An example of a MOPLAN in two dimensions, ,is explored in chapter 4 of PVI Claerbout (1992) where the main goal is to estimate the -variation of px. Another family of MOPLANs arise from multidimensional prediction-error filtering as described in PVI chapter 8. These have two additional interesting features: (1) they work on aliased information, and (2) they are a factor of the inverse covariance matrix that can be helpful in any regression.
Here I hypothesize that a MOPLAN may be a valuable weighting function for many estimation problems in seismology. Perhaps we can estimate statics, interval velocity, and missing data using the principle of minimizing the power out of a LOcal MOno PLane ANnihilator (LOMOPLAN) on a migrated section. Thus, those embarrassing semicircles that we have seen for years on our migrated sections may hold one of the keys for unlocking the secrets of statics and lateral velocity variation. I do not claim this concept is as powerful as our traditional methods. I merely claim that we have not yet exploited this concept in a systematic way and that it might prove useful where traditional methods break.
|For an image model of nonoverlapping curved planes a suitable choice of weighting function for regression (model covariance) is the local filter that destroys the best fitting local plane.|