Numerical Comparison of Ensemble Kalman Filter and Randomized Maximum Likelihood

Abstract

In recent years, more traditional history matching methods have been increasingly challenged by sequential data assimilation techniques such as the ensemble Kalman filter (EnKF). There are strong similarities between EnKF and the non-sequential method, randomized maximum likelihood (RML). For a linear forward model the two methods are equal, for a nonlinear forward model there arises some differences (in addition to sequential/batch data assimilation): RML can be iterative, while EnKF is not; RML uses realization-specific gradients/sensitivities to change a model realization while EnKF uses the same covariance for all realizations. We assess the sampling capabilities of RML and EnKF for a weakly nonlinear forward model. Results are compared to a Markov chain Monte Carlo (McMC) method, which samples correctly from the posterior. Our aim is to clarify which of the above mentioned differences between RML and EnKF has the biggest impact on the sampling capabilities. We apply the methods to a two-phase reservoir models small enough to be suitable for McMC. The assessment of RML and EnKF is performed by comparing history matching capabilities, and properties of their posterior distributions to those of the posterior distributions obtained with McMC.