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\def\figdir{./Figs}
The geophysicist attempts to characterize the model covariance 
through a Prediction Error Filter (PEF).  The geophysicists notes that 
if we solve
\beq
\bold M \bold a \approx \zero \label{eq:pef} ,
\eeq
where $\bold M$ is convolution with a field that has the same properties
as the model, $\bold a$ is our PEF which
will be a filter with the inverse spectrum, 
of $\bold M$. By changing the shape of $\bf a$ we can
control how many 
and  which dips 
of the model   we wish  to see.
If we construct  $\bf a$ to find dips at all possible
angles and then
apply (\ref{eq:pef}) we
get  Figure~\ref{fig:gp-mis} as the impulse response of our filter.
The PEF captured the prominent dip going up at approximately 15 degrees
and also found a minor dip going down at approximately 30 degrees.
The right panel of Figure~\ref{fig:gp-mis} show the result of applying
the PEF to our missing data problem.  We have done a substantially better
job filling in the missing data compared to our laplacian result,
Figure~\ref{fig:qdome-lap}, but still far from ideal.
The filter has introduced both dips
at ever location as a result we have a choppy model that is generally
unreasonable.
\activeplot{gp-mis}{width=6.0in,height=3.0in}{ER}
{
The left panel shows the impulse response  of the PEF found from
the velocity field (left panel of Figure~\ref{fig:well-logs}).
The right panel shows the result of applying the PEF
he missing
data problem ( the input being the right side of Figure~\ref{fig:well-logs}).}

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