EXPLICIT AND TACIT ASSUMPTIONS 



271 



The reason for the 6-db value for the case of surface 

 reverberation is that in equation (28) the volume of 

 integration explicitly includes only the semi-infinite 

 region below the ocean surface. Thus in calm seas the 

 total intensity of the received surface reverberation 

 is obtained by adding up four integrals of the form 

 (28) without any reduction in the volume of integra- 

 tion. However, this conclusion depends on the 

 properties of the surface scattering layer. If the sur- 

 face scattering layer absorbs sound very strongly, 

 sound may never be able to penetrate the layer to 

 reach the actual air-water interface. In this event, the 

 inferred value of m' from equation (39) will equal the 

 true value of the backward scattering coefficient of 

 the surface scatterers. A situation of this sort in which 

 the surface layer is assumed to consist of a dense layer 

 of resonant bubbles is discussed in Section 14.2.5. 



If the water is shallow enough for rays reflected at 

 the bottom to be important, the situation becomes 

 more obscure; as shown in Figure 3C, some of the 

 possible paths between and X involve both re- 

 flection at the sea surface and reflection at the sea 

 bottom. It has already been pointed out that in this 

 situation no simple relation exists between the in- 

 ferred value of 10 log m and the true value of the 

 backward scattering coefficient. In fact, it may be 

 remarked generally that equations (20), (39), and 



(52), for reverberation from the volume, surface, and 

 bottom, respectively, are invalid when ray paths in- 

 volving several reflections between the projector and 

 the scatterer become important. 



12.5.7 



Overall Evaluation 



This section has been concerned with the physical 

 ideas behind the assumptions which have been used 

 to derive the theoretical formulas for reverberation. 

 It has been seen that most of the assumptions used 

 are probably justified, but that no definite proof of 

 their vaUdity is possible at this time. If the assump- 

 tions are not satisfied, reverberation may not depend 

 on range and ping length in the manner predicted by 

 the theoretical formulas (24), (43), and (54). None of 

 the considerations of this section affect the possibility 

 of using these formulas as an einpirical means of in- 

 vestigating reverberation and computing in each 

 case a value of the backward scattering coefficient 

 from comparison of the theoretical formulas with 

 experiment. However, if the assumptions which have 

 been made are not justified, the magnitude of the 

 backward scattering coefficient deduced in this way 

 will not have the simple physical significance implied 

 in assumption 4 of Section 12.1. 



