Chapter 6 



SHALLOW- WATER TRANSMISSION 



IN CHAPTER 5, it was shown how the propagation 

 of sound in deep water is affected by temperature 

 gradients in the sea and by the sound frequency. 

 In shallow water, these factors continue to operate; 

 added to them is the effect of the bottom. The bottom 

 affects the sound field in two different ways. Some of 

 the sound incident on the bottom will be reflected and 

 may penetrate into shadow zones. Also, some of the 

 sound incident on the bottom will be scattered back- 

 ward and will form part of the reverberation back- 

 ground against which an echo must be recognized in 

 echo ranging. This latter effect of the bottom will be 

 considered in Chapters 11 to 17 of this volume. In 

 this chapter, only the transmitted sound reaching a 

 receiving hydrophone will be considered. 



6.1 PRELIMINARY CONSIDERATIONS 



In deep water, it was found that the most impor- 

 tant single factor determining the transmission of 

 sound of a given frequency is the vertical temperature 

 structure of the ocean. The roughness of the surface 

 of the sea plays a poor second, and nothing is known 

 concerning the effects of other oceanographic varia- 

 bles on sound transmission. In shallow water, the 

 number of factors which may conceivably affect 

 sound transmission is greater; it would be impractical 

 to make a large number of sound transmission runs 

 and then obtain rules of sound propagation empiri- 

 cally merely by subjecting the data amassed to an 

 unprejudiced statistical analysis. Rather, it was found 

 necessary to assess beforehand the possible effects of 

 bottom character, roughness of the sea surface, and 

 refraction conditions, and then to analyze the trans- 

 mission run data purposefully. This procedure proved 

 successful in bringing order into a mass of data, and 

 it will also be followed in this discussion. 



6.1.1 



Effects of Sea Bottom 



If bottom-reflected sound is added to the sound 

 field which reaches the receiving hydrophone (or the 

 target in echo ranging), interference between the 

 signals transmitted via the different possible paths 



may be either constructive or destructive, depending 

 on the geometry of the paths. However, if the sound 

 field intensity is averaged over a volume of the ocean 

 sufficiently large to include several maxima and 

 minima of the interference pattern, the averaged 

 sound field intensity will be the algebraic sum of the 

 intensities of sound resulting from each path by itself. 

 In this sense, averaged sound field intensities in 

 shallow water are always higher than sound field 

 intensities in deep water under otherwise identical 

 conditions. The extent to which bottom-reflected 

 sound will increa.se the "deep water" sound field in- 

 tensity and to which it will eliminate shadow zones 

 depends on a number of factors, which will be treated 

 in this chapter. One of these factors is the reflectivity 

 of the sea bottom. 



A theoretical treatment of bounding surfaces indi- 

 cates that the reflectivity of a surface is determined 

 by two factors : the degree of roughness of the surface 

 itself, and the density and elastic moduli of the two 

 adjoining media, such as sea water and granite. For 

 the special case of two fluid media, it was shown in 

 Section 2.6.2 that the percentage y^ of reflected 

 energy depends on the ratio of the densities as well 

 as the angles of incidence and refraction, according 

 to the formula 



7e = 



PiCi - pcVl -f tan^e (1 - ^J&) 



(1) 



.Pici -H pcVl -F tan^e (1 - c\/&) 



in which p and pi are the densities of the two adjoining 

 media, c and c\ are the sound velocities, and Q is the 

 angle of incidence. This quantity 7e is called the coef- 

 ficient of reflection of the separating surface. The 

 coefficient of reflection equals unity when the angle 

 of incidence exceeds the critical angle for total re- 

 flection. 



Equation (1) is based on the assumption that a 

 smooth plane interface separates two perfect fluids. 

 This assumption is not entirely correct for either the 

 surface or the bottom of the ocean. The surface of the 

 ocean is not smooth. With high winds, it may contain 

 a large number of air bubbles (whitecaps), which 

 absorb and scatter sound. The bottom often consists 



137 



