Accounting for model errors in iterative ensemble smoothers

TL;DR

This paper develops a theoretical framework for incorporating model errors into iterative ensemble smoothers, addressing the risk of unphysical parameter updates caused by unaccounted uncertainties in history matching.

Contribution

It introduces practical procedures for including model errors in ensemble methods like ESMDA and IES, enhancing their robustness.

Findings

Including model errors improves parameter estimation accuracy.

Neglecting model errors can lead to unphysical parameter updates.

Theoretical foundation supports better uncertainty quantification.

Abstract

In the strong-constraint formulation of the history-matching problem, we assume that all the model errors relate to a selection of uncertain model input parameters. One does not account for additional model errors that could result from, e.g., excluded uncertain parameters, neglected physics in the model formulation, the use of an approximate model forcing, or discretization errors resulting from numerical approximations. If parameters with significant uncertainties are unaccounted for, there is a risk for an unphysical update, of some uncertain parameters, that compensates for errors in the omitted parameters. This paper gives the theoretical foundation for introducing model errors in ensemble methods for history matching. In particular, we explain procedures for practically including model errors in iterative ensemble smoothers like ESMDA and IES. Also, we demonstrate the impact of adding (or neglecting) model errors in the parameter-estimation problem.