Breaker and O'Neil 



the phase angle difference between the two should be essentially 

 uniformly distributed from -ir to tt , with no pulse-to-pulse corre- 

 lation. Thus, including the "I height" merely introduces a white 

 noise which will have no effect upon the shape of the spectra. 



The next step in data reduction then is to compute the 



"D heights" where possible and "D+I+S heights" for each pulse in the 

 event. The logarithms of these are taken and the average log is 



later subtracted off to give the fluctuation. (In order to save on 



multiplications the factor of 20, necessary to convert the units to 



dB/s, is applied only to the final estimates.) The variance is 

 computed in the usual manner. 



Sample estimates of the normalized power spectrum, P(f), 

 are next computed. The statistical procedures of Ref. 6 will be 

 followed but the mechanics of computing the "raw" estimates will 

 differ significantly. The computational methods of Ref. 6, 

 involving calculation of the sample autocorrelation function 

 followed by Fourier transformation to obtain the sample spectrum, 

 would be most time consuming for so large an accumulation of data. 

 Instead, a modification of the "fast Fourier transform method" of 

 Ref. 7 will be employed to compute the raw spectral estimate 

 directly from the data, using the relation 



I '^' 2 



-T/2 



Certain precautions will have to be observed in "grading" the data 

 much as one does in analogue spectral analysis. The spectral 

 analysis has not yet begun, but the necessary computer programs 

 are complete. 



Temperature and current-velocity data taken near the 

 experiment site will be used to provide independent estimates of 

 C^ , via Eq. (3). For the period of each event the estimate of the 

 structure function, Dj(r), will be computed directly from the 

 definition, 



D^(r) =Avgy [(T(y)-T(y-r)fj 



where the ergodic hypothesis plus our "frozen-in" assumption will be 

 used to translate the time intervals between temperature observations 

 at the array's fixed position plus the mean local current velocity 

 into an equivalent value of r. This has not yet been undertaken 

 due to some technical problems with the records. 



380 



