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Ground-roll

As a final example, consider the problem of separating spatially-aliased ground-roll from body waves in land data. This a more challenging application of the algorithm because the body waves have curvature that changes rapidly with both offset and time so to match it I need small filters in relatively small patches. The ground-roll, on the other hand, has little global curvature (although it may have strong local curvature due to aliasing) and matching it is more successful with large filters in large patches. A refinement to the method could use different regularization operators or at least different regularization parameters $\epsilon$ on the non-stationary filters for the primaries and the multiples. For the sake of simplicity, I used the same regularization for both.

Figure 15 shows the original shot as well as the initial estimates of the body waves and the ground-roll. The ground-roll estimate was computed simply by high-cut filtering the data to 24 Hz using a Butterworth filter with six poles. I allowed significant energy from the body waves to leak into the estimate of the ground-roll to illustrate the problem described in the previous paragraph. Similarly, the estimate of the body waves was computed by low-cut filtering the data to 18 Hz also with a Butterworth filter with 6 poles. Since I don't want to reduce the low frequency components of the signal too much, I allowed strong ground-roll to leak into the estimate of the body waves. The purpose is to eliminate this ground-roll without hurting the signal and ideally, mapping back some of the body-waves from the estimate of the ground-roll.

shot1-estimates1
shot1-estimates1
Figure 15.
Land shot gather with strong ground-roll (a), initial estimate of ground-roll (b), and body waves (c).
[pdf] [png]

shot1-matched-bw
shot1-matched-bw
Figure 16.
Estimate of body waves after one outer iteration (a), after 5 outer iterations (b) and after 10 outer iterations (c). Notice how after the fifth iteration the ground-roll is essentially gone.
[pdf] [png]

shot1-matched-gr
shot1-matched-gr
Figure 17.
Estimate of ground-roll after one outer iteration (a), after 5 outer iterations (b) and after 10 outer iterations (c). Some of the body waves have been removed in panel (c) but much still remains.
[pdf] [png]

Figure 16 shows the estimate of the body-waves after one, five and 10 outer iterations of the proposed algorithm. Even after just the first iteration, most of the ground-roll has been eliminated and after five iterations it is almost gone. For this example I used just two patches in time and one in offset. Figure 17 shows similar results for the ground-roll. Since the patches were so large, the energy of the leaked body-waves were only slightly attenuated (see the reflector at about 1.7 secs). This energy was mapped back to the estimate of the body-waves.
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Next: Discussion and conclusions Up: Examples with real data Previous: Gulf of Mexico data

2007-10-24