\def\figdir{./Figs}
Figure~\ref{fig:anti-vel1} shows our velocity model after one non-linear iteration
of all four methods.  Smoothing the slowness, ({\it depth-laplacian} and
{\it tau-laplacian})  rather than the change
in slowness  (Chapter~\ref{chap:tau}) creates a more reasonable
velocity model.  This is most apparent
when looking at the low
velocity layer. When smoothing the slowness
we have added significantly more energy into the low velocity
layer within the anticline structure.  The resulting migration
images, Figures \ref{fig:res.vel1.lapz}
and \ref{fig:res.vel1.tau}, are also better than the depth counterpart.  
As expected, the {\it tau-laplacian} result is better than the
{\it depth-laplacian} result reconfirming the conclusions from 
Chapter~\ref{chap:tau}. 

\activeplot{res.vel1.lapz}{width=6.0in,height=3.0in}{CR}{The migration result after
one iteration of  {\it depth-laplacian}}
\activeplot{res.vel1.tau}{width=6.0in,height=3.0in}{CR}{The migration result after
one iteration of  {\it tau-laplacian}}
\activesideplot{anti-vel1}{width=4.0in,height=4.0in}{CR}{The velocity after one iteration using
the four different methods.  Top-left is  {\it depth-laplacian}; top-right is
{\it depth-steering}; bottom-left  {\it tau-laplacian}; and 
bottom-right {\it tau-steering}.}

If we replace the isotropic regularizer with a steering filter our
results improve significantly.  In the {\it depth-steering} and
{\it tau-steering} case the anticline structure is very evident.  The
low velocity layer also does a good job following the anticline.
In the depth result, an artificial second low velocity layer appears
in the anticline (the top of which coincides with the low velocity
layer in the original model). The tau result shows much less of
this artifact. The migration results Figures~\ref{fig:res.vel1.steerz}
and \ref{fig:res.vel1.steer} are both impressive. Both results have
done a  good job flattening the basement reflector and show little
residual moveout in the CRP gathers.  The tau result does a slightly better
job defining the edges of the anticline and positioning the reflectors.

%we see that our ew slowness model is beginning to take on the
%anticline form.  The  low velocity layer has begun to bow up and
%the top of the anticline is beginning to form nicely.  The steering
%filters have also better localized the velocity anomaly.  If
%we compare the migration result (Figure~\ref{fig:res.vel1.z})
% we see overall better positioning
%of the reflectors and less moveout in the CRP gathers.
\activeplot{res.vel1.steerz}{width=6.0in,height=3.0in}{CR}{The migration result after
one iteration of  {\it depth-steering}}
%
%The best result is obtained with {\it tau-steering}.
%The anticline shape is showing up significantly better than 
%using the laplacian regularizer ({\it tau-laplacian}) and somewhat
%better than the {\it depth-steering} result.  Again we
%see that tau, compared to depth, does a better job
%isolating the sides of the anticline (the depth continues
%smear changes  into shallow depth).  If we look at
%the migration result, Figure~\ref{fig:res.vel1.steer}, we
%see that we have the best positioning so far of the reflectors. All
%but the bottom reflector is positioned almost perfectly.  The residual moveout
%is also significantly reduced compared to any of the other methods.

\activeplot{res.vel1.steer}{width=6.0in,height=3.0in}{CR}{The migration result after
one iteration of  {\it tau-steering}}
