The theory in this chapter assumes that
the data are *wide-sense stationary*.
A data sequence is considered to be wide-sense stationary
if it has constant mean and if its autocorrelation is
strictly a function of lag

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We want to look at data with more than one dimension.
Thinking in helical coordinates, we can view a set of
traces as a super trace and take its autocorrelation.
Equation station says that we should be able to
get the same autocorrelation function for different
subsets of the data (different starting samples *n _{1}*).
Intuitively, this coincides with the statement in the
introduction (taken from Spitz 1991) that the
data should be made up of linear events of constant slope.
Figures stationdata and nonstationdata show examples.
Figure stationdata shows a window from the
far offsets of a synthetic CMP gather, and
autocorrelation sequences made from identical numbers
of samples, starting at different places within the
window.
Figure nonstationdata shows a window from the
inner offsets of the same gather, and autocorrelation
sequences.
The far offsets, where data tends to be made up of
linear events as hyperbolas approach their asymptotes,
are by appearance nearly stationary, and the autocorrelations
are approximately equal except for a scale factor.
The inner offsets, where the events are obviously changing dip,
do not look stationary and do not have
approximately equivalent autocorrelation functions.

Figure 12

Figure 13

Seismic data are not, as a rule, stationary. The slopes of seismic events change with offset and time, and when the geology is nontrivial, with surface locations also. This just means that we can not use a single PEF to represent the spectrum of all the data, but only as much data as we can reasonably assume to be stationary.

1/18/2001