\def\figdir{./Figs}
Another option is to characterize our model in terms of
PEFs rather than steering filters. 
Normally we estimate a PEF by solving
\begin{equation}
\bold M \bold a \approx \zero \label{eq:pef} ,
\end{equation}
where $\bold M$ is convolution with a field that has the same properties
as the model  and $\bold a$ is our PEF.
The output of this convolution is white \cite{pvi}. Therefore $\bf a$ must
have
the inverse spectrum
of  the model. 
When the model varies continuously we must
add a slight twist to our PEF estimation.  
Instead of breaking up our model space into regions
where our stationary assumption is valid we
are going to modify the PEF.
Our PEF ($\bf a$) is now going to be composed of several different
PEFs operating in micro-patches (Figure~\ref{fig:patch}).
With so many filters, and therefore filter coefficients, our filter
estimation problem
goes from being over-determined to under-determined.
We can force the system to again be over-determined by adding a
regularization equation to
our original filter estimation fitting goals,
\begin{eqnarray}
\zero \pox \bf M \bf a \\
\zero \pox \epsilon \bf F \bf a   \nonumber 
\end{eqnarray}
where the regularization operator $\bf F$ smoothes the filter coefficients
\cite{Clapp.sep.100.bob3}.

\activesideplot{patch}{width=3.0in,height=3.0in}{NR}{Non-stationary PEF construction.  
The model is broken up into micro-patches.  Each micro-patch has its
own PEF.}
