Hybrid Iterative Ensemble Smoother for History Matching of Hierarchical Models

Abstract The choice of a prior model can have large impact on the ability to assimilate data. In standard applications ensemble-based data assimilation, all realizations in initial ensemble are generated from same covariance matrix with implicit assumption that this is appropriate for problem. hierarchical approach, parameters function, example, variance, orientation anisotropy and ranges two principal directions, may be uncertain. Thus, approach much more robust against misspecification. paper, three approaches sampling posterior parameterizations discussed: an optimization-based (randomized maximum likelihood, RML), iterative smoother (IES), novel hybrid previous (hybrid IES). approximate methods applied linear-Gaussian inverse problem which it possible compare results exact “marginal-then-conditional” approach. Additionally, IES tested two-dimensional flow uncertain covariance. method shown perform poorly examples because poor representation local sensitivity by method. method, however, samples well even relatively small size.