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
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 pxz and pyz dip field I used the same methodology as Fomel (1999) estimating the dip field from the known data using a non-linear estimation scheme.
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.