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\subsection{Static optimization}  In the second step of the algorithm, realizations of each set are iteratively combined using the gradual deformation (GD) method \citep{Hu_2000} as a optimization technique.  The GD is a parametrization method that allow us to iteratively perturb one realization a set of realizations  towardsanother  until we obtain a new realization that minimize the mismatch with some observed data. This method was first developed for history matching purposes \citep{Roggero_1998} and involves the linear combination of Gaussian random fields with weight, which are adjusted to minimize the data mismatch. mismatch while preserving the spatial covariance.  Many variations of this technique have since been presented \citep{Roggero_1998,Hu_2000,Hu_2002,Hu2001,LeRavalec2000,LeRavalec2012}. The key idea behind the GD is that the sum of two Gaussian random field (Y1 and Y2) is also a Gaussian random field: \begin{equation}   Y(r)=Y_1\ cos(r) + Y_2\ sin(r)   \end{equation}