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Increasing the focusing power of the Radon transform is critical in real situations
in which the primaries and the multiples may map close together in the Radon
domain. Therefore, taking into account the ray bending of the multiples, at least
to first order, is an improvement. The cost of the new transform is essentially the
same and no additional information is required. Although the new transform
explicitly depends on the ratio () between the multiple velocity and the
migration velocity, in practice this ratio can be fixed to something reasonable
like 1.5 and the results are good. The new transform may also be advantageous in
the implementation of the apex-shifted Radon transform for the attenuation of
diffracted multiples Alvarez et al. (2004).
Taking into account the ray bending of the multiple raypaths at the multiple
generating interface improves the focusing power of the Radon transform
when applied to ADCIGs. This in turn improves our ability to separate the primaries
from the multiples and, therefore, allows a better estimate of the multiple model
to be computed. The new transform can be implemented at essentially no extra
cost compared with the tangent-squared approximation designed to treat the primaries
ignoring ray bending.

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Stanford Exploration Project

4/5/2006