Figure 9 shows the result of applying PEF texture synthesis to a 2-D stacked seismic section. The residual panel is interesting; notice uncollapsed diffraction hyperbolas, two highlighted fault planes, and also statics-like artifacts in the earlier times. PEF's easily predict straight lines (plane waves) and sinusoids, but hyperbolas and discontinuities are quite another matter.
Matthias Schwab used the ``plane wave prediction'' property of the PEF in his Ph.D. thesis Schwab (1998) to create so-called ``coherency cubes'' from 3-D seismic data by nonstationary convolution with small PEF's. Development of viable seismic coherency attributes merits considerable industrial interest, as evidenced by the concentration of related articles in the March, 1999 edition of The Leading Edge.
If a good velocity model is used, poststack migration should collapse these hyperbolas, so one measure of the fitness of a given velocity model could be the relative amount of residual energy in the data*PEF panel. Additionally, to the same end, this technique could be used to measure the relative amount of residual curvature in common reflection point (CRP) gathers, which are flattened when the correct migration velocity is used Biondi (1997). This preprocessing could be done quickly, for the necessary PEF's are small.