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\section{Introduction}   One of the major challenges limiting large-scale Carbon Capture and Storage (CCS) operations, is the issue of \ce{CO2} \num{2}  storage. As the reservoir often determines all design and operational conditions of the complete CCS from the very beginning, having a sound knowledge of the physical characteristics of a storage site is crucial to determine the optimal rate of CO$_2$ injection, which influence the rate of capture, as well as to assess a proper monitoring strategy to prevent the migration of the CO$_2$ up to the surface. \\ A common goal in CCS projects is to use the monitoring data to verify the CO$_2$ distributions that are predicted by simulations produced for geological models of the reservoir. However, CO$_2$ distributions that are imaged through monitoring are often inconsistent with the model-based simulations to varying degrees \citep{Ramirez2013}. This is mainly due to the lack of data and uncertainties that limits the understanding of the subsurface and therefore the ability to produce accurate reservoir models. \\  To build a numerical reservoir model, the spatial distribution of reservoir properties (e.g., lithology, porosity, permeability) first needs to be described. Because of the geological complexity and the scarcity of direct observation (i.e. well data) the probabilistic methods appears to be the most appropriate choice for reservoir modeling. Seismic measurements are well suited in reservoir modeling as provide indirect, but nevertheless spatially extensive information about reservoir properties that are not available form well data alone. In addition to the static information and in order to evaluate the performance of the reservoir in term of CO$_2$ storage, reservoirs models need to constrained to dynamic data obtained from the CO$_2$ injection operations. Ideally, reservoir models should match the observed dynamic behavior of the reservoir to within some accepted tolerance. To check the model's consistency with dynamic data, flow simulation is required. The process to adjusting/perturbing an initial reservoir model is commonly know as history matching and extensively used in the oil and gas industry.\\  The estimation of model parameters from seismic data is a complex, ill conditioned, nonlinear inverse problem due to the intrinsic limitations of the geophysical method: the limited bandwidth and resolution of the seismic data, noise, measurement errors, and physical assumptions about the involved forward models \citep{Tarantola_2005}. Seismic inverse problems may be developed following deterministic or probabilistic approaches and can be divided into two main categories: (1) multistep inversion methods and (2) stochastic inversion methods \citep{Grana2012}.\\