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Robust computation of ADCIGs in presence of geological structure

Our first application of the CIG kinematic properties analyzed in the previous section is the definition of a robust method to compute high-quality ADCIGs for all events, including steeply dipping and overturned reflections. In presence of complex geological structure, the computation of neither the conventional HOCIGS nor the new VOCIGs is sufficient to provide complete velocity information, because the image is stretched along both the subsurface-offset axes.

According to equation (9), as the geological dip increases the horizontal-offset axis is stretched. At the limit, when $\alpha$ is equal to 90 degrees, the relation between the horizontal-offset and the geological-dip offset becomes singular. Similarly, VOCIGs have problems when the geological dip is close to flat ($\alpha=0$ degrees) and equation (10) becomes singular. This dip-dependent offset-stretching of the offset-domain CIGs causes artifacts in the corresponding ADCIGs.

The fact that relationships (9) and (10) diverge only for isolated dips (0, 90, 180, and 270 degrees) may falsely suggest that problems are limited to rare cases. However, in practice there are two factors that contribute to make the computation of ADCIGs in presence of geological dips prone to artifacts:

These considerations suggest that, in presence of complex structures, high-quality ADCIGs ought to be computed using the information present in both HOCIGs and VOCIGs. There are two alternative strategies for obtaining a single set of ADCIGs from the information present in HOCIGs and VOCIGs. The first method merges HOCIGs with VOCIGs after they have been transformed to GOCIGs by the application of the offset stretching expressed in equation (16). The merged GOCIGs are then transformed to ADCIGs by applying the radial-trace transformation expressed in equation (18). The second method merges HOCIGs with VOCIGs directly in the angle domain, after both have been transformed to ADCIGs by the radial-trace transforms expressed in equations (4) and (7).

The two methods are equivalent if the offset range is infinitely wide, but they may have different artifacts when the offset range is limited. Since the first method merges the images in the offset domain, it can take into account the offset-range limitation more directly, and thus it has the potential to produce more accurate ADCIGs. However, the second method is more direct and simpler to implement. In both methods, an effective, though approximate, way for taking into account the limited offset ranges is to weight the CIGs as a function of the apparent dips $\alpha$ in the image. A simple weighting scheme is:
   \begin{eqnarray}
w_{x_h}= \cos^2{\alpha},
\nonumber
\\ w_{z_h}= \sin^2{\alpha},\end{eqnarray}
(20)
where the weights wxh and wzh are respectively for the CIGs computed from the HOCIGs and the VOCIGs. These weights have the attractive property that their sum is equal to one for any $\alpha$.We used this weighting scheme for all the results shown in this paper.



 
next up previous print clean
Next: ADCIGs in the presence Up: Biondi and Symes: ADCIGs Previous: Demonstration of kinematic properties
Stanford Exploration Project
7/8/2003