Inverse B-spline interpolation |

stolt
Stolt migration impulse response. Left: using
linear interpolation. Right: using seventh-order B-spline
interpolation. Migration artifacts are removed by a more accurate
forward interpolation method.
Figure 25. |
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Another simple example is radial trace transform (Ottolini, 1982) Figure 26 shows a land shot gather contaminated by nearly radial ground-roll. As discussed by Claerbout (1983), Henley (1999), and Brown and Claerbout (2000), one can effectively eliminate ground-roll noise by applying radial trace transform, followed by high-pass filtering and the inverse radial transform. Figure 27 shows the result of the forward radial transform of the shot gather in Figure 26 in the radial band of the ground-roll noise and the transform error after going back to the original domain. Comparing the results of using linear and third-order B-spline interpolation, we see once again that the transform artifacts are removed with a more accurate interpolation scheme.

radialdat
Ground-roll-contaminated shot
gather used in a radial transform test
Figure 26. | |
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radial
Radial trace transform results. Top: radial
trace domain. Bottom: residual error after the inverse transform.
The error should be zero in a radial band from 0 to 0.65 km/s radial
velocity. Left: using linear interpolation. Right: using third-order
B-spline interpolation.
Figure 27. |
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Inverse B-spline interpolation |

2014-02-15