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\subsection{Geostatistical methods}  In our approach, elastic properties (i.e.,$V_p$, $V_s$, density ($\rho$) and porosity ($\phi$)) are first simulated using Sequential Gaussian Simulation (SGS) \citep{Deutsch1998,Doyen2007}.\\  SGS is a method for simulating continuous reservoir properties that requires only knowledge of a variogram and an histogram. Starting from a prior information available form well-log, the algorithm visit each node of the grid along a random path. At each step along this path, the algorithm co-simulate a value for each variable by sampling from a Gaussian conditional PDF whose mean and variance are given respectively by a kriging mean and variance. At each node, the prior information and the previously simulated values are used to compute the kriging mean and variance of each variable. This feedback loop ensure that the simulation is spatially correlated. By construction, SGS simulation will be conditioned by the well data, i.e., the simulations reproduce the well observations and thus have the same overall statistical properties. Multiple simulation are generated by using different random paths in order to obtain independent set of realization. For an extended review about SG methods refer to \cite{Deutsch1998,Doyen2007}.\\