The missing data problem is probably the simplest to understand and
interpret.  Following the methodology of \longcite{gee} we solve
the
problem in its preconditioned form using
\beqa
\data &\approx& \bf J \prec \pvar \\ \nonumber
\zero &\approx&  \iop \pvar \label{eq:miss-prec} ,
\eeqa
where:
\begin{description}
\item [$\data$] is a binned version of our known points
\item [$\bf J$] is our known data selector
\item [$\prec$] is our preconditioning operator in this case:
\beq
A_{3d}^{-1} = A^{-1}_x A^{-1}_y
\eeq
and
\item [\pvar] is our preconditioned variable.
\end{description}


To test the interpolation I used the `qdome' dataset \cite{gee}. 
I began by zeroing 90\% of the data (Figure~\ref{fig:mod-in}).
To obtain the $p_{xz}$ and $p_{yz}$ dip field I used the same methodology
as \longcite{Fomel.sep.102.sergey3} estimating the dip field
from the known data using a non-linear estimation scheme.

\plot{mod-in}{width=6.0in,height=8.0in}{3-D qdome model. The top plot shows
the original data.  The bottom plot shows the decimated data used as
input for interpolation.}


Using the calculated dip field I then constructed $A_x$ and $A_y$ and 
iterated 50 times using fitting goals (\ref{eq:miss-prec}).
Figure~\ref{fig:mod-out} shows the resulting interpolation.  In general
it 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.

\plot{mod-out}{width=6.0in,height=8.0in}{3-D qdome model. The top plot shows
the original data.  The bottom plot shows the  interpolation result.}


