A steering filter  is  an effective regularizer 
when  it can accurately describe the model covariance.  For
a certain class of velocity models, models with discontinuities,
a steering filter  has more of a problem accurately describing 
the model's covariance.  
\par
PEFs are not as limited as steering filters in the shapes
that they can describe.  
To predict a PEF we must have a model with stationary statistics.
We can often satisfy this requirement by breaking up our
problem into small patches.  \longcite{Crawley.segab.98}
showed that this true when solving a data interpolation problem.
Unfortunately, we can only make our patch size so small before
we can't generate sufficient statistics to estimate our PEFs.
\par
An alternative  approach,
proven to be more effective when dips change
quickly, is  to estimate PEFs in micro patches with
a space varying PEF \cite{Crawley.segab.99}.
When dealing with discontinuities regularizing with a non-stationary PEF
can be more effective in describing the model covariance than a steering
filter. A non-stationary PEF does a better job honoring sharp boundaries and
can be more effective when characterizing complex models.
I will begin this appendix by
showing how steering filters can fail at discontinuities.
I will then show how to  build and estimate a space-varying PEF.  I will
use  the space varying PEF in the context of a missing data problem. 
I will move into using the PEF for regularization.  I will show how
we can estimate our non-stationary filter from a warped version of our velocity
model. I will conclude by showing that using a non-stationary PEF  as
the regularizer to tomography on the anticline
synthetic produces comparable results to the steering filter approach.
