SURFACE REVERBERATION 



259 



taining respectively the reverberation strength or 

 standard reverberation strength. 



The quantity J„, which specifies the relevant di- 

 rectivity characteristics of the transducer, is known 

 as the volume reverberation index. For standard Navy 

 gear at 24 kc, J„ is very nearly —25 db. It is shown' 

 that for transducers which are circular pistons 7„ can 

 be very closely approximated by 



J„ = 20 log y - 42.6, (27) 



where y is defined as in Figure 4. Numerically, y is 

 half the angle in degrees in the plane 6 = between 

 those two rays of the composite directivity pattern 



Figure 4. Half-width y for circular piston trans- 

 ducers. 



for which the product bb' is 0.25. Thus for a trans- 

 ducer in which b = b',y is half the angle between the 

 two rays for which the response as a projector or re- 

 ceiver is 3 db less than the response on the transducer 

 axis. The angle y is known as the "half width" of the 

 composite directivity pattern 66'. Reference 3 also 

 gives methods for calculating /„ for transducers which 

 are not circular pistons. 



12.3 



SURFACE REVERBERATION 



Surface reverberation is defined as the totality of 

 sound scattered back to the transducer by scattering 

 centers in or near the ocean surface. This simple 

 definition is not completely adequate, since it would 

 make surface reverberation a particular part of vol- 

 ume reverberation. We differentiate between these 

 two types of reverberation by assuming that the sur- 

 face reverberation arises from a thin surface layer of 

 scatterers. The scatterers in this surface layer are 

 assumed to owe their existence to the proximity of 

 the surface and therefore differ in character from the 



volume scatterers which supposedly may be found 

 anywhere in the volume of the ocean. 



The strength of these surface scatterers would be 

 expected to be a function of the state of the sea sur- 

 face, increasing with increasing agitation of the sea 

 surface. In practice, surface and volume reverbera- 

 tion are frequently distinguished from each other in 

 just this way;, surface reverberation is regarded as 

 that part of the received reverberation which seems 

 to depend on the sea state. 



We now derive an expression for the intensity of 

 surface reverberation as a function of range and gear 

 parameters, with the aid of Figure 5. We may pro- 



FiGURB 5. Coordinate system used in derivation of 

 surface reverberation formula. 



ceed exactly as in the development for volume rever- 

 beration, and arrive finally at an equation similar to 

 equation (13). This equation for the surface rever- 

 beration intensity G{t) is 



G{t) 



F-F' C 

 = I? 



47r J 



mh'bid,(j>W(d,<i>)dV, 



(28) 



where the integral is taken over that section of the 

 volume S'iS'2 which contains the surface scatterers. 

 This section need not be of uniform depth, although 

 it is drawn so in Figure 5. The factor m in equation 

 (28) is the backward scattering coefficient in the 

 surface scattering layer and is very probably a func- 

 tion of the depth below the surface. In equation (28), 

 reflection from the surface is explicitly neglected; 

 that is, the r.ay paths are assumed to go directly from 



