\subsection{Covariance}
With no other information, the Laplacian might be the best regularization 
operator that we could use. But if we know something else
about out model, can we do better?  According to \longcite{tarantola-ipt},
we should be using the inverse model covariance for our
regularization operator.
The statistics of the model vary spatially, but by breaking
up into four patches, one above the anticline, one below the anticline,
and two within the anticline we can at least approximate stationary
statistics.
If we calculate the covariance within patches where the statistics
are relatively stable, we get Figure~\ref{fig:covar-change}.

%We can calculate the model covariance $C(\bf x)$ by
%\beq
%C({\bf x})={1 \over N({\bf x})}
%\sum_{(i,j)| xdist={\bf x}}
%d_i d_j-m_{-{\bf x}} m_{+{\bf x}}
%\eeq
%where  we have the data values $d_1 ... d_n$.
%We are summing the   $N({\bf x})$  points that
%have $\bf x$ separation and subtract the product
%of  
%the mean ($m$) of data points  $+{\bf x}$ and $-{\bf x}$
%away from a given data point \cite{geostat}.
%Figure~\ref{fig:model-covar} shows the model covariance matrix obtained
%from Figure~\ref{fig:well-logs}.
%%Geophysicists and geostatisticians both  use the model covariance,
%%although in different ways, to solve the missing
%%data problem.  
%\par


\plot{covar-change}{width=6.0in,height=3.0in}{The covariance at four
different regions of our model (left panel of Figure~\ref{fig:well-logs}.)
The top left is above the upper unconformity; top right, the upper portion
of the anticline; bottom left, lower portion of the anticline; and bottom
right, bellow the lower anticline.}








%\sideplot{model-covar}{width=3.0in,height=3.0in}
%{Model covariance matrix for velocity model in Figure~\ref{fig:well-logs}.
%Note that the dip below the lower unconformity dominates
%the covariance calculation.}
%\subsection{Geophysical approach}
%\sepinput{geophysics}
%
%\subsection{Geostatistical approach}
%\sepinput{geostat}


