BOTTOM SCATTERING COEFFICIENTS 



317 



coefficient. The values of 10 log m" shown hi the 

 first column of Table 2 are true values, that is, they 

 are 6 db smaller than the values found from com- 

 parison of equation (54) of Chapter 12 with the ob- 

 served reverberation levels. On the other hand, no 

 such 6-db correction for surface reflection was neces- 

 sary for 30-degree data, since at the latter transducer 

 orientation almost none of the projected sound 

 strikes the surface before reaching the bottom.* 



Having described the procedure for calculating the 

 0- and 30-degree columns in Table 2, we now proceed 

 to use these entries for an estimate of the angular de- 

 pendence of m". It will be recalled that for all the 

 0-degree entries the grazing angle of the sound on the 

 bottom lay between 9 and 13 degrees; for present 

 purposes the grazing angle for all the 0-degree entries 

 may be taken as 10 degrees. The grazing angle for all 

 the 30-degree entries may be taken as 30 degrees, 

 since at such a great angle of depression the effect of 

 refraction is negligible. Thus for each of the bottom 

 types considered, we have in Table 2 an m" for a 

 1 0-degree grazing angle and an m" for a 30-degree 

 grazing angle. By assuming a relationship of the 

 form 



m" ~' sin* {d), 



it is possible to calculate k for each bottom type. The 

 resulting values of k, rounded off to the nearest half- 

 digit, are displayed in the last column of Table 2. 



These values of k are not too reliable, since in order 

 to calculate the individual scattering coefficients in 

 Table 2 a number of assumptions were required 

 about such questions as the proper method for 

 averaging data obtained on different days, and the 

 proper comparison between the point and band 

 methods of averaging when the reverbeffetion levels 

 are changing rapidly. These assumptions, described 

 in detail in reference 2, mean that the results of 



» It will be recalled that a 6-db correction was argued in 

 Section 12.5 for surface scattering coefficients. It may be 

 thought that a similar correction should be applied to bottom 

 scattering coefficients, to take account of possible reflections 

 in the layer of scattering material at the bottom. This correc- 

 tion arises, in the case of surface scattering, because the scat- 

 terers are thought to extend an appreciable distance into the 

 water side of the air- water boundary; sound can penetrate the 

 scattering layer and strike the air-water boundary at which 

 most of the actual reflection takes place. For bottom scatter- 

 ing, on the other hand, although the bottom scattering layer 

 is not infinitely thin, most of it does lie on the solid side of the 

 twilight region separating the sea volume from the earth's 

 crust. Thus, there is no need to introduce a correction to 

 bottom scattering coefficients due to reflection at the bottom; 

 in fact such a correction, if introduced, would have no physical 

 significance. 



Table 2 may be somewhat in error. Nevertheless, 

 Table 2 does indicate that the value of m" increases 

 at least as rapidly as the first power of sin d for 

 grazing angles between 10 and 30 degrees. 



The data of reference 2 give no information on the 

 nature of m"{d) for grazing angles d less than 10 de- 

 grees. It was assumed in reference 1, from which 

 Figure 4 was taken, that m" is proportional to sin^ d 

 for angles d greater than 9 degrees, and was constant 

 independent of 6 for angles 6 less than 9 degrees. The 

 solid lines in Figure 4 are the reverberation levels 

 predicted on this basis and fit the observed points 

 very well, even at the extreme range of 360 yd on the 

 lower curve, where the grazing angle is only 4 degrees. 

 The very good fit evidenced in Figure 4 seems to indi- 

 cate that m" is constant independent of grazing angle 

 at angles less than 10 degrees. However, there is al- 

 most no other information on the dependence at 

 angles less than 10 degrees; and a constancy of scat- 

 tering coefficient as the grazing angle decreased be- 

 low 10 degrees would make the law of scattering a 

 very complicated function of angle at these small 

 angles. For these reasons it is probably best to regard 

 the dependence of m" on grazing angle for angles less 

 than 10 degrees as still uncertain. More measure- 

 ments of this dependence are needed; to obtain values 

 of m" at small grazing angles, it will be necessary to 

 make measurements in isothermal water. 



Impossibility of Determining m"{e) with 

 Horizontal Beams 



We shall now discuss why it was not possible, from 

 the 0-degree data alone, to determine the dependence 

 of m" on grazing angle on the bottom. Two factors 

 are involved: (1) uncertainty in the beam pattern 

 correction, and (2) the lack of any large variation in 

 the grazing angle, owing to the effect of refraction. 



For horizontal transducers, the beam pattern cor- 

 rection as determined from equation (41) of Chapter 

 12 is small for values of 6 less than 6 degrees (see 

 Table 1, Chapter 12). At larger angles the correction 

 increases rapidly because of the sharp decline in the 

 measured beam pattern at the edge of the main lobe. 

 At an angle of 10 degrees, for example, the correction 

 is about 20 db. The application of this large correc- 

 tion appeared to seriously overcorrect the data 

 analyzed in reference 2, giving very large values of 

 m" at close ranges. It is not difficult to find reasons 

 for this inability to calculate m" correctly at angles 

 well off the main lobe. In the first place, the very use 

 of equation (41), Chapter 12, for the beam pattern 



