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