Introduction

In all of the flattening methods presented thus far Guitton et al. (2005a,b); Lomask et al. (2005, In press); Lomask and Claerbout (2002); Lomask (2003a,b) a key selling point is that they require no picking. This would be fine if all data sets had perfectly estimated dips, but in the real world flattening without picking can produce results that are not perfect. Noise, both coherent and otherwise, can overwhelm the dip estimation causing reflectors in those areas to not be flat. Consequently, it would be useful to have the ability to add some geological constraints to restrict the flattening result in areas of poor data quality while allowing it to efficiently tackle other areas where the dips are accurate.

Here, we present two flattening methods with hard constraints. The hard constraints can be manually picked horizons or individual picks. Both methods require regularization in time (or depth) which carries along with it certain disadvantages as compared to unregularized methods. The largest disadvantage being that increasing regularization reduces local accuracy. In one method the hard constraints are implemented as model mask within the inversion. In the other method, the hard constraints are set as lower and upper bounds of a Limited-memory BFGS with Bounds (L-BFGS-B) algorithm Zhu et al. (1997). We envision a tool that interpretors can run once completely unconstrained, then quality control the results. The interpreter can then adjust some horizons and then run the flattening method again honoring their changes. The algorithm is fast enough so that this process can be repeated several times. In the future, computational and algorithmic improvements can result in a flattening method that is so efficient that the flattening process can be run between picks. This method also has the potential of combining other information into the flattening such as well log picks.