Impact of Ensemble Size and the Need for Localization in Ensemble History Matching

This paper investigates the implications of ensemble size and the importance of localization in ensemble history matching. Increasing the ensemble size is known to reduce the impact of sampling errors, but determining the appropriate size, N, to ensure a strong signal-to-noise ratio remains challenging. Ensemble history-matching methods use the correlation between uncertain parameters and predicted measurements to compute linear updates to the input parameters. However, the nonlinear relationship reduces the correlations.

Practical limitations in computational resources and simulation time restrict the ensemble size, often leading to spurious updates in the posterior ensemble when computing the global analysis. To address this issue, we introduce a consistent correlation-based localization method. Instead of using physical distances, this method selects measurements based on their correlation strength with the updated parameter.

The paper presents examples using the REEK model, demonstrating how increasing the ensemble size improves the correlation functions and how localization reduces spurious updates and avoids underestimating the posterior variance.

The paper also indicates the need to include uncertainties in historical-rate controls and account for measurement error correlations when computing update steps. An ensemble size of around 200 is suggested for the current example to ensure physically significant correlations.