In order to add constraints, regularization is required to enforce conformity between horizons. In many geological settings this is desirable, however there are some notable exeptions such as angular unconformities. If these unconformities can be identified, it may be necessary to add a residual weight to essentially disable the regularization at those regions of the data.
The ability to incorporate some picking will likely allow the reconstruction of horizons across faults that cut across the entire data cube. As described in Lomask et al. (2005), in order to automatically flatten a data cube with faults, at least half of the fault's tip line must be encased within the data. That is, the fault must die out. With the ability to add some picks, faults that do not die out can be reconstructed. We envision an interpreter can pick a few points on a 2D line and then flatten the cube. With computational improvements in both the algorithm and hardware, this method could be applied on the fly, as the interpreter adds new picks.
More efficient algorithms may not be far off. It seems plausible to add constraints to the flattening method with the cosine transform described in Lomask and Fomel (2006). Alternatively, we can apply the cosine transform method as either an initial solution or a preconditioner to conjugate gradients in an approach similar to Ghiglia and Romero (1994) for 2D phase unwrapping. Lastly, we maybe able to precondition the full equation with the cosine transform, this method would seem to have the most promise for achieving superior computational efficiency.