Using a machine learning proxy for localization in ensemble data assimilation

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Ensemble data assimilation methods, particularly iterative forms of ensemble smoother, are very useful assisted history matching techniques. One of the main challenges in the application of these methods is the excessive variance loss due to sampling errors occasioned by the limited size ensembles used in practical cases. The standard procedure to mitigate this problem is called distance-based localization. However, in this case, the data assimilation performance becomes highly dependent on the choice of the localization region. Moreover, there are several relevant examples of non-local model parameters and data types, in which cases, distance-based localization does not apply. This paper proposes a distance-free localization procedure that combines a least-squares support vector (LS-SVR) proxy with a non-isotropic tapering function proposed in the literature. We tested the proposed method in two versions of the PUNQ-S3 problem. In the first version, we tested the method to localize scalar (non-local) parameters. The results show relevant improvements, especially in terms of preserving the posterior variance of the ensemble compared to methods investigated in Lacerda et al. (J. Pet. Sci. Eng. 172,690–706, 2019). The second version considered the problem of localization of grid parameters. In this case, the proposed method outperformed a distance-based localization approach proposed in the literature.