258 



THEORY OF REVERBERATION INTENSITY 



energy travels between the transducer and a scat- 

 terer along one path, or along many paths. 



Evaluation of the various integrals of the form (14) 

 corresponding to each possible route from to X and 

 back, is very difficult. These integrals depend on the 

 reflecting power of the surface, on the depth and 

 orientation of the transducer, and on how the back- 

 ward scattering coefficient varies with the direction 

 of the incident sound. Also, the possibility must be 

 considered that for small values of t some of the 

 integrals should not be included, since there may not 

 be time for energy to reach the ocean surface along 

 any path and return to by the time instant t. 

 High seas, with the possibility of a great increase in 

 the number of alternative paths, further complicate 

 the problem. 



To avoid these difficulties, the customary pro- 

 cedure has been to assume that equation (22) fully 

 describes the volume reverberation intensity, despite 

 the complications introduced by the ocean surface. 

 The quantity 10 log m then becomes an adjustable 

 parameter which measures not only the actual back- 

 ward scattering power of the ocean for incident plane 

 waves, but also the effective increase in the volume 

 of scatterers caused by the existence of a number of 

 alternative paths. 



If the water is deep and the echo-ranging gear is 

 directional, the ocean surface can complicate the 

 problem only if the main transducer beam strikes the 

 surface. If the transducer beam is directed down- 

 ward at a sufficiently large angle, the predictions of 

 equation (22) should not be put in error by the 

 presence of the surface. Using a depressed beam has 

 proved to be one of the most convenient ways of 

 studying volume reverberation. 



Most reverberation studies, however, have been 

 made with the transducer near the surface, and the 

 beam horizontal. Under those circumstances it is 

 shown in Section 12.5.6 that the value of 10 log m 

 computed from measured volume reverberation in- 

 tensities and transmission anomalies by means of 

 equation (22) will usually be about 3 db greater than 

 the true value of 10 times the logarithm of the back- 

 ward scattering coefficient. If the water is shallow 

 enough for rays reflected from the bottom to be im- 

 portant, no simple relation exists between the in- 

 ferred value of 10 log m from comparison of equation 

 (22) with experiment, and the actual value of the 

 backward scattering coefficient. However, when the 

 bottom is close enough to affect the validity of equa- 

 tion (22), the volume reverberation will almost al- 



ways be masked by bottom reverberation so that the 

 failure of equation (22) is of only academic interest. 

 We shall next define the concepts of "reverberation 

 level" and "standard reverberation level," which 

 facilitate the comparison of reverberation measure- 

 ments performed with different gear and different 

 ping lengths. From equation (13), the average value 

 of the volume reverberation intensity is proportional 

 to the product F-F' where F is the power output 

 of the projector and F' is the receiver sensitivity. It is 

 convenient to eliminate these variables in comparing 

 the reverberation received on different gear. To this 

 end we define the reverberation level R'{t) as 



R'{t) = 10 log G{t) - 10 log {F-F'). (23) 



For volume reverberation, we have specifically, from 

 equation (22), 



Car 



R'{t) = 10 log — + 10 log m 



20 log r + Jr, 



- 2A -t- Ai. (24) 



In words, R'{t) is the level of the received reverbera- 

 tion in decibels relative to the power output which 

 would be produced at the terminals of the receiver 

 by an incident plane wave, parallel to the acoustical 

 axis, of intensity equal to the projected intensity on 

 the axis at 1 yd. 



It is often convenient to go one step further. Since 

 the intensity of reverberation is in principle propor- 

 tional to the ping length, it is both desirable and 

 practical to convert all reverberation levels to the 

 same ping length. We define the standard reverbera- 

 tion level for the reverberation at the ping length r as 

 that which would have been received if the ping 

 length had been some standard value tq. Let the 

 standard reverberation level be denoted by R(t). 

 Then we have 



R{t) = 101ogG(<) - 10 log {F-F') + lOlogf-V 



(25) 



The predicted standard level of volume reverberation 

 is therefore given by 



R{t) = dO log ^° -f- 10 log m - 20 log r 



+ J„ - 2A + Ai. (26) 



The standard ping length ro is usually chosen as 100 

 milliseconds. It is also frequently useful to convert 

 reverberation levels to reverberation strengths. This 

 is done by adding 40 log r to the computed reverbera- 

 tion levels in equations (24) and (25), thereby ob- 



