216 



TRANSMISSION OF EXPLOSIVE SOUND IN THE SEA 



RANGE 



FIRST ARRIVAL OF GROUP 

 RANGE 



SECOND AND THIRD ARRIVALS, 

 COINCIDENT IF, AS SHOWN HERE, SOURCE 

 AND RECEIVER ARE AT THE SAME DEPTH 

 RANGE 



RANGE 



• SOURCE LAST ARRIVAL OF GROUP 



©RECEIVER 



Figure 20. Grouping of arrival times for sound chan- 

 nel rays. The four ray paths shown each have two 

 lower half-cycles, and the corresponding times of travel 

 are therefore close together, so that the four arrivals 

 form a group. 



receiver are both on the axis they cease before the 

 "piling up" of the sound channel rays. This is shown 

 in Figure 19B for the particular set of conditions 

 chosen for that figure. 



The bottom-reflected rays (type III in Figure 17) 

 have times of arrival which are also interspersed 

 among those of type I, but which continue after the 



latter have ceased. Figure 19C shows these arrivals 

 for the example treated. The grouping for these rays 

 is again in threes or fours, according to whether 

 source and receiver are at the same or different 

 depths. 



Let us now consider the energies and intensities of 

 the system of impulses arriving at the receiver. First 

 of all, it may be noted that all the energy emitted 

 by the source in directions giving rays of type I, i.e., 

 for the cases of Figure 18 in directions within + 12.2° 

 of the horizontal, is propagated along the sound 

 channel and cannot disappear except by volume 

 absorption or scattering in the water. If the latter 

 processes are neglected, the total energy in the 

 system of impulses transmitted by these unreflected 

 rays, that is, the system exemplified by Figure 19A, 

 must be inversely proportional to the horizontal 

 range. This contrasts with propagation in an infinite 

 homogeneous medium, where the energy given to a 

 receiver varies inversely as the square of the distance. 

 The intensities of the individual arrivals can be calcu- 

 lated in the usual way from ray theory, which should 

 be applicable to the earlier arrivals, before there is 

 appreciable overlapping of consecutive pulses. It will 

 be apparent after a little pondering on Figure 17 that 

 in general these individual intensities must vary ap- 

 proximately as the inverse square of the range, the 

 slower rate of decay of the total energy being due 

 to the increase in the number of arrivals as the range 

 increases. For certain positions of source and re- 

 ceiver, however, some of the arrivals may have an 

 anomalously high intensity due to the fact that two 

 rays of infinitesimally different initial inclinations 

 are tangent at the receiver. This condition will be 

 more closely approached for the latest sound channel 

 arrivals to reach the receiver than for the earher ones, 

 and accordingly these latest arrivals should be the 

 strongest. 



The energy traveling along paths involving reflec- 

 tion from the surface or the bottom is channeled in a 

 similar manner. The bottom-reflected rays, however, 

 lose a considerable part of their energy at each re- 

 flection, and therefore die out more rapidly with in- 

 creasing range than the others. (See Figure 21 of 

 Section 9.3.2 and Section 9.4.1.) For the same reason 

 successive arrivals of this type have progressively de- 

 creasing intensities. 



9.3.2 Experimental Results 



Two series of experiments on long-range transmis- 

 sion in deep water have been conducted by WHOI.-"' ^' 



