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Many land data are recorded irregularly or in a pseudo-regular fashion
in source and receiver coordinates.
On the other hand, many data processing algorithms need regularly sampled data.
A source equalization algorithm, which is based on
reciprocity, requires that at each source location there is
a geophone location.
In reality this poses a problem: it is very common for an acquisition
geometry to have interlaced
source and receiver stations. Certain kinds of interpolation
algorithms will handle that problem very efficiently.
However, usually the geometry has additional twists to it, like
unequal near offset distances.
An algorithm which is to be applied to real data has to be able to
handle such irregular spacings.
For my application, I chose to use slant stacks of shot gathers for two
reasons. Source equalization operates under the assumption of
varying source behaviour and quasi regular receiver properties.
Under that assumption it is more convenient to reposition receivers.
Slant stacks have the property that the
data decomposition can be carried out in a least squares sense
incorporating irregular geometry; Clement Kostov (1990) describes the
linear properties of that operator in detail.
The least squares approach greatly reduces artifacts
introduced by data boundaries. It can be shown that the
least-squares slant stack operator
easily handles irregular spacing in *x*-*t*.

** Next:** SLANT STACK AS GEOMETRY
** Up:** Karrenbach: slant stack redatuming
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Stanford Exploration Project

12/18/1997