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\subsubsection{Synthetic seismograms}  The aim of the CO$_2$ modeling is to simulate a time-lapse VSP surveys. We are interested in analyzing what is the effect of the injected CO$_2$ after 5,10,  15 and 50 years from the start of injection as shown in figure \ref{fig:fig8} and \ref{fig:fig9}.\\ Large offset AVO analysis (\textgreater\ 700 m) in our work are compromised due to a refracted wave (Fig. \ref{fig:fig7}) that arise at interface Lorraine/Utica shales and Trenton group preventing a proper separation of upgoing and downgoing waves. The parameters for the synthetics seismograms are summarized on Table 2.