The inversion results shows a SSIM index of about 0.6 for $V_p$, $V_s$ and $\rho$. Compared to the random SGS realizations set, the inversion results are significantly improved in terms of similarity with the reference models. The $\phi$ field shows a SSIM index close to 1 for both SGS realization and inversion results. This is quite normal as the $\phi$ distribution shows a low variance for each layers (refer to table \ref{tab:well-log}). If we focus at the reservoir level (1050 m to 1300 m) we observe a clear improvement of the similarity for the inversion results (SSIM=0.89) over the SGS realization result (SSIM=0.82) as shown in figure \ref{fig:SSIM_res}. Indeed, as we perform the CO_2 flow simulation within this unit, we increase the number of data in the optimization (i.e.\ the optimization is done for both static and dynamic data), resulting in an increased similarity at the reservoir level compared to the rest of the model.
    
    
  