Chapter 12 

 THEORY OF REVERBERATION INTENSITY 



THE AMOUNT and character of the sound heard or 

 recorded as reverberation depends not only on 

 the properties of this sound in the water, but also on 

 the nature of the gear in which the reverberation is 

 received. The intensity of the reverberation actually 

 heard or recorded, after the sound in the water has 

 been converted to electrical energy by the receiver, 

 amplified, and passed to the ear or recording scheme, 

 will be called the "reverberation intensity," and will 

 be given the symbol G. As so defined, G equals the 

 watts output across the terminals of the receiving 

 gear. Although in practice the reverberation may be 

 measured in terms of volts, or the height of a line on 

 a motion picture film, or some other convenient 

 quantity, these measurements can always be con- 

 verted to watts output by the use of known param- 

 eters of the receiver system. In general, the reverbera- 

 tion intensity G is a function of time and is related to 

 the sound intensity in the water by such parameters 

 of the receiver system as receiver directivity and re- 

 ceiver gain. 



Since G depends on the gear parameters, its abso- 

 lute magnitude is usually not of great significance in 

 research. For this reason it is customary to relate G 

 to the reverberation intensity which would be regis- 

 tered under certain standard conditions. This stand- 

 ard reverberation intensity, in decibels, is called the 

 "reverberation level" and will be defined precisely 

 later. Reverberation levels are more useful than re- 

 verberation intensities for comparing measurements 

 made with different systems. 



This chapter is devoted to a theoretical analysis of 

 expected reverberation intensities and reverberation 

 levels. Formulas will be derived giving the depend- 

 ence of these quantities on various gear parameters, 

 oceanographic conditions, and elapsed time since 

 emission of the signal. First, however, we must dis- 

 cuss the scattering of sound, since scattering is 

 usually regarded as the fundamental source of re- 

 verberation. 



12.1 



SCATTERING OF SOUND 



The analysis in this chapter is based on some very 

 definite assumptions about the nature of reverbera- 

 tion. It is assumed that not all of the sound in the 

 outgoing ping proceeds outward in accordance with 

 the elementary theory in Chapters 2 and 3, but that 

 some of the sound is "scattered" in other directions. 

 The reverberation is thought to be that part of this 

 scattered sound which returns to the transducer. 

 Volume, surface, and bottom reverberation are as- 

 sumed to result, respectively, from scattering in the 

 volume of the ocean, at the surface of the ocean, and 

 at the ocean bottom. 



In an ideal unbounded fluid in which the sound 

 velocity is everywhere the same, it is shown in 

 Chapters 2 and 3 that sound always travels outward 

 from its source along straight lines. In such a medium, 

 then, scattering never occurs and no reverberation 

 should be heard. There is no reason to doubt the 

 validity of this theoretical result. Scattering arises 

 because the ocean is not an ideal unbounded medium 

 with constant sound velocity. It can be shown theo- 

 retically that whenever a sound wave travels through 

 a portion of a fluid where the density or sound velocity 

 varies with position, some energy is radiated in direc- 

 tions differing from the original direction of the wave. 

 Similarly, whenever a sound wave in the ocean im- 

 pinges on a new medium, for example a bubble, in 

 which the density or sound velocity differ from their 

 values in the surrounding water, energy is radiated 

 in directions differing from the original wave direc- 

 tion. 



Whet'her or not this deviated energy is called 

 "scattered energy" is to some extent a matter of 

 definition. If the inhomogeneity in density or sound 

 velocity extends over a large region of space, a sound 

 beam travehng through the medium may be changed 

 in direction with little or no loss of energy from the 

 beam; if this happens the sound wave is not regarded 



250 



