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The performance of the Radon transform to focus the primaries and multiples to
separate regions of the transformed domain, depends on the choice of curvature
parameters and apex-shift values. In particular, curvatures should range from
small negative values to allow for the possibility of slightly under-migrated
primaries, to large enough values to accommodate the maximum curvatures of the
over-migrated
multiples. I have found that these are not particularly critical parameters as
long as the curvature sampling is fine enough to avoid aliasing in the Radon domain.
Similarly for the apex-shift parameters. They are
not critical, since their role is only to provide room for the
mapping of the diffracted multiples, thus preventing them from interfering with
the primaries and the specular multiples that map to the zero apex-shift plane.
A critical step is the design of the mute pattern to eliminate the primaries and
keep the multiples. There are several ways that this could be implemented. I
constructed a mask of ones for the multiple regions and zeros for the primary
region, smoothed it laterally and in depth and multiplied it by the transformed
data.
An important, and somewhat difficult parameter to estimate, is the one that
controls the Cauchy regularization (parameter in equation 33).
We want the data in the ADCIG to be explained
in the Radon domain by as few parameters as possible but avoiding the risk of
attenuating the contribution from weak subsalt primaries. This is a trial and
error parameter and it requires some testing to get a satisfactory value.

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2007-10-24