286 



DEEP-WATER REVERBERATION 



33" 



32" 



31° 



30° 



29° 



2 8° 



119° 



118° 



117" 

 LONGITUDE 



116° 



115° 



Figure 6. Locations where reverberation was meas- 

 ured in 1943 cruise. 



straight line. The slope of this line will determine a, 

 the attenuation coefficient in decibels per kiloyard; 

 and the intercept of the line at zero range will deter- 

 mine the value of the true scattering coefficient m. 



However, the very existence of the systematic in- 

 crease in reverberation levels at about 1,000 ft ob- 

 served in Figures 7 and 8 means that the ocean is 

 probably not homogeneous with depth; thus a 

 straight-line dependence of 10 log M on depth could 

 hardly be expected in this experiment. Figure 10 is a 

 plot of the mean values of 10 log M for the nine sets 

 of records observed in the period January 17 to 20, 

 1943, at the positions shown in Figure 6. It is obvious 

 from Figure 10 that even if the points in the deep 

 layer between 1,000 and 1,500 yd are ignored, no 

 good fit to the data could be obtained with a straight 

 line. 



The failure to obtain a straight-line dependence in 



Figure 10 means that either m or a, or both, change 

 with depth. It is possible to obtain further informa- 

 tion from Figure 10 by comparing the dependence on 

 depth at different frequencies. From equation (1), for 

 any two frequencies /i and f^, 



101ogS^ = 101og''^^^^^ 



'M(f,) 



in(j2) 

 - 2[a(/i) 



a(/2)] 



1,000 



(2) 



If the variations in m are caused only by changes in 

 the number of scatterers per unit volume, then 

 w(/i)/m(/2) should be independent of depth. Thus, 

 if the attenuation is independent of depth, 10 log 

 M{Ji)/M{f2) in equation (2) should be a hnear func- 

 tion of depth in these runs with the transducer di- 

 rected vertically downward. Figure 11 is a plot of 

 this ratio against depth, from the data of Figure 10, 

 for the six pairs of frequencies involved. Only three 

 of the ratios are independent ; the other three can be 

 calculated from the first three. All the ratios are 

 shown in Figure 11 for comparison. Although most 

 of the graphs show general tendencies to slope in the 

 direction of increasing attenuation at higher fre- 

 quencies, systematic deviations from the straight 

 line predicted by equation (2) are noted. It appears 

 then that either the kind of scatterer changes with 

 depth or the attenuation coefficient varies with 

 depth. 



At distances less than 250 ft, attenuation is small, 

 even at 80 kc. Thus the scattering coefficients in the 

 upper 250 ft of the ocean can be computed from 

 vertical reverberation runs without knowledge of the 

 attenuation coefficient. Mean values of 10 log M = 

 10 log m, averaged over seven depths between the 

 surface and 250 ft, are plotted in Figure 12 as a func- 

 tion of frequency, for each of the nine positions of the 

 sending-receiving ship during January 1943 (Figure 

 6). The solid lines are empirical curves and the dashed 

 lines represent a theoretical relationship discussed 

 later. The shapes of the empirical graphs for the 

 different positions bear little resemblance to each 

 other. However, the two curves for position III, 

 which represent data taken 20 hours apart, reproduce 

 each other almost to within sampling error. The 

 curves for positions I and VIII, which were close to- 

 gether in space but separated by 72 hours in time, 

 are also nearly identical. If these resemblances are 

 not accidental, they suggest that position is a more 

 important factor than time in determining the value 



