Application limitation with faults

The accuracy of predictive painting depends on the accuracy of dip estimation (Fomel, 2002). However, local dip attribute may not characterize the fault displacement correctly. For example, Figure 1a shows a synthetic 2D image which contains a fault with a constant slope 1, but the local fault slip is nonstationary changing from -10 to 10 samples. To estimate the local fault slip, we extract the traces in the opposite sides of the fault (as indicated by the dashed lines in Figure 1a) and use local similarity scan (Fomel, 2007a) to measure the local shifts. Local similarity scan involves two steps: scanning and picking. Figure 1b shows the similarity scan and the black curve on it represents the picked local fault throw, which is the vertical component of the fault slip. The curve is picked by regarding the local similarity as a velocity field and then solving Eikonal equation twice with a source on the top and bottom boundaries, respectively (Fomel, 2009). The picked local fault slip matches the theoretical value (a sine function), and we can utilize it in the application of predictive painting.

syn,pick
Figure 1. (a) A 2D synthetic image containing a fault which has the constant slope 1 but nonstationary fault slips; (b) fault throw (the vertical component of slip) measured using local similarity scan.