Iterative Ensemble Smoother as an Approximate Solution to a Regularized Minimum-Average-Cost Problem: Theory and Applications

Summary The focus of this work is on an alternative implementation of the iterative-ensemble smoother (iES). We show that iteration formulae similar to those used by Chen and Oliver (2013) and Emerick and Reynolds (2012) can be derived by adopting a regularized Levenberg-Marquardt (RLM) algorithm (Jin 2010) to approximately solve a minimum-average-cost (MAC) problem. This not only leads to an alternative theoretical tool in understanding and analyzing the behavior of the aforementioned iES, but also provides insights and guidelines for further developments of the smoothing algorithms. For illustration, we compare the performance of an implementation of the RLM-MAC algorithm with that of the approximate iES used by Chen and Oliver (2013) in three numerical examples: an initial condition estimation problem in a strongly nonlinear system, a facies estimation problem in a 2D reservoir, and the history-matching problem in the Brugge field case. In these three specific cases, the RLM-MAC algorithm exhibits comparable or better performance, especially in the strongly nonlinear system.