deletions | additions       diff --git a/The_inversion_results_shows_a__.tex b/The_inversion_results_shows_a__.tex  index 5533840..42dc2f0 100644  --- a/The_inversion_results_shows_a__.tex  +++ b/The_inversion_results_shows_a__.tex 
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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 term of similarity with the reference models. The $\phi$ field shows a SSIM index close to 1 for both SGS realization and inversion results. Thismeans that both are very similar to the reference porosity field. This  is quite normal as the $\phi$ distribution shows a low variance for each layers (see (refer to  table \ref{tab:well-log}). If we focus at the reservoir level (1050m to 1300m) we observe a substantial clear  improvement on 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}. In effect, as we perform the CO$_2$ CO_2  flow simulation within this unit, we increase the number of parameters to optimize (i.e., the optimization is done for both static and dynamic data), resulting in an increased similarity with at  therespectively  reservoir level compared to the rest  of thereference  model. \\