Fortunately,
the boundary artifacts can be effectively attenuated
by applying a post-processing filter on the prestack image
that preserves only the events for which the source and receiver
rays are coplanar at the imaging point.
This condition must be fulfilled by all the events
that are correctly focused at zero offset
because two lines passing through the same point are coplanar.
The *coplanarity condition* can be easily
applied on the prestack image after transformation
into the Fourier domain,
possibly at the same time that ADCIGs are computed
using a 3-D generalization of the method described by
Sava and Fomel (2003),
as presented in
Tisserant and Biondi (2003).

The coplanarity condition can be derived by simple geometric considerations starting from the common-azimuth condition expressed as Biondi and Palacharla (1996):

(1) |

As for the common-azimuth condition,
the coplanarity condition can be expressed
as a relationship that links the cross-line offset wavenumber
*k*_{yh} to the other wavenumbers in the image.
For events with azimuth aligned along the in-line direction
(*x*_{m} in my notation),
the expression of the coplanarity condition is:

(2) |

The condition expressed in equation (2) can be easily generalized to be valid for an arbitrary azimuthal direction Tisserant and Biondi (2003). The wavenumber axes are rotated by in both the midpoint wavenumber plane and the offset wavenumber plane .

As discussed in Tisserant and Biondi (2003), in a prestack image each event fulfills the coplanarity condition for one value of the azimuth. However, streamer data illuminate the reflectors only within a fairly narrow azimuthal range. Therefore, the coplanarity condition can be used to remove from the prestack image all the events that are imaged outside a given azimuthal range. For example, if we image only events within a range of degrees, we will remove the 75 % of the events in the image that are least likely to be real reflection events.

7/8/2003