It was necessary to digitize the analog records for computer process- 

 ing. A sampling interval, AT, of 5 seconds was chosen to permit resolution 

 of energy at spectreil periods as low as 10 seconds ((2AT)"-'- = the Kyq.uist 

 frequency) and to avoid aliasing. Since the gravimeter records showed little 

 energy with periods less than 10 seconds, aliasing was no problem. However, 

 there was some short-period, hut low amplitude, energy visible on the micro- 

 barograph records. It was not considered appreciable; hence a sampling 

 interval of 5 seconds was used to produce both time series. 



Power spectrum and cross-spectral analyses were then computed directly 

 from these time series. No low frequency filtering was applied to the data, 

 because drift and tidal effects, although observable, had less amplitude than 

 the measiired waves. This long-period energy is assigned to the first few lags 

 of the spectrum. Therefore, with the number of lags used in the following 

 analyses (100, 50, and 20), the best spectral estimates are found for periods 

 of 100 or less seconds. 



b. Power Spectra and Cross-Spectra 



Given two time series 77^(1) and "^5(1) , their time average 



^rs *^' = '7r (tl-^glt + r) 



is called covariance of the two series. 

 The quantities Crs(f)= / /0,e(r) cos ZTrfrdr 



(5) 

 (6) 



and 



(f ) 



-L 



/o^glr) sin ZvrfT dr 



(7) 



are the co- and quadrature spectra, respectively. For the special case when 

 r = s, Qrr(f) = 0, and Crr(f) is called the power spectriom. The quantity 

 Crr(f) has been used in this work for computing spectral estimates of single 

 time series. 



When a pair of time series was compared for coherence, as in the case 

 of simultaneous micropressure and gravity records or slmiiltaneous gravity 

 records from two different locations, the following relationships were used: 



«rs(^) = 



C 2 + 



2 n 



1/2 



(8) 



L c c J 



rr ss 



and 



0^ rf)= tan-l 



(9) 



15 



