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As described by Hale 1991, the zero
offset rays bouncing off an ellipsoidal reflector of foci *S*
(source) and *G* (geophone) emerge on the segment [*SG*].
Therefore, the DMO operator is really a 2-D operator working
along the source-geophone line, even in a 3-D space.
Consequently, applying the operator in three dimensions is
not much different than in two dimensions except
that the trace smearing is performed for an irregular spatial
sampling according to the azimuth. The technique used in this
3-D DMO code consists of computing the bins affected by the
segment [*SG*]. More precisely, whenever the center of a bin
is closer to the [*SG*] segment than half the bin size, the
bin receives an output trace. This operation is repeated
for all input traces, gradually filling the output space.
This technique is equivalent to the nearest neighbor interpolation
in space and linear interpolation in time described by Nichols
1993.
This algorithm requires some evenly distributed data
so that the fold over any bin is nearly constant.
Dividing the trace amplitude by the fold of the corresponding
bin seems an attractive solution, but it may spoil the AVO
properties of the data.

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Stanford Exploration Project

11/17/1997