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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.
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combo
Figure 7. |
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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
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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). |
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