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\section{Vertical \section{Time-lapse  seismic response  modeling} Vertical seismic profiling (VSP) methods are well suited for pilot carbon sequestration projects as, on one side, they provide higher vertical resolution information than surface seismic \citep{Yang2014} and, on the other side, they allow for multiple economical repeat survey. Indeed, VSP surveys for CO$_2$ monitoring have been used at pilot-scale CO$_2$ injection sites such as Ketzin \citep{Yang2010}, SACROC \citep{Yang2014,Cheng2010}, Frio \citep{Daley2008}, and Otway \citep{Urosevic2008}. For this study,a  numerical simulation of a time-laspe  VSP monitoring campaign surveys  has been conducted as a preparatory work for a future VSP survey. monitoring program.