Plane wave prediction in 3-D

3-D missing data interpolation

qdome Figure 8. Claerbout's ``qdome'' synthetic model.

qslope
Figure 9. Plane wave slope estimates in the $x$ and $y$ directions (left and right plots, respectively) from the ``qdome'' model.

Figures 8 and 9 show Claerbout's ``qdome'' synthetic model (Claerbout, 1999,1993) and its corresponding slope estimates. In a missing data interpolation experiment, I remove 75% of the traces in the original model, arriving at the missing data model, shown in the left plot of Figure 10. The missing data interpolation result is shown in the right plot of Figure 10. Most of the original signal, except for some high-curvature areas, has been restored. Local 3-D plane-wave predictors allow us to use the efficient interpolation technique of Fomel et al. (1997), based on recursive filter preconditioning.

qmiss
Figure 10. Left: ``qdome'' model with 75% of the randomly chosen traces removed. Right: result of missing data interpolation with a 3-D local plane-wave prediction filter.

Plane wave prediction in 3-D