304 



DEEP-WATER REVERBERATION 



easy to see from the derivation of Chapter 12 that 

 this expected signal depends on the integral J^b{fi,4>) 

 V{0,<i> + a)dQ, where h and h' are defined as in Chap- 

 ter 12, and a is the angle between the projector 

 and hydrophone. 



2 4 6 8 10 12 



RATIO OF TWO PING LENGTHS IN DB 



Figure 30. Observed dependence of reverberation in- 

 tensity on ping length. 



The values of the above integral were computed 

 for a equal to 0, 30, 60, and 90 degrees, and the pre- 

 dicted reverberation intensities were then compared 

 with the observed intensities. It was found that the 

 calculated levels were within 1 to 2 db of the observed 

 average levels for ranges up to about 200 yd, beyond 

 which no measurements were made. Since the experi- 

 mental error of the measurements was not less than 

 1 to 2 db, these results show that at short ranges 

 multiple scattering makes a negligible contribution 

 to the received reverberation. However, these results 

 give no information about the effect of multiple 

 scattering at longer ranges. 



It is easy to show that multiple scattering can 

 certainly be neglected if the volume scattering in all 

 directions is the same as in the backward direction. 

 For, in this event, the total energy scattered per 

 second per unit intensity at dY is just mdV (see 

 Section 12.1). The loss in intensity (i/ in a distance dx 

 of a plane wave of intensity / traveling in the x 

 direction is then 



dl = mldx 

 which gives / = /oe~"". 



Thus under these circumstances the attenuation of a 



sound wave by scattering is 4.34 X lO'm db per kyd. 

 It is shown later that m is rarely greater than 10~'. 

 By using this value of m, the attenuation due to 

 scattering is 4.34 X 10~^ db per kyd. Now, with any 

 kind of a transducer, but especially with a direc- 

 tional transducer, multiple scattering will not be im- 

 portant in reverberation until the amount of singly 

 scattered energy in the ocean becomes appreciable 

 compared to the amount of energy remaining in the 

 direct sound beam. ObViously, with a scattered 

 energy loss of only 4.34 X 10"^ db per kyd, scattered 

 energy in the ocean is negligible compared to the 

 energy in the direct beam for ranges less than 

 20,000 yd where the total scattered energy loss is 

 not yet 1 db. 



Despite the arguments of the preceding paragraph, 

 more experimental evidence bearing on multiple 

 scattering would be desirable especially since the 

 obhque scattering may be appreciably different from 

 the backward scattering. One way to check the im- 

 portance of multiple scattering would be to compare 

 with experiment at long ranges the predicted de- 

 pendence of received reverberation intensity on trans- 

 ducer directivity. If multiple- scattering is important, 

 the difference between reverberation levels measured 

 with directional and nondirectional transducers will 

 not be given by J„ [equation (21) of Chapter 12]. No 

 such measurements have been reported; in fact, the 

 whole question of comparing with experiment the 

 dependence of reverberation on the theoretical rever- 

 beration indices J„ and 7» seems to have been neg- 

 lected. Knowledge of this dependence is required for 

 comparison of measurements made with different 

 gear, and also for prediction of the effect on reverber- 

 ation in echo-ranging gear of changes in gear direc- 

 tivity. There is no reason for doubting the vahdity 

 of the formulas of Chapter 12 for ordinary gear, but 

 with highly directive gear, multiple scattering and 

 other effects may produce deviations from the theo- 

 retical formulas. A UCDWR internal report '^ de- 

 scribes experiments in which the measured vertical 

 directivity patterns in the ocean were very different 

 from the patterns obtained at a caUbrating station. 

 Pitch and roll of the echo-ranging vessel will also 

 cause deviations from the predicted reverberation in- 

 tensities, especially for surface reverberation." 



14.2.4 Average Levels 



Figure 31 is a sununary of the measured 24-kc re- 

 verberation levels reported in reference 4. The levels 

 shown are standard reverberation levels, as defined 



