Instead of independent problems in patches, we smooth between micropatches. We apply a smoother between values at identical lags of different PEFs, in such a way that PEFs which are applied at similar data coordinates are averaged together. For statistical robustness, we want to smooth as much as possible, but we want to avoid making a roundabout assertion of stationarity where the data are not stationary. To maximize the area in data space over which PEFs are averaged, without averaging nonstationary regions together, we can choose the directionality of our smoother. CMP gathers tend to have nearly constant dips in regions along radial lines, so we choose the radial direction.

The filter calculation part of the problem becomes large and underdetermined. Happily, however, it converges in few iterations, and turns out to be cheaper and lead to better interpolation results than interpolation in independent patches.

- Arguments against patching
- Implementation of adaptive PEFs
- Radial smoothing
- Parameter space
- Shots versus receivers, 2-D versus 3-D
- Data examples
- Smoothing and damping, accuracy and convergence

1/18/2001