Moveout-based filtering

Primaries and multiples exhibit hyperbolic moveout in CMPs but their curvature is different. After Normal Moveout (NMO) correction with the NMO velocity of the primaries, ideally the primaries exhibit flat moveout whereas the residual moveout of the multiples can be approximated by parabolas or hyperbolas (, ,). This difference in moveout can be exploited to separate the primaries from the multiples in either the $f$-$k$ domain or the $\tau$-$p$ (Radon) domain.

The performance of an $f$-$k$ filter in suppressing multiples strongly depends on primary and multiple reflections being mapped to separate regions of the $f$-$k$ plane. This is in general the case on far-offset traces, for which the difference in moveout can be large, but not on short-offset traces for which the difference in moveout is small. The performance of $f$-$k$ filtering, therefore, is poor at small offsets even if the subsurface geology is not very complex. This usually makes $f$-$k$ filtering an undesirable option for multiple elimination.

Radon demultiple in data space (, ,) has proven successful in attenuating specular multiples if the subsurface is not very complex. In complex subsurface areas, such as under salt, the hyperbolic or in fact any NMO approximation breaks down. The NMO velocities are inaccurate and therefore, after NMO, the primaries are unlikely to be flat. Furthermore, the residual moveout of the multiples is unlikely to be well approximated by parabolas or hyperbolas. The quality of the separation between primaries and multiples in the Radon domain, and their focusing, therefore, deteriorates. As a result, multiples are imperfectly attenuated and, worse, the attenuation is offset dependent. In such complex areas, Radon demultiple in data space is not a good option.