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This article has practical goals, educational goals,
and research goals.
The practical goal is to illustrate a subroutine
that interpolates missing seismograms by the most rudimentary,
and generally effective method.
The basic assumption is that the data can be locally
(in space and time) fit to a plane wave which can
be used for linear interpolation.
It further assumes that the filling in of a gap between two seismograms
can be based on only the two seismograms
and that no additional seismograms are needed.
Effectively, this assumes good quality data.
Thus, it should be particularly effective
for crossline marine surveys where the line separation
is uncomfortably large and irregular,
but the data quality is high because of in-line stacking.
The educational goal is to introduce
what amounts to Burg handling of edge effects.
Since dips change rapidly in time and space,
and since we will work in small windows where
we presume constant dip,
edge effects can be overwhelming and great care is needed.

The research goal is to begin bridging the gap between conventional processing
and general inversion.
Since PVI Claerbout (1992)
I am associating 2-D PEFs with
(factorizations of) inverse covariance matrices
that need to be estimated simultaneously with the missing
data (or model parameters).
This makes the inversion problem fundamentally nonlinear
and dependent on a reasonable initial method.
Ultimately, I plan to show that the interpolation method expounded here
(which approximates conventional processing)
fits the framework of a general inverse problem.
Thus this method, limited though it is,
is a natural basis for iterative improvement.

** Next:** RESULTS AND METHOD
** Up:** Claerbout: Data gap filling
** Previous:** Claerbout: Data gap filling
Stanford Exploration Project

11/18/1997