Plane waves in three dimensions

Crossing dips

conflict
Figure 5. Conflicting dips before and after application of a local monoplane annihilator.

Figure 5 deserves careful study. The input frame is dipping events with amplitudes slowly changing as they cross the frame. The dip of the events is not commensurate with the mesh, so we use linear interpolation that accounts for the irregularity along an event. The output panel tends to be small where there is only a single dip present. Where two dips cross, they tend to be equal in magnitude. Studying the output more carefully, we notice that of the two dips, the one that is strongest on the input becomes irregular and noisy on the output, whereas the other dip tends to remain phase-coherent.

I could rebuild Figure 5 to do a better job of suppressing monodip areas if I passed the image through a lowpass filter, and then designed a gapped deconvolution operator. Instead, I preferred to show you high-frequency noise in the place of an attenuated wavefront.

The residual of prediction-error deconvolution tends to have a white spectrum in time. This aspect of deconvolution is somewhat irritating and in practice it requires us to postfilter for display, to regain continuity of signals. As is well known (PVI, for example), an alternative to postfiltering is to put a gap in the filter. A gapped filter should work with 2-D filters too, but it is too early to describe how experimenters will ultimately choose to arrange gaps, if any, in 2-D filters. There are some interesting possibilities. (Inserting a gap also reduces the required number of CD iterations.)

Plane waves in three dimensions