III-66 



an ascent of 200 meters in about one hour. It is probable (though not observed) 

 that such an animal can effect the converse operation during a sunrise descent. 



Scattering by Many Organisms 



Up to now v/e have considered only scattering by single marine organ- 

 isms. We proceed to consider scattering by many organisms. The approach is 

 more qualitative than in the case of air bubbles . A scattering or reverberation 

 coefficient m is defined as the power scattered by a unit volume per unit inten- 

 sity of an incident plane wave, with the scattering being equal in all directions. 

 Tliere is some physical evidence from dragging operations to indicate that the 

 population density of scatterers causing volume reverberation is normally of 

 the order of 10 - 15 per cubic meter, and may occasionally be as high as a few 

 hundred scatterers per cubic meter. This is low enough so that interaction be- 

 tween scatterers, or multiple scattering, can be ignored. U there is no inter- 

 action between scatterers, then the volume reverberation coefficient, m, is 

 simply the sum of the scattering cross sections of the scatterers in a unit volume. 



Consider a transducer located at the center of a spherical coordinate 

 system (r, 9, cp) and assume that the energy emitted by the source per unit solid 

 angle ( 9, cp) is described by F( t , 9, cp ), where t is measured from the beginning 

 of a pulse . The intensity of volume reverberation at the receiver at time t is re- 

 lated to m(r, 9 , cp), the volume scattering coefficient of the medium, by 



/^ 



!(,). , -v,^,^) m(r, 9,j)b(9, cp) ^^ ^^^^_^^^ 



V 



where b(9, cp) describes the directional properties of the transducer as a re- 

 ceiver and r = (c/2)(t- T), where c is the velocity of sound in sea water. 



The following assumptions are implicit in Equation III- 41: 



- The sound velocity in the medium is constant. 



- The definition of m has the effect of averaging the 

 contributions of individual scatterers. 



- A volume element begins to scatter sound at the 

 instant it is insonified and stops when the pulse has 

 passed- -i.e. , there are no time lags or storage of 

 energy in the scatterer. 



S-7001-0307 



