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Berryhill (1984) generalized his earlier work for zero-offset
data to constant-offset (prestack) data by downward continuing the geophones
and the sources to a datum in a two pass algorithm.
The same idea can be used for extrapolating data using different
phase-shift algorithms for downward (or upward) continuing
common-source and common-receiver sections to a datum.
Moreover, due to the inherent simplicity of the algorithm
the 3-D implementation is straightforward.
Another research direction was given by Yilmaz and Lucas (1986)
and Berryhill (1986) who both describe a velocity replacement
technique using a Kirchhoff based datuming algorithm twice. The layer
replacement method consists of downward extrapolating the data
to a datum using a known velocity and then upward extrapolating
the data back to the surface with a different velocity in order to
reduce the effect of the velocity contrast at the datum.
Using the phase-shift datuming algorithm described in this
paper we can apply the same technique to zero-offset data
and to prestack data to obtain the same results.

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Stanford Exploration Project

11/17/1997