Novel iterative ensemble smoothers derived from a class of generalized cost functions

Abstract

Iterative ensemble smoothers (IES) are among the state-of-the-art approaches to solving history matching problems. From an optimization-theoretic point of view, these algorithms can be derived by solving certain stochastic nonlinear-least-squares problems. In a broader picture, history matching is essentially an inverse problem, which is often ill-posed and may not possess a unique solution. To mitigate the ill-posedness, in the course of solving an inverse problem, prior knowledge and domain experience are often incorporated, as a regularization term, into a suitable cost function within a respective optimization problem. Whereas in the inverse theory there is a rich class of inversion algorithms resulting from various choices of regularized cost functions, there are few ensemble data assimilation algorithms (including IES) which in their practical uses are implemented in a form beyond nonlinear-least-squares. This work aims to narrow this noticed gap. Specifically, we consider a class of more generalized cost functions, and establish a unified formula that can be used to construct a corresponding group of novel ensemble data assimilation algorithms, called generalized IES (GIES), in a principled and systematic way. For demonstration, we choose a subset (up to 30 +) of the GIES algorithms derived from the unified formula, and apply them to two history matching problems. Experiment results indicate that many of the tested GIES algorithms exhibit superior performance to that of an original IES developed in a previous work, showcasing the potential benefit of designing new ensemble data assimilation algorithms through the proposed framework.