Receiver Cable interpolation

The interpolation of flip-flop shots has the benefit of many in-line samples on which a PEF can be estimated. For receiver cable interpolation, the samples are fewer and farther between. For this data, an ideal interpolation would be a factor of 4. Since there are only 12 cables on which to estimate a PEF, the size of the PEF in the cross-line is much more limited, since increasing the size of the PEF decreases the number of fitting equations in the inverse problem due to increased edge effects.

 

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Figure 4 Receiver cable interpolation, factor of 2. From left to right: original input shot gather; result of 2D interpolation; result of 3D interpolation.

As we can see in Figure , here interpolating in 2D is noticeably worse than in 3D. In particular, the water-bottom multiple, the diffractions at near offset, and the diffracted multiples at far offset were not correctly interpolated with the 2D filter, and were correctly interpolated in 3D. This is because the 2D interpolation acted over receiver-cable and time, so no trends along the receiver cable axis were captured. The added in-line receiver axis in the 3D PEF interpolation allowed much more information to be gathered from the data.

Once the number of receiver cables has been doubled by interpolation, it can be doubled again to get to the desired factor of 4. This is shown in Figure . The interpolation differences are even more pronounced between the 2D and 3D interpolations. The end result of the cross-line interpolation in 3D is quite promising, and the poor performance of the 2D result shows that extra dimensionality is a much more important factor when the axis of interpolation is poorly sampled.

 

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Figure 5 Receiver cable interpolation, factor of 4. From left to right: original input shot gather; result of 2D interpolation; result of 3D interpolation.

Twelve receiver cables is not typical for a marine acquisition. Many 3D surveys use a smaller number of cables, which can be as low as 4 in a speculative survey. Figure shows the results of interpolating from 6 receiver cables up to 24. While the result is not poor, it is not nearly as good as with the original 12 cables. This is most noticeable at the near offsets.

 

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Figure 6 Receiver cable interpolation, factor of 2. Only 6 cables were used for the left and center images. From left to right: original input shot gather with 6 cables; result of 3D interpolation; result of 3D interpolation with 12 cables as input.