Results

The gradient magnitude operator does have its desired edge enhancing effect on non-oscillatory images, such as the synthetic data in Figure 13 or the Bay Area map in Figure 14. The synthetic test image on the left of Figure 13 consists of three constant-amplitude regions that are separated by two parallel planes. The gradient magnitude map on the right delineates the two boundary planes.

The top panel of Figure 14 shows the Bay Area topography. The gradient magnitude operator distinguishes topographic features by their slope. In contrast to the Bay Area's smooth sloping hills, the magnitude map's multiple areas of zero gradient surprisingly imply a step-like landscape. I assume that the original topography data was probably sloppily interpolated from a contour map. In general, edge detection and discontinuity attributes often reveal such image shortcomings.

 

bayGrad
Figure 14 Gradient magnitude operator applied to Bay Area topography. The top panel shows the topographic elevation of the San Francisco Bay Area. In the bottom panel, the gradient magnitude operator successfully enhanced the topographic edges, such as ravines and canyons. The terraced appearance is an artefact of the original data.

However, applied to oscillatory images, such as the synthetic test case in Figure 15, the gradient magnitude operator indiscriminately amplifies the plane-wave layer boundaries as well as the discontinuity between the plane-wave volumes. Consequently, the plane-wave layers are not suppressed and the central fault is not isolated. The amplitude along the enhanced discontinuity surface varies irregularly depending on the amplitude contrast of the adjacent sedimentary layers.

 

zeroFoltGrad Figure 15 Gradient magnitude operator applied to synthetic test case. The gradient magnitude operator fails to isolate the fault, because it cannot differentiate between the amplitude change across the fault and the amplitude change across the sedimentary layers.

Similarly, the gradient magnitude operator fails to delineate the faults of the seismic image example of Figure 16. The operator increases the overall frequency contents of the image, but does not suppress the sedimentary layer packages. The steeply inclined layers appear aliased in the vertical sections. The faults are hidden among the layer boundaries. Faults, such as the exemplary R fault of the original image 8, can be identified only if one knows where to search for them. The so-identified faults are, however, often only one-pixel wide and, consequently, well resolved. The salt truncating fault is not particularly enhanced. Its position is indirectly indicated by a change in the salt bodies average gradient magnitude. Similarly, the boundaries of the salt dome are not clearly pinpointed.

In the case of the Gulf salt dome and the North Sea horst, the gradient operator fails to isolate the faults and yields a map that is as difficult to interpret as the original seismic image.

 

gulfFoltTotGrad
Figure 16 Gradient magnitude operator applied to salt image. The gradient magnitude operator fails to suppress the image's sedimentary layers.

 

gulfFoltTotWGrd
Figure 17 Weighted gradient magnitude operator applied to salt image. In contrast to Figure 16, this image is the gradient magnitude of the pseudo-depth space, not simply the pixel space.