Results

The backprojected residual of the synthetic image example (Figure 28) resembles the individual components of the crossproduct operator. The fault is outlined but directly bordered by large residual amplitudes of the neighboring plane wave regions. Consequently, the resolution is about the size of the patch. Otherwise, the plane wave patches away from the discontinuity are zeroed.

 

zeroFoltDXGAA Figure 28 Forward and adjoint of cross-product operator applied to the synthetic image. The back-projected residual of the synthetic test image suppresses the pure plane-wave patches of the image and broadly delineates the input's fault location.

In the case of the Gulf salt dome image (Figure 29), the back-projecting crossproduct operator removes the image's sedimentary layers successfully, but the delineated faults are slightly corrupted by the image's considerable noise. Some of the noise forms short north-south streaks - best visible in the triangular area in the south-west corner - and might be due to the image's acquisition footprint. The border of the central low-amplitude region is outlined by a broad and fuzzy zone of higher average discontinuity amplitudes. The salt region shows some internal features, such as the linear north-south streaks in its center. The salt's pentagonoid region is visible but its western border is strangely distorted. The salt image's vertical north-south section shows a disappointing amount of remaining sedimentary layers. In contrast, the east-west section shows only a few weak hints of the former layering. Naturally, the near-vertical faults are more visible among the coherent layers of the north-south section than the rather incoherent east-west section.

 

gulfFoltTotDXGAA
Figure 29 Back projection of cross-product residual of the salt image. The discontinuity map successfully suppresses the layers in the time slice and delineates the radiating faults. Overall, the image's noise makes it unattractive for interpretation.

The back-projected crossproduct operator applied to the North Sea horst image generates an extremely noisy discontinuity map. A few linear features can be seen at a grazing angle. The features include the fault marked F in the original image 12. The sparsity of features contrasts positively with the complexity of the same time slice when processed by competing discontinuity operators. However, the fault surfaces are not isolated in the image noise, and the vertical sections show considerable layering.

 

nseaFoltTotDXGAA
Figure 30 Back projection of cross-product residual of the North Sea horst image. The image is dominated by noise. At a grazing angle, the time slice depicts a few gently bending linear features (faults?).

In summary, the back-projection operator highlights many interesting details that other discontinuity attributes miss. However, its overall low signal-to-noise ratio does prevent interpreters from quickly and conveniently assessing the geological information.