BOTTOM SCATTERING COEFFICIENTS 



319 



value of m" for ROCK in Table 2. It is seen that there 

 is very good agreement with Table 2 for Area I, but 

 there is a difference of 10 db between the value of m" 

 (30 degrees) obtained at Area II and the value of w" 

 (30 degrees) in Table 2. This difference could be due 

 to sampling error; it is estimated later that the 

 quartile deviation of m" for areas of similar bottom 

 classification is + 5 db. In this regard it is significant 

 that reference 6 states that the bottom of Area II 

 had patches of SAND-AND-MUD. Thus, it is not 

 too surprising that the mean bottom scattering coeffi- 

 cient in Area II should be lower than in Area I, 

 where, according to reference 6, the bottom was 

 covered with boulders. 



The results of reference 6 give no information on 

 the dependence of m" on frequency for other types of 

 bottom thanROCK. There is no reason to expect that 

 any marked dependence on frequency would be dis- 

 covered. However, it is necessary to definitely know 

 the frequency dependence, if any, in order to predict 

 the effect on bottom reverberation of varying the 

 frequency of echo-ranging gear. Also, knowledge of 

 this frequency dependence would enable us to assess 

 accurately the present information on the dependence 

 of m" on bottom type, much of which is based on the 

 assumption that m" does not depend on frequency. 

 For these reasons it would be desirable to obtain 

 additional measurements over all types of bottom of 

 the dependence of m" on frequency. 



15.3.3 Dependence on Bottom 



An analysis of bottom-scattering data obtained 

 with horizontal beams is given in reference 3. These 

 data include many more records than are analyzed 

 in reference 2, among which are data at 10, 20, and 

 24 kc. A portion of the data was analyzed in a manner 

 similar to that used in reference 2, except that absorp- 

 tion was not included in the transmission anomaly; 

 the transmission anomaly A in equation (54) was 

 computed from the refraction pattern alone. This 

 analysis gave the results listed in Table 4 for a graz- 

 ing angle at the bottom of 10 degrees. In Table 4, as 

 in Table 2, the values of to" have been corrected to 

 the true values. Table 4 should, of course, be com- 

 parable with the 0-degree column of Table 2, since 

 the grazing angle on the bottom (10 degrees) is the 

 same for both tables. 



In reference 3, in addition to this analysis, a more 

 complicated analysis was also attempted to deter- 

 mine the variation of the bottom-scattering coeffi- 



cient with angle of incidence. Some evidence that m" 

 increased with increasing grazing angle was found, 

 but it was not possible to decide which of the three 

 laws, m" constant, m" proportional to sin 6, or m" 

 proportional to sin^ d, was most nearly representative 

 of the bottom scattering. In view of the inconclusive 

 nature of the results, and also because this analysis 

 rested on some questionable assumptions, these re- 

 sults for the angular dependence of to" were not in- 

 cluded in Section 15.3.1. 



Table 4. Average values of 10 log m" for various bottom 

 areas for grazing angle at bottom of 10 degrees. 



The value of to" for the ray leaving the projector 

 at an angle of 5 degrees was relatively independent of 

 the assumptions made. The values of to" for this ray 

 are given in Table 5. Table 5 includes, for some of the 

 records studied, the grazing angle of the 5-degree ray 

 as calculated from the measured BT pattern. It is 

 seen that in general the 5-degree ray strikes the bot- 

 tom at -a grazing angle of about 10. degrees; thus 

 Table 5 should be comparable with Tables 2 and 4. 



From Tables 2, 4, and 5 we can now determine, for 

 each bottom type, the average value of m" for a 

 grazing angle on the bottom of 10 degrees. To do 

 this, we recall that Tables 4 and 5 were obtained on 

 the assumption that the transmission anomaly was 

 due to refraction alone, that is, that the absorption 

 loss was negligible. However, the values of m" in 

 Tables 4 and 5 can be corrected for absorption in the 

 following waj'. It can be assumed, from previous dis- 

 cussions in this chapter, that on the average the 

 ranges at which the data of Tables 4 and 5 were 

 evaluated were six times the depth of the projector 

 above the bottom. These depths are given for the 

 measurements listed in Table 5; for the items in 

 Table 4 they can be obtained from Table 2 of refer- 

 ence 6. Thus, the average absorption loss can be cal- 

 culated at each frequency for each entry in Tables 4 

 and 5, by assuming median values of the attenuation 

 coefficient at each frequency (see Figure 17 of Chap- 

 ter 5). If we increase m" by the average two-way 



