138 



SHALLOW-WATER TRANSMISSION 



of material capable of shear stress, like rock, and is 

 frequently rough. It is, therefore, simpler to deter- 

 mine the coefficient of reflection experimentally than 

 to attempt to obtain it from the mechanical param- 

 eters of the two substances separated by the inter- 

 face. 



A rough bottom will not only give rise to a trans- 

 mitted sound wave, which disappears from the ocean, 

 and a specularly" reflected wave, but will also scatter 

 soimd in a random fashion. The soimd beam resulting 

 from the reflection of a plane wave incident on a 

 bottom of moderate roughness has a certain direc- 

 tivity pattern. If the roughness is not excessive, this 

 directivity pattern will show an intensity maximum 

 in the direction which corresponds to specular re- 

 flection from the bottom. The smoother the bottom, 

 the more highly directive or collimated is the re- 

 flected sound beam. 



Any nonspecularity of the reflection at the bottom 

 has essentially the same effect as would a broadening 

 of the directivity pattern of the projected beam. This 

 increased divergence will not, however, always cause 

 a decrease in the peak level of the received signal. If 

 the bottom is smooth or only moderately rough, and 

 if projector and receiver are not too highly directional, 

 there should be little or no decrease in the peak signal 

 level. This is because, on the average, as much energy 

 will be deflected toward the hydrophone by non- 

 specular reflection as will be lost out of the main beam 

 through the same mechanism. Excessive roughness 

 of the bottom, however, should cause a decrease in 

 the peak signal level unless the projector is nondirec- 

 tional and a long pulse is used. The reason for speci- 

 fying a long pulse is that some of the sound scattered 

 toward the hydrophone by a very rough bottom will 

 travel paths much longer than the path correspond- 

 ing to specular reflection. Thus, when short pulses of 

 sound are projected over a rough bottom, the re- 

 ceived signal will last longer than the transmitted 

 signal. Although the total energy received at the 

 hydrophone may be the same as if the bottom were 

 smooth, the peak signal level will be lower. 



6.1.2 Velocity Gradients and 



Wind Force 



The magnitude of the contribution of bottom-re- 

 flected sound to the total sound field will depend not 

 only on the acoustic properties of the bottom, but 



" Specular reflection is reflection for which angles of inci- 

 dence and reflection are equal. 



also on refraction conditions in the body of the sea 

 and on the reflectivity of the sea surface. 



The bottom should probably be of little importance 

 if upward refraction in the sea volume prevented 

 most of the sound energy from ever reaching the 

 bottom. We may therefore tentatively predict that 

 in the presence of positive gradients there will be no 

 difference between deep-water transmission and shal- 

 low-water transmission. On the other hand, in the 

 presence of downward refraction the bottom should 

 usually play a role of some importance. If the bottom 

 is a very poor reflector of sound, then the sound field 

 should not differ significantly from the sound field in 

 deep water under similar refraction conditions, since 

 bottom-reflected sound will make only a slight con- 

 tribution to the total sound field. But if the ocean 

 bottom is a good reflector, then the contribution of 

 bottom-reflected sound will be significant. This con- 

 tribution will increase in importance as the down- 

 ward refraction becomes sharper and removes more 

 and more energy from the direct sound field at long 

 range. 



In addition, if the ocean bottom reflects sound 

 fairly well, the sound field intensity at long range will 

 probably be increased appreciably by sound which 

 has been reflected several times between the ocean 

 surface and the ocean bottom. We should, therefore, 

 look for a dependence of the shallow-water sound field 

 on the roughness of the sea surface. 



The quantitative prediction of sound field levels in 

 shallow water, by combining the information on bot- 

 tom and surface reflectivity with that on refraction 

 conditions, would be very difficult. The bulk of the 

 reliable information on shallow-water transmission 

 has been obtained directly by means of transmission 

 runs. The qualitative considerations of this section, 

 however, have been valuable in planning these trans- 

 mission runs and in interpreting the resulting sound 

 field data. 



6.1.3 Effects of Frequency on 

 Spreading Factor 



It was shown in Section 5.2.2 that the attenuation 

 of sound in deep water depends strongly on the 

 frequency. It has been tentatively suggested that the 

 observed dependence of attenuation on frequency 

 might be fitted by a 1.4th power law.^ It might be 

 expected that a formula of the form 



H = aR + 20 log R (2) 



would not be applicable for transmission in shallow 



