

A 3-D filter can be constructed by cascading two perpendicular 2-D filters,
one oriented in the $x-z$ plane and one oriented in the $y-z$ plane.
We can write this new filter as,
\beq
\bf A^{-1}_{3d} = \bf A^{-1}_x \bf A^{-1}_y ,
\eeq
where $\bf A^{-1}_{3d}$ is our inverse
 3-D steering filter operator, $\bf A^{-1}_x$ is an inverse
steering filter oriented in the x-direction, and 
$\bf A^{-1}_y$ is an inverse y-direction
steering filter. 
The result is a slightly asymmetric 3-D pancake.
%\sideplot{3d-response}{width=3.0in,height=3.0in}{3-D steering filter response.}
\par
The construction of two 2-D filters allows for a large degree of freedom
in filter construction.
The method can deal with a range of spatial dips with little
variation in bandwidth response, Figure~\ref{fig:angles}.  
In addition we can vary the {\it range} over which the smoother operates, 
both isotropically (Figure~\ref{fig:iso}) and to some degree
anisotropically (Figure~\ref{fig:aniso}).


\plot{angles}{width=6.0in,height=3.2in}{An example of filter behavior
at different dip angles. Note how the bandwidth response is approximately
the same.}

\plot{iso}{width=6.0in,height=3.2in}{By changing what the non-zero lag
coefficients sum to the area over which the filter acts can be drastically
altered.}
\plot{aniso}{width=6.0in,height=3.2in}{The cascading of two filters allows us
to create a filter that acts over different range in the x and y direction.}





