222 



TRANSMISSION OF EXPLOSIVE SOUND IN THE SEA 



e.2 



2.0 



o 

 HI o 1.6 



O III '" 



1.4 



«¥ 



o 5 



III o 



1.0 



0.8 



0.6 



0.4 



o.e 



800 



RANGE IN YARDS 

 2400 3200 



4800 



"T I I I I I *T I I I 1 I 1 1 I I I I I I I I I 1 I T" 



02 



0.4 



0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.2 2.6 2.8 



TRAVEL TIME OF DISTURBANCE PROPAGATED THROUGH THE WATER IN SECONDS 



3.0 3.2 3.4 



Figure 24. Typical plot of travel time against range showing layer structure of the bottom. Location near Solomons, 

 Md., at mean depth of 52 ft, charge and hydrophone both resting on bottom. Lines cross at r/c = 1.08 seconds. Depth of 

 upper layer in bottom = r/c Vci — Ci/c» + Ci = 1,240 feet, where r = range at which hnes cross, c = velocity of sound 

 in water, ci = velocity of sound in upper layer of bottom, and Cj = velocity of sound in lower layer of bottom. 



as well as the velocities of all these strata can be de- 

 termined from this plot of arrival times. This type 

 of analysis has long been familiar in geophysical 

 prospecting. 



Figure 24 shows a typical plot of arrival times con- 

 structed from some of the data obtained by WHOI,^^ 

 with the layer depths and velocities deduced from it. 

 The shots were made with both the charge and the 

 hydrophone on the bottom, so the depth of the upper 

 layer of the bottom can be calculated from equation 

 (8) by replacing c by ci and Ci by C2. When more than 

 two layers are involved, the plot of times of first ar- 

 rival will still consist of straight-line segments, but 

 the calculation of the depths of the second and 

 deeper layers involves more complicated formulas 

 in that case. 



The representation of the plotted points by two 

 straight lines is fairly easy for this case; however, 

 data are often obtained for which the times of first 

 arrival seem to form an almost smooth curve. This 

 may sometimes be due to the absence of any well- 



defined layer structure in the bottom, as might be 

 the case for example for a thick mud bottom whose 

 compactness increases continuously with depth. It 

 will be shown in Section 9.4.3, however, that there 

 are many cases where there are recognizable layers 

 in the bottom but where fluctuations of one sort or 

 another prevent them from being accurately identi- 

 fied from mere arrival time data. For such cases the 

 proper choice of straight lines to fit a plot such as 

 Figure 24 may sometimes be facilitated by a study 

 of the predominant frequencies in the first and 

 subsequent arrivals (see Figure 32, Section 9.4.3). 



9.4.2 Simplified Theory of Normal 

 Modes 



We have seen in the preceding Section 9.4.1 that if 

 the range is sufficiently long compared with the dis- 

 tances of source and receiver above the bottom, the 

 first sound to arrive must come by a path lying 

 within the material of the bottom over most of the 



