**AAPG GEO 2010 Middle East**

**Geoscience Conference & Exhibition**

Innovative Geoscience Solutions – Meeting Hydrocarbon Demand in Changing Times

**March 7-10, 2010 – Manama, Bahrain**

3D High Resolution Parabolic Radon Filtering

(1) CGGVeritas, Pau, France.

(2) CGGVeritas, Massy, France.

(3) Total E&P, Pau, France.

2D parabolic Radon filtering is a widely used method for multiple attenuation, based on velocity discrimination between the primaries and multiples. The CMP gathers after NMO are modelled by a superposition of constant amplitude parabolas:

t = tau + q.h^2, (h = offset)

The most curved parabolas, assumed to be the multiples (slower than the primaries), are retained and subtracted from the data. High Resolution (sparseness) constraints introduced in the Radon domain further improve the capability of the method to process spatially aliased data and to preserve the primaries.

The existing 2D implementations, time-offset, are perfectly suited to 2D or 3D narrow azimuth data. However, for dense and wide-azimuth data that exhibit azimuthal variation effects (whatever the reasons), this approach can fail. Because of the variation of the curvatures with the azimuth, the bin gathers can not be processed in one go but must rather be split into sub-collections (e.g. azimuth sectors): this is not always satisfactory (difficult balance to find between small enough azimuthal variations and large enough fold). These modern acquisition geometries hence provide the motivation for the development of one pass, 3D, HR, de-aliased parabolic Radon filtering solutions.

In a wide azimuth gather, we consider the offset vector (x,y) instead of the scalar offset. The azimuthal variations of the curvature are handled with an elliptical model. The gathers are now modeled by the superposition of constant amplitude, squeezed and rotated paraboloids, representing either primaries or multiples:

t = tau + q.(x^2+y^2)+r.(x^2-y^2)+s.2.x.y

The rest of the implementation is similar to the 2D algorithms as described in the literature. The curvature cutoff is determined with respect to the average curvature of the paraboloids, and we end up with the decomposition of the input gathers into three terms: primaries, multiples, and “noise” (everything that is not fitted by the constant amplitude paraboloids model). The actual 3D geometry of the gathers is now honoured, and the full fold can be used because azimuth sectoring is no longer required: all of this result in more consistent decompositions with the 3D algorithm, and eventually in a better filtering of the multiples along with a better preservation of the primaries.