Results

Figure 25 shows the cross-product output for the synthetic test case of Figure 4. Each component of the local residual vectors is displayed as an individual image volume. In the regions away from the fault, where the image satisfies the plane-wave assumption, the residual is zero. At the fault, the output image is non-zero and the fault is broadly outlined. Within a patch that straddles the fault, the plane-wave dip estimation encounters two contradictory plane-wave events. The least-squares solution averages the two dips so that the dip estimate does not approximate either of the two dips. Consequently, within a patch that straddles the fault, all pixels show a significant residual. The patch-wide residual reduces the resolution of the discontinuity image to the size of the patches and does not imply a meaningful interpretation of the discontinuity amplitude.

Because a three-dimensional vector field is difficult to interpret, the schemes of the two next sections summarize the information of the three volumes into a single discontinuity image.

 

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Figure 25 Cross-product operator applied to synthetic image. The cross-product operator applied to the synthetic fault model broadly delineates the fault in each of its three output volumes. Each output volume is a component of the cross-product vector. However, the three-dimensional output vector at each pixel of the three-dimensional image is not suited to interpretation.