\def\figdir{./Figs}
There is one aspect of using non-stationary PEFs that I have glossed
over to this point: the requirement that we have field with similar
statistics to estimate the PEF from.
Viewed one way this is a significant weakness to the approach, viewed
another it can be seen as a useful feature.  One of the largest problems
in seismic imaging is how to put the geologist's conception of geology
into the geophysicist's inversion problem.  The non-stationary PEF can
be estimated from the geologist's model.  Therefore, our regularization
operator directly incorporates the geologist's conception of the velocity
structure into the velocity estimation.  
\par
For this simple model, we will use as our conception of geology
a vertically warped version of our initial velocity estimate.  I
measure how much a migrated reflector positions varies from an initial
flat estimate, Figure~\ref{fig:warp-diag}.   From the reflector
deviations I calculate a space-varying warp function.  I apply this
warp function to the initial slowness model and obtain, Figure~\ref{fig:warp}.
This warped model is then used to estimate my non-stationary filters.

\activesideplot{warp-diag}{width=3.0in,height=3.0in}{NR}{How the model was warped
to construct a field to estimate the non-stationary PEFs from.  The
movement at each point along the reflector was calculated.  The movement
function was then applied to the initial slowness estimate.}

\activesideplot{warp}{width=3.0in,height=3.0in}{ER}{Warped velocity model
used to estimate non-stationary filters from.}
