis is much too qualitative to be 

 accepted without further study. It can be seen that 

 phenomena in high sea states may actually tend to 

 make the reverberation increase with increasing 

 range rather than decrease. For example, in high sea 

 states, at long range, the sound rays may make large 

 angles of incidence with the wave troughs, thereby 

 increasing considerably the sound returned back to 

 the transducer. A quantitative evaluation of the 

 shadowing effect of waves is difficult and requires a 

 detailed examination of surface roughness. Several 

 papers issued by UCDWR '~^' are initial attacks on 

 the theory of surface scattering. That the nature of 

 the surface irregularities will affect surface rever- 

 beration seems almost intuitively obvious. Another 

 report " describes measurements in which definite 

 structure was found in surface reverberation. On this 



day there were strong swells with a wind speed of 

 16 to 19 mph. Distinct blobs were observed in the 

 reverberation, and these blobs altered their range at 

 a rate equal to the rate at which the surface swells 

 were moving. These blobs could be identified much 

 more readily on the chemical recorder than on the 

 oscilloscope record, where the wealth of detail con- 

 fused the general picture. In Section VII of reference 

 1, no difference was observed in reverberation meas- 

 ured with the projector beam parallel to and perpen- 

 dicular to the wave fronts. 



A wave in water reflected at the water-air bound- 

 ary suffers a change in phase of the sound pressure 

 (see Chapter 2). This change of phase results in inter- 

 ference between the direct and surface-reflected rays; 

 the transmission loss between the projector and 

 points near the surface may be increased to a value 

 much greater than the inverse square loss used in 

 deriving equation (43) of Chapter 12. Furthermore, 

 the increase in transmission loss will be a function 

 of the range and of the distance of the scatterer from 

 the surface, and will increase with decreasing depth 

 and increasing range. Thus if the scatterers are lo- 

 cated in a thin layer near the surface, this interfer- 

 ence between direct and surface-reflected waves may 

 explain the observed rapid decrease of surface rever- 

 beration. As with the previous hypothesis of wave 

 shadowing, it is necessary to make a quantitative 

 investigation of this image interference effect before 

 accepting it as an explanation of the range depend- 

 ence of surface reverberation. For a plane surface, it 

 is shown in Section VI of reference 1 that image inter- 

 ference can lead to a decrease of surface reverbera- 

 tion proportional to the seventh power of the range; 

 consequently, this effect could account for the ob- 

 served slopes of Figures 23 and 24. However, the 

 surface is not plane. An approximate treatment of 

 the effect of surface roughness in reference 1 shows 

 that the image interference effect becomes less im- 

 portant as the surface roughness is increased. Thus 

 if image interference is causing the range dependence, 

 the slope of surface reverberation should decrease 

 with increasing sea state, which is contrary to what 

 is observed. Another inference from the theory of the 

 image interference effect is that surface reverbera- 

 tion should increase rapidly with frequency at ranges 

 where the interference is important. Unfortimately, 

 there are no experiments on the variation of surface 

 reverberation with frequency. 



It may be concluded from this discussion of the 

 range dependence of surface reverberation that the 



