The magnitude of the residuals of the synthetic image example (Figure 26) resembles its constituent components (Figure 25). Patches that contain pure plane waves are zeroed. Patches that straddle the fault and contain two plane waves of distinct dip show significant residual amplitudes. The limit of resolution of the operator is the patch and, again, the fault is broadly outlined but not pinpointed. The discontinuity amplitude does not have a simple interpretation, except that it indicates plane-wave elements that are not well approximated by the somewhat arbitrary best-fitting local plane wave. Interestingly, the generally lower amplitudes of the horizontal plane-wave region indicate that the the best-fitting local plane waves tend to approximate the horizontal events better than the dipping ones. The side of the local cubic patch is 12 pixels long; the side of the total input cube is 80 pixels long.
Figure 26 Pixel magnitude of cross-product residual of the synthetic image. The pixel magnitude of the cross-product residual of Figure 25 roughly delineates the fault of the input image. Again, instead of pinpointing the fault, the operator highlights any local patch that violates the plane-wave assumption.
Applied to the Gulf salt dome image (Figure 27), the magnitude of the crossproduct operator generates a noisy discontinuity map that is void of sedimentary layers but only hints at the image's faults. The attribute suppresses the sedimentary layers successfully, even the steeply dipping ones in the north-west corner. The radiating faults (e.g., the one marked Rin the original image 8) are depicted as linear features of high discontinuity amplitude. However, the image's general random noise obscures its faults. The internal area of the salt body does not generate high amplitudes. The pentagonoid region within the salt, the diagonally truncating fault, and the salt-sediment boundary are broadly outlined by a fuzzy zone of high discontinuity.
The interpretability of the image features suffers from its high noise-to-signal ratio that spoils its contrast and sharpness. The resolution of the radial faults is again the size of the patches. Moderate temporal smoothing might slightly improve the image without loss of resolution.
In the case of the North Sea horst image (not shown), the randomness of the time slice defeats interpretation, even though a few linear features are discernible. Disappointingly, the vertical section of the North Sea horst image depict traces of sedimentary layers. In summary, the magnitude of the cross-product residual failed to compute an interpretable discontinuity map.