IV -45 



obtain the results shown in Table IV- 4 for the mean square values of the phase and 

 the amplitude. We note that amplitude and phase fluctuations become equal in the 

 interference range. We also observe that the coefficient of variation of the ampli- 

 tude in the focusing range behaves as the three-halves power of the range. This 

 is just the result to be expected for ray acoustics and was already hinted at in 

 Chapter II. It is possible in a similar fashion to evaluate the cross correlation 

 between the phase and amplitude fluctuations at a given point, < Bi Si >. It is 

 more interesting, however, to evaluate the cross correlation coefficient between 

 the logarithmic amplitude and the phase: 



bs 



< Bi Si > 



-y^Bi^> ^Si^ > 



(IV-93) 



Chernov shows that for a Gaussian correlation function this cross correlation 

 coefficient becomes, in the two extreme ranges: 



R ^0.6 

 bs 



R -1^^ 

 bs D 



for D < < 1 (focusing range) (IV- 94a) 



for D < < 1 (interference range) (IV-94b) 



TABLE IV- 4 



THEORETICAL AMPLITUDE AND PHASE FLUCTUATIONS 



D> > 1 (Interference Range) D<< 1 (Focusing Range) 



<S, 



I 



< L^ > k^ L I R (r) dr 



2 < u^ > k^ L I R (r) dr 

 o 



1 



<Bi > 



< u" > k= L r 



R (r) dr 



/ 



|<\j^ > L^ I V^^ v^ R(r)dr 



S-7001-0307 



