DEEP-WATER REVERBERATION LEVELS 



335 



using a standard ping length. For this purpose we 

 define the standard reverberation level R 



17.1.6 



Coherence 



R = R' + 10 log 



(;) 



(2) 



where R' is the observed reverberation level with 

 ping duration t, and to is a standard ping duration 

 usually chosen as 100 msec. 



17.1.4 Backward Scattering 



Coefficients 



By "backward scattering" is meant scattering back 

 along the incident ray path. If there is only one ray 

 path from the projector to the scatterers, only sound 

 which is scattered directly backward can give rise to 

 reverberation. Thus the more efficient a portion of 

 the ocean is in backward-scattering, the higher will be 

 the level of the received reverberation. The efficiency 

 of a small volume V of the ocean in scattering sound 

 backward is specified in terms of the backward-scat- 

 tering coefficient m, which is defined by the relation 



mV 

 47r 



(3) 



where 6 is the average energy scattered by the volume 

 V per second per unit incident intensity per unit 

 solid angle in the backward direction. The factor 4ir 

 is introduced so that in cases where the scattering is 

 the same in all directions, the average energy scat- 

 tered in all directions per second per unit incident 

 intensity will be just mV. 



17.1.5 



Fluctuation 



The reverberations from two successive pings 

 never reproduce each other exactly. This short-term 

 variabiUty is called "fluctuation." A numerical meas- 

 ure of fluctuation is provided by the variance of the 

 reverberation intensity at a time t seconds after mid- 

 signal. More specifically, suppose that a large number 

 n of successive pings are sent out, that records are 

 taken of the n resulting reverberations, and that the 

 n intensities at a time t seconds after midsignal are 

 read off the records. Then if 7 is the average of these 

 n intensities, and /i, /a, •••,/» are the n individual 

 intensities, then the fluctuation corresponding to the 

 time t seconds after midsignal is measured by the 

 variance 



1 n 



IT- 



(4) 



The term "coherence" applied to reverberation re- 

 fers to a tendency of the received reverberation to 

 occur in the form of pulses or "blobs." The possession 

 of coherence means that if at any instant the rever- 

 beration level is high, it is likely that the level will 

 remain high for a little while, and that if the rever- 

 beration level is low, it is not likely to become large 

 in a short time. The degree of coherence can be de- 

 scribed mathematically in terms of the correlation 

 coefficient p between the reverberation intensities at 

 two different times on the same record. 



Uik) - /(Cl)][/(<2) - I{k)'] 



(5) 



The bar signifies an average over many successive 

 records. 



17.2 DEEP-WATER REVERBERATION 

 LEVELS 



In deep water the reverberation heard at ranges 

 past 1,500 yd is almost always volume reverberation. 

 At shorter ranges surface reverberation may exceed 

 volume reverberation, if the sea state is sufficiently 

 high and the transducer beam is horizontal. Pointing 

 a directional transducer downward will usually result 

 in the surface reverberation being less than volume 

 reverberation at all ranges past 100 yd. 



17.2.1 



Volume Reverberation 



The following subsections summarize the known 

 information concerning reverberation from the vol- 

 ume of the ocean. The statements apply only to that 

 portion of the received reverberation resulting from 

 scattering in the ocean volume; the salient facts 

 about reverberation from the sea surface are sum- 

 marized in section 17.2.2. 



Theoretical Formula for Volume Reverbera- 

 tion Level 



The expected volume reverberation level R'{_t) at a 

 time t sec after midsignal is given by the formula 



R'it) = 10 log ^ + 10 log m + J, 



- 20 log r -2A+ Ai, (6) 



where Co is the sound velocity in yards per sec ; t is the 

 ping duration in sec; m is the volume scattering 



