314 



SHALLOW-WATER REVERBERATION 



Table 1. Ranges at which rays leaving the projector at different angles strike the bottom. 



15.3 BOTTOM SCATTERING COEFFICIENTS 



Having established the probable limits of the 

 range to the reverberation peak, it is desirable to 

 estimate the height of the reverberation peak. This 

 height has been found to depend markedly on the 

 type of bottom. Id general, reverberation is highest 

 over ROCK, less over SAND-AND-MUD or MUD, 

 and least over SAND, although in some cases rever- 

 beration over SAND has been reported to be quite 

 high, especially after a storm when rippling of the 

 bottom may be the cause.' The relative values of 

 the reverberation over these bottoms may be ex- 

 pressed in terms of the bottom-scattering coefficient 

 m", by using equation (54) of Chapter 12 if the trans- 

 ducer directivity and the transmission to the bottom 

 are known in detail. Detailed information concerning 

 directivity and transmission has not usually been 

 available, but it has proved possible to determine 

 average values for the bottom scattering coefficients 

 by making reasonable assumptions about the trans- 

 mission. 



In this section, we shall summarize present infor- 

 mation concerning the variation of the' bottom scat- 

 tering coefficient m". The three factors which are ex- 

 pected to be most important in determining the value 

 of m" are (1) the grazing angle of the sound incident 



on the bottom, (2) the frequency of the incident 

 sound, and (3) the nature of the bottom. These 

 factors will be considered in the same order. 



15.3.1 Dependence on Grazing Angle 



Knowledge of the nature of the dependence of m" 

 on grazing angle is necessary for the detailed predic- 

 tion of bottom reverberation as a function of range; 

 in addition, the nature of this dependence is of 

 theoretical interest. It has been shown in Chapter 14 

 that, with simple assumptions about the law of 

 scattering, for a very thin scattering layer the value 

 of the backward scattering coefficient should de- 

 crease with decreasing grazing angle at least as 

 rapidly as sin d; and for scattering obeying Lambert's 

 law the backward scattering coefficient should be 

 proportional to sin'' 0. Thus, determination of the 

 dependence of m" on angle can furnish information 

 about the law of scattering at the bottom and can 

 also be used to check the validity of our ideas about 

 bottom reverberation. 



However, determination of this dependence is not 

 easy. It would appear at first thought that the de- 

 pendence would be an easy by-product of the analysis 

 of ordinary reverberation runs with horizontal trans- 

 ducers if temperature-depth data were also available. 



