Comparing the Adaptive Gaussian Mixture Filter with the Ensemble Kalman Filter

Over the last years the ensemble Kalman filter (EnKF) and related versions have become a very popular tool for reservoir characterization. The EnKF presents the history matching result and uncertainty in terms of an ensemble of models generated from a prior model and updated sequentially in time to account for the measurements. From a statistical point of view, the optimal solution to the history matching problem is the posterior distribution of the parameters in the reservoir given all the measurements. However, since the EnKF update is linear it has severe limitations when the posterior distribution to be estimated is multimodal and/or strongly skewed due to nonlinearity of the system. As standard sequential Monte Carlo (SMC) techniques are too expensive for large models. Several methods have been proposed to combine the EnKF with SMC methods. In this paper we apply, for the first time, the recently proposed Adaptive Gaussian Mixture filter (AGM), introduced by Stordal et al. 2009, on a reservoir model and compare the results with the traditional EnKF. The AGM tries to loosen up the requirement of a nearly linear/Gaussian model by combining a relaxed EnKF update with an importance weights resampling approach, thereby taking advantage of some of the higher order moments information as in standard SMC methods such as particle filter whilst keeping the robustness of EnKF. The reservoir is a 2D synthetic reservoir model with 4 producers and 1 injector. The permeability and porosity fields are estimated. Although both methods produce good history matching, the results show that the AGM better preserves the geology of the prior model. Moreover, the last updated fields with AGM are closer to the truth than the corresponding EnKF results.