Solution steering with space-variant filters

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# SHOT-GATHER BASED INTERPOLATION

Another possible application for using recursive steering filters is to interpolate seismic data. As an initial test we chose to interpolate a shot gather. We used a velocity function to construct hyperbolic trajectories, which in turn were used to construct our dip field (similar to the seismic dips used in the previous section).

For a first test we created a synthetic shot gather using a model as input to a finite difference code. We then cut a hole in this shot gather and attempted to recover the removed values. As Figure 7 shows we did a good job recovering the amplitude within a few iterations.

combo
Figure 7.

Left, synthetic shot gather; center, holes cut out of shot gather; right, inversion result after 15 iterations.

To see how the method reacted when it was given data that did not fit its model (in this case hyperbolic moveout) we used a dataset with significant noise problems (ground roll, bad traces, etc.). Using the same technique as in Figure 7 we ended up with a result which did a fairly decent job fitting portions of the data where noise content was low, but a poor job elsewhere (Figure 8). Even where the method did the best job of reconstructing the data, it still left a visible footprint. A more esthetically pleasing result can be achieved by using the above method followed a more traditional interpolation problem using the operator and the fitting goal

 (19)

where is initialized with the result of our previous inversion problem and not allowed to change at locations where we have data. The bottom right panel in Figure 8 shows the result of applying a few iterations of fitting goal (19) to the bottom left result in Figure 8. By using both methodologies the interpolated data does a much better job blending into its surroundings but still is a poor interpolation result.

wz-combo
Figure 8.
Top left, original shot gather; top right, gather with holes (input); bottom left, result applying equation 18, bottom right, result after applying equation (18) followed by (19).

 Solution steering with space-variant filters

Next: FUTURE WORK AND CONCLUSIONS Up: Clapp, et al.: Steering Previous: WELL LOG/DIP INTERPOLATION

2013-03-03