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\subsubsection{Geological model}  We consider an idealized geometry and physical model of the sedimentary basin of the St. Lawrence Lowlands. The geological model consists of a tabular succession of 6 horizontal layers corresponding to the Lorraine group, Utica shales, Trenton group, Beekmantown group, Cairnside formation, Covey Hill formation and the Grenville basement. The grid size is 1000 x 1500 $m^2$ with a cell size is 1 x 1 $m^2$, leading to a total of 1.5 million cells. For each cell, 12 parameters ($K_m,K_s,K_f,\phi,G_s,\rho_s,\rho_f,\tau,\eta,\kappa,Q,f0$) characterize the medium. Table 2 resume the main properties of the model. \\  A sequential Gaussian simulation (SGS) framework is used to build the geological model in order to obtain a more realistic model, especially at the layers transition. First, for each layers, we compute the mean ($\mu$) and the standard deviation ($\sigma$) of the physical properties ($V_{clay},V_{calcite},V_{quartz},V_{dolomite},\phi,\rho$) derived from log available in well A196. Cainrside and Covey Hill parameters are derived from laboratory measurements. Distribution of the physical properties are then obtained by simple kriging under Gaussian hypothesis and used for compute the model parameters as the following:  the dry-rock bulk modulus ($K_m$) is estimated using inverse Gassmann's equation \citep{Carcione2007} \citep{Carcione2007}:  \begin{equation}   K_{dry} = \frac{(\phi K_s/K_f + 1 - \phi)K_{sat} - K_s}{\phi K_s/K_f + K_{sat}/K_s - 1 - \phi}  \end{equation}  where $K= \rho V_{P}^{2} - (4/3)G$ is the wet-rock modulus.\\ The bulk ($K_s$) and shear ($G_s$) moduli of the solid are estimated using equation ??. \ref{eq:Ks} and \ref{eq:Gs}.  Tortuosity ($\tau$) is estimated using \citet{Glover2009}:  \begin{equation}   \tau = \phi^{1-m},