USING PREDICTION TO DESIGN THE WINDOW FUNCTION

The partial failure of using the windowing operator to isolate the multiples is caused mainly by the presence of reverberating energy outside the window range. This failure becomes critical for low-order reverberations, which are located close to the primaries and are therefore near the boundary of the window. A possible solution would be the use of an offset-dependent weighting function in the transform, which would favor the contribution of more velocity-sensitive large offsets. As a result, the velocity stack would have a better resolution, with less spreading of energy outside the central velocity. However this procedure would also imply a decreased resolution in the near-offset traces where the multiples are already hard to remove. To overcome this limitation, we need a way to separate primaries and multiples in the whole range covered by the velocity domain. A look at the semblance spectrum (Figure ) shows that the reverberation trends are aligned semi-vertically in a reasonably predictable way. It is possible, then, to design a short operator that predicts the reverberation of order n+1 from the reverberation of order n.

The prediction error has the semblance of the primaries almost unaffected and the semblance of the reverberations reduced, while the prediction itself is predominantly formed by the semblance of the reverberations. As a result, the prediction can be used as the weighting operator in the CG regression. However, instead of using the predicted semblance as a weighting function, we use it to define a window function according to where ${\bf J_p}$ is the predicted semblance, and J_cut defines the cutting value for the window. The actual window function also has a tapering zone to make the transition smoother.