Multiresolution Approach to Condition Categorical Multiple‐Point Realizations to Dynamic Data With Iterative Ensemble Smoothing

Abstract

AbstractA new methodology is presented for the conditioning of categorical multiple‐point statistics (MPS) simulations to dynamic data with an iterative ensemble smoother (ES‐MDA). The methodology relies on a novel multiresolution parameterization of the categorical MPS simulation. The ensemble of latent parameters is initially defined on the basis of the coarsest‐resolution simulations of an ensemble of multiresolution MPS simulations. Because this ensemble is non‐multi‐Gaussian, additional steps prior to the computation of the first update are proposed. In particular, the parameters are updated at predefined locations at the coarsest scale and integrated as hard data to generate a new multiresolution MPS simulation. The performance of the methodology was assessed on a synthetic groundwater flow problem inspired from a real situation. The results illustrate that the method converges towards a set of final categorical realizations that are consistent with the initial categorical ensemble. The convergence is reliable in the sense that it is fully controlled by the integration of the ES‐MDA update into the new conditional multiresolution MPS simulations. Thanks to a massively reduced number of parameters compared to the size of the categorical simulation, the identification of the geological structures during the data assimilation is particularly efficient for this example. The comparison between the estimated uncertainty and a reference estimate obtained with a Monte Carlo method shows that the uncertainty is not severely reduced during the assimilation as is often the case. The connectivity is successfully reproduced during the iterative procedure despite the rather large distance between the observation points.