Given some initial data d0 with missing traces filled by gapfill() I use lomoplan() to solve for the array of prediction-error filters A in
I will not have courage to begin the iterative migrations until I am able to define everything so that the -planes seem to have the general character of the removed data. A problem above is that beats down all the coefficients in the model A, and I wish it was more selective. Below is the filter I began with.
There was much too much high frequency in ,because, as you see, the inverse covariance matrix appears twice in .In ordinary deconvolution, we may gap the filter to avoid an output dominated by near Nyquist frequencies. Thus I experimented with gapping this filter, and I decided to work with
Inspecting the -plane I saw too much unrealistically steep dip. First I thought, maybe the semicircular smiles need it. Then I realized, our concern is defects in the data plane, not the model plane. So I decided to cut back on the number of filter coefficients to match that in Claerbout Claerbout (1992c). Thus, finally, I am working with the filter
Figures 1 and 2 show the ingredients of .Since figure captions do not seem tolerant of mathematics these days I will explain here that the left column is without missing data. The 6 panels, in vertical order, are Md, d+g (g is unknown data estimated by the gapfill program), K(d+g), AK(d+g), A'AK(d+g) and .