Given some initial data *d _{0}* with missing traces
filled by

(3) | ||

(4) |

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.

(5) |

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

(6) |

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

(7) |

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
.

Figure 2

11/18/1997