The missing data problem is probably the simplest to understand and interpret. Following the methodology of Claerbout (1999) we solve the problem in its preconditioned form using

(3) | ||

- is a binned version of our known points
- is the known data selector
- is the preconditioning operator (in this case equation (2))
**p****is our preconditioned variable.**

To test the interpolation I used the `qdome' dataset (Figure 4).
I began by zeroing 95%
of the original data (Figure 5)
in vertical sections (somewhat simulating well logs).
To obtain the *p*_{xz} and *p*_{yz} dip field I used the same methodology
as Fomel (1999) estimating the dip field
from the known data using a non-linear estimation scheme.

Figure 4

Figure 5

Using the calculated dip field I then constructed and and iterated 50 times using fitting goals (4). Figure 6 shows the resulting interpolation. In general the 3-D steering filters did an excellent job recovering the original data. There is some lower frequency behavior around the fault boundaries but the fault position is still quite obvious.

Figure 6

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