Clapp et al. 1998 show how to control the direction of smoothing.
In certain cases, it may make sense to specify some preferred direction of filter smoothing.
For instance, CMP gathers tend to have approximately constant dip spectra at constant values of x/t, which correspond to radial lines.
So it makes sense to arrange patches and smooth filter coefficients
in the radial direction on a CMP gather, to accelerate convergence and
get good results with as few coefficients as possible.
Very small patches are desirable where the data has the most curvature, which
tends to be at smaller times and offsets.
At larger times and offsets,
however, events in CMP gathers tend to be near their asymptotes, and
much more linear.
Smoothing and patching in radial coordinates has the pleasing result
that the largest patches fall at far offsets and late times, where
they are most appropriate.
Figure bob, which comes from Clapp 1999,
shows randomly scattered points smoothed with radial-steering filters.
bob
Figure 1 Radial smoothing. Panel shows result of smoothing random scattering of dots with the adjoint radial steering operator. The forward operator points out from the origin. Figure borrowed from Clapp (1999).
