Fault-zone replacement method

To remove the effect of faults, we can also replace fault zones with smooth transitions, and then the original image becomes an image without faults. The smooth transition is designed with the fault slip information, and the width of fault zone can be chosen based on the magnitude of the fault slip. When the fault slip is large, it is easier to avoid aliasing in the smooth transition zone by selecting a wider fault zone.

If the width of a fault zone is $N$ samples, we can extract two traces at $-N/2$ samples (left side) and $N/2$ samples (right side) of the fault, and then do linear interpolation to generate the traces from $-N/2+1$ to $N/2-1$ as the transition zone. Note that the linear interpolation can not be done horizontally if the fault slip is not zero. It has to be along the slip vector direction. A simple way to follow such direction is to do linear interpolation through predictive painting and set the dip to be fault throw (the vertical component of slip) divided by $N-1$. Specifically, the fault transition would be distance-weighted sum of the predictive painting results of the two selected traces. This method is also simple to implement, but if the faults are close to each other, an appropriate fault zone width may be hard to choose.