SHORT-RANGE PROPAGATION IN DEEP WATER 



197 



tion data from the standpoint of Fourier analysis will 

 be given in Section 9.2.4. In comparing the attenua- 

 tion of explosive sound with that of sinusoidal sound, 

 however, it must be kept in mind that the mechanism 

 responsible for attenuation of the peak pressure in the 

 initial pulse from an explosion is somewhat different 

 at short and long ranges. At long ranges one may ex- 

 pect that linear absorption and dispersion will ac- 

 count for the decay and change of form of the pulse ; 

 while at short ranges, as explained in Section 8.3 to 

 8.5, the nonhnear Riemann overtaking effect plays 

 the predominant role, causing the time constant of 

 the pulse to increase with time and causing an at- 

 tenuation of the peak pressure whose magnitude is 

 independent of the specific mechanism responsible 

 for the dissipation of energy. The range at which the 

 transition from the latter type of attenuation to the 

 former takes place is probably roughly the range at 

 which the attenuation given by the short-range law 

 (24) of Section 8.5 equals the attenuation computed 

 by Fourier analysis from the linear laws of absorp- 

 tion and dispersion which hold for weak sinusoidal 

 sound. 



Observations on the variation of peak pressure with 

 range do not suffice to determine the magnitude of 

 the attenuation of this quantity, or even to establish 

 that it is different from zero. For example, the data of 

 Figures 3 and 4 of Section 9.2, taken from UCDWR 

 experiments cited in reference 8, are in good agree- 

 ment with intensity calculations which ignore at- 

 tenuation. It would hardly be reasonable, however, 

 to assume that there was practically no attenuation 

 in these experiments, since the increa.se of time of 

 rise with increasing range indicates that dissipative 

 processes were appreciable. Measurements on a larger 

 scale have been made at CUDWR-NLL.'- These 

 show an attenuation of about 2 db per kyd, that is, 

 slightly more than that predicted by equation (24) of 

 Section 8.5 for shock waves in an ideal fluid. Because 

 of the difficulty of correcting accurately for the effect 

 of refraction on the intensity, and because of the pos- 

 sibility of nonlinear behavior of the hydrophone in 

 CUDWR-NLL experiments, none of these results 

 can be given much weight. 



Pulses have been propagated to very long ranges 

 in the strata of the ocean where the velocity of sound 

 is less than at shallower or deeper depths. These will 

 be discussed in Section 9.3.2. Attenuation measure- 

 ments have been made for these pulses with the use 

 of recording equipment responsive to particular bands 

 of frequencies. Because of the limited frequency re- 



sponse of the equipment, the results cannot be inter- 

 preted in terms of peak pressure; however, as will be 

 .seen in Section 9.3.2, they indicate that the low- 

 frequency part of the pulse is transmitted with very 

 low attenuation. 



9.2.2 



Eifects of Refraction 



This section and the next will be concerned with 

 effects which can be correlated with the variation of 

 the velocity of .sound with depth, as determined from 

 bathythermograph data, at ranges up to a few thou- 

 sand yards. At these ranges few if any of the ray 

 paths will cross one another. In Section 9.3, on the 

 other hand, we shall consider propagation over long 

 ranges in a layer of minimum sound velocity where 

 many different ray paths can be found leading from 

 the source to the receiver. Most of the results dis- 

 cussed in this section and the next will be taken from 

 experiments conducted by UCDWR, and described 

 in references 8, 9, and 11. Similar though less detailed 

 results have been obtained in England at His Ma- 

 jesty's Anti-Submarine Experimental Establish- 

 ment, Fairlie.^ 



In the UCDWR experiments considerable atten- 

 tion was devoted to the securingof bathythermograph 

 data at as nearly as possible the same time as the 

 firing of the shots. From these data ray paths were 

 computed and graphs of predicted intensity as a func- 

 tion of depth were prepared for various values of the 

 ranges, the intensities being computed from the 

 geometrical divergence of the rays by the methods 

 described in Chapter 3. Figure 3 shows a typical 

 comparison between computed and observed peak 

 pressures for a day when the upper layers of water 

 were nearly isothermal. The pressure levels are 

 all plotted in decibels, that is, the abscissas are 

 10 logio Pmax- It will be seen that in the direct zone the 

 observations are in reasonable agreement with the 

 ray theory but that they would not agree at all well 

 with an inverse square law. It is a little surprising 

 that the agreement with ray theory should be so good, 

 since the theoretical intensities were computed with- 

 out any allowance for attenuation. Particularly note- 

 worthy is the decrease in intensity as the cap is raised 

 into the shadow zone from below. The 3,600-yd points 

 are all in the shadow zone. Figure 4 shows a similar 

 comparison for another day. On this day conditions 

 were rather variable. Of the three bathythermograph 

 runs taken during the morning, one showed a very 

 shallow split-beam pattern while the other two 



