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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 *v*(*z*) 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 *v*(*z*)=*a*+*bz* 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 8 shows we did a good job
recovering the amplitude within a few iterations.

**shot-s-combo
**

Figure 8 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 8
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 9). 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 9 shows
the result of applying a few iterations of fitting goal (19)
to the bottom left result in Figure 9.
By using both methodologies the interpolated data does a much better job
blending into its
surroundings but still is a poor interpolation result.
**wz-25-combo
**

Figure 9 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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** Up:** Clapp, et al.: Steering
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Stanford Exploration Project

10/9/1997