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Inevitably, we get involved with nonstationarity
and we become interested in continuously variable PEF's.
Again, 1-D theory guides us.
We can do regional averaging of *c*'s
and that preserves minimum phase.
Likewise, we can independently
average across micropatches the numerator and denominator of (2).
Many people did this in the old days
when filter theory was basically one dimensional.
Polynomial division by
nonstationary PEFs made up from
an assemblage of stationary ones
need not, however, be necessarily stable,
as shown by
Rickett (1999).
He demonstrated instability
when two stable PEFs alternated at alternate time points.
Whether this kind of instability would
arise in practice remains to be seen.

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Stanford Exploration Project

4/27/2000