B. Correlation and Spectrum Analysis 
Autocorrelation and power spectrum computations were carried out 
on all records according to the methods of Tukey, ‘> 
who gives formulae 
for the digital computation of these quantities for data obtained at equal 
time intervals. The formulae are summarized below. 
Let the N+l numbers 
A OSS aL 
be the time series taken at time intervals At , with zero mean. The 
quantity corresponding to the autocorrelation function is the mean lagged 
product 
C == X X E-On Ane Siegen 
The raw spectral density estimate is formed by 
m-1] 
agli SLs 
Ve = ne(c, + 2 2 oe cos a + Ch cos | _ 
which is the estimate of the two-sided spectral density at the frequency 
ie = (r/2mAt) Peaw Ok Mee 2ee 2 em 
This process of obtaining spectral density estimates is analogous to ob- 
taining the power spectrum of electrical signals by determining the strength 
of the signal transmitted by various bandpass filters. Just as these filters 
respond to components of the signal whose frequencies lie outside the main 
passband and at a side lobe, so the raw spectral density estimate gives an 
erroneous reading for signals at the side lobes of the effective passband for 
this computation. Several procedures are available for reducing this error 
by reducing the amplitude of the side lobe response. We have used the pro- 
cedure known as hanning, which reduces the maximum side lobe response to 
3 R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra 
(Dover Publications, New York, 1958). 
