\section{Methodology} 
The flowchart of the stochastic inversion that we propose is shown in Figure \ref{fig:workflow}.  It is a three step approach. Firstly, many sets of initial realizations are simulated from available static data (well logs, deterministic elastic inversion, etc...) using a geostatistical cosimulation algorithm. Secondly, an optimization loop is applied to each set before modeling CO_2 injection in order to obtain a static model of petrophysical properties that maximize the match between computed and observed seismic traces. Finally, the resulting models are then combined in an iterative history-matching loop where, at each step, we simulate CO_2 injection and transport, compute the elastic properties of the corresponding model, and run a seismic forward model to calculate the mismatch between simulated and observed traces. In the following sections, we focus on each step of the algorithm. 

    
  