LONG-RANGE SOUND CHANNEL PROPAGATION 



215 



-1.9 



-».» 



TIME IN SECONDS 

 -O.a O 0.5 



1.5 



-I — 



2.S 



' — , — ' > >— 



S 6 



6 9 10 



I 



II 121 



TYPE I OR SOUND CHANNEL RAYS WHICH STRIKE NEITHER SURFACE NOR BOTTOM 



TYPE m OR BOTTOM REFLECTED RAYS 



Figure 19. Times of arrival for the various rays connecting two points on the axis of a sound channel. Range, 400 kyd = 

 197 miles. Velocity-depth curve assumed same as for Figures 17 and 18. The numeral below each arrival gives the num- 

 ber of lower half-cycles in the corresponding ray path. The zero of time is taken as the time of arrival of the axial ray. 



dependent on the number of lower half -cycles which 

 occur during the passage from source to receiver. In 

 the example of Figure 20, there are four rays which 

 have two lower half-cycles between source and re- 

 ceiver; however, two of these four, namely, the ones 

 with two upper half -cycles, arrive at the same time so 

 there will be only three resolvable arrivals. When 

 source and receiver are at different depths, the rays 

 analogous to those in Figure 20 will all arrive at 

 different times, and the hydrophone will receive 

 pulses in groups of four. For the later arrivals, the 

 upper half -cycles have more nearly the same travel 

 time as the lower half-cycles, and the pulses no longer 

 arrive in clearly separated groups of three. 



When either the source or the receiver is at some 

 distance from the axis of the sound channel, the 

 piling-up effect shown in Figure 19A will not occur, 

 since only a limited number of rays will be possible 

 between source and receiver. 



So far we have not considered sound which arrives 

 at the receiver by paths involving surface or bottom 

 reflection. The rays which undergo surface reflection 

 and upward refraction without reaching the bottom 

 (type II in Figure 17) have mean horizontal velocities 

 which, according to Figure 18, are slower than the 

 fastest unreflected, or type I rays, but faster than the 

 axial ray. Thus the arrivals for rays of this sort are 

 mixed in with those of type I, but when source and 



