Characterizing residual moveout

In migration velocity analysis there is always a debate on the best method to describe the moveout seen in CRP gathers. One approach is to measure and invert the moveout at many depths in each offset/angle of the CRP gather independently. Using this approach, complex residual moveouts can be accurately described. The downside is that these estimates are more prone to noise (cycle skipping for example). The other extreme is to use a single parameter (at many depth locations) that best describes the moveout as a function of offset or angle. A single parameter is more robust but in complex situations may not accurately describe moveout. In addition, selecting the parameter usually involves selecting the moveout with the maximum semblance at a given depth, a non-linear problem that can often lead to unrealistic solution if not properly handled Clapp et al. (1998).

Often a good compromise between robustness and flexibity is to describe moveout with two parameters. Unfortunately, selecting these two linked parameters is more problematic than the single parameter approach. One approach is to scan over both parameters at all desired depths, for every CRP, and pick the maximum. In addition to being costly, this approach makes picking a consistent and spatially realistic model very challenging. A potentially better approach is outlined in Harlan (1998). He suggests a dual scanning approach: scan over the first-order term fitting the outer offsets, then scanning over the second-order term to best fit the middle offsets. This approach is more efficient than scanning over the entire model space. The dual scanning approach amounts to linearizing the problem arround the first order term, with all of the associated linearization drawbacks. In additional spatial consistency is also problematic.

A general weakness of the scanning approach is that moveout is being determined from semblance amplitude. Flattening offers an interesting alternative to the scanning approach. Flattening inverts for a time shift field (moveout). By incorporating an operator that estimates moveout parameters from time shift field, arbirtrary moveout descriptions can be estimted from dip.