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Joint Inversion of Multiple Images (JMI)

We can pose the problem as an inversion for the individual (baseline and monitor) images. Then, the modeling equation becomes

\begin{displaymath}\begin{array}{ccc} \left [ \begin{array}{cc} {\bf L}_{0} & {\...
... {\bf d}_{0} \\ {\bf d}_{1}\\ \end{array} \right ] \end{array}.\end{displaymath} (A-29)

Using the same assumptions and procedure as in the previous section, we arrive at the following formulation:

\begin{displaymath}\begin{array}{ccc} \left [ \begin{array}{cc} {\bf H}_{0} & {\...
...e m}_{0} \\ {\bf\tilde m}_{1} \end{array} \right ] \end{array},\end{displaymath} (A-30)

where the baseline and monitor velocities are known. Where the monitor has been aligned with baseline, we have

\begin{displaymath}\begin{array}{ccc} \left [ \begin{array}{cc} {\bf H}_{0} & {\...
..._{0} \\ {\bf\tilde m}^{b}_{1} \end{array} \right ] \end{array},\end{displaymath} (A-31)

which holds approximately whether or not we migrate the monitor data with the baseline or monitor velocity.