Interpolation

This step can be accomplished either by interpolating linearly along the picked dip or by finding missing traces which minimize the filtered output. A shortcoming of the former approach is that it cannot handle more than one dip at a point, which happen at the crossing of linear events. I choose the latter approach, which finds missing traces by minimizing the filtered output using the filter simulated from the previous section.

For minimization, I use Claerbout's conjugate-gradient algorithm (Claerbout, 1991) because other algorithms must formulate the problem in the form of known values, splitting unknown values, which is very difficult if unknown values are randomly spread among known values.