270 



THEORY OF REVERBERATION INTENSITY 



the principle still holds that the transmission losses 

 due to inverse square spreading and refraction from 

 to X and X to are the same along that ray, ir- 

 respective of the directivities of the sources. In addi- 

 tion, the principle of reciprocity applies also to ab- 

 sorption losses ' if absorption in the ocean arises from 

 so-called linear processes. Actually, studies of trans- 

 mission loss show that the processes involved in the 

 transmission of sound in the ocean are only imper- 

 fectly understood; but there appears to be no justi- 

 fication at this time for ascribing the absorption 

 losses of sound waves of ordinary amplitudes to non- 

 linear processes. 



Because the scattering coefficients are so small, 

 transmission losses due to scattering may be neglected 

 at all ranges of interest in echo ranging. It follows 

 therefore from the preceding paragraph, and from the 

 definitions of the quantities h and h' in Section 12.2 as 

 cransmission losses along the ray, that the principle 

 of reciprocity may be applied to transmission be- 

 tween the points and X of Figure 2 if refraction and 

 boundary conditions are constant. It is still necessary 

 to consider the effects of the variation of these con- 

 ditions with time; but by an argument similar to that 

 made in the discussion of Fermat's principle, it seems 

 vahd to assume that these time variations will not 

 affect the relation between the transmission losses of 

 the outgoing and incoming sound on a series of pings 

 lasting about a minute. In other words it appears 

 justifiable at this time, in the light of the principle 

 of reciprocity and our present understanding of 

 absorption losses, to assume that on the average the 

 one-way transmission losses h and h' are equal. 



12.5.6 Effect of Surface Reflections 



The complications induced by such variations in 

 boundary conditions as rough seas are exemplified by 

 the difficulties encountered in extending equation 

 (20), derived for an infinite unbounded ocean, to the 

 more nearly realistic semi-infinite ocean. In rough 

 seas (Figure 3B), with the transducer horizontal, it is 

 very difficult to determine exactly the effective vol- 

 umes from which reverberation is being received at 

 any instant. In calm seas (Figure 3A), however, the 

 volumes corresponding to the various alternative 

 paths should be very nearly identical at ranges 

 greater than a few hundred yards, since at these 

 rather long ranges the path differences between OAX 

 and OBX are usually very small. These volumes will 

 all be about half of the original volume S'lS'^ because 



of the presence of the ocean surface; at long ranges 

 and shallow transducer depths the initial angle of ray 

 elevation B is restricted almost completely to values 

 between — 7r/2 and in the integral (14), instead of 

 varying from — Tr/2 to ir/2, as it does when the ocean 

 surface is far away. Since all four of the scattering 

 volumes described in Section 12.2 are very nearly 

 equal, all of the integrals of the form (13) correspond- 

 ing to these volumes should also be nearly equal, be- 

 cause at these ranges the rays OAX and OBX (Figure 

 3 A) leave the transducer in almost the same direction, 

 and because in a calm sea the reflection coefficient of 

 the surface is very nearly unity. Thus, in a calm sea, 

 with the transducer near the surface and the beam 

 horizontal, the total intensity of the received volume 

 reverberation is obtained by adding up four integrals 

 of the form (13), with the region of integration for 

 each just half the volume S'lS'^. 



Therefore, the presence of the surface increases the 

 received volume reverberation under these conditions 

 to about double the value predicted by equation (17), 

 or to a value about 3 db greater than predicted by 

 equation (22), with the important proviso that the 

 quantities A and Ax used in that equation are the 

 transmission anomalies that would have been meas- 

 ured if there had been no reflected rays. The trans- 

 mission anomaly is usually obtained by measuring 

 the transmission loss from a point about 100 yd from 

 the transducer. If so, it is easily seen that with shallow 

 transducers the inferred transmission anomaly is 

 about the same as the transmission anomaly that 

 would have been measured if the surface was far 

 away. It follows, therefore, that in calm seas, with 

 shallow transducers and horizontal beams, the value 

 of 10 log m computed from measured volume rever- 

 beration intensities and transmission anomalies by 

 means of equation (22) will be about 3 db greater 

 than the true value of 10 times the logarithm of the 

 backward scattering coefficient. 



For rough seas it is not possible to make so precise 

 an analysis. However, it can be argued that the dif- 

 ference between the computed and actual value of 

 10 log m will be about 3 db in rough seas also since on 

 the average the existence of many paths (Figure 3B) 

 will be compensated for by the loss of reflecting 

 power of the surface. For surface reverberation the 

 existence of surface-reflected paths causes the value 

 of 10 log m' computed from measured surface rever- 

 beration intensities by means of equation (39) to be 

 about 6 db greater than the actual value of the back- 

 ward scattering coefficient of the surface scatterers. 



