Conditioning groundwater flow parameters with iterative ensemble smoothers: analysis and approaches in the continuous and the discrete cases
Date de parution
Data assimilation (DA) consists in combining observations and predictions of a numerical model to produce an optimal estimate of the evolving state of a system. Over the last decade, DA methods based on the Ensemble Kalman Filter (EnKF) have been particularly explored in various geoscience fields for inverse modelling. Although this type of ensemble methods can handle high-dimensional systems, they assume that the errors coming from whether the observations or the numerical model are multi-Gaussian. To handle potential nonlinearities between the observations and the state or parameter variables to estimate, iterative variants have been proposed. In this thesis, we first focus on two main iterative ensemble smoother methods for the calibration of a synthetic 2D groundwater model. Using the same set of sparse and transient flow data, we analyse each method when employing them to condition an ensemble of multi-Gaussian hydraulic conductivity fields. We then further explore the application of one iterative ensemble smoother algorithm (ES-MDA) in situations of variable complexity, depending on the geostatistical simulation method used to simulate the prior geological information. The applicability of a parameterization based on the normal-score transform is first investigated. The robustness of the method against nonlinearities is then further explored in the case of discrete facies realizations obtained with a truncated Gaussian technique and updated via their underlying variables. Based on the observed limitations and benefits of the forementioned parameterizations, we finally propose a new methodology for the conditioning of categorical multiple-point statistics (MPS) simulations to dynamic data with a state-of-the-art ensemble Kalman method by taking the example of the Ensemble Smoother with Multiple Data Assimilation (ES-MDA). Our methodology relies on a novel multi-resolution 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 multi-resolution 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 multi-resolution MPS simulation. The results on the synthetic problem 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 multi-resolution MPS simulations. Moreover, thanks to the proposed parameterization, 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.
, Doctorat, Neuchâtel, Faculté des sciences, Hydrogéologie et géothermie
Type de publication
Resource Types::text::thesis::doctoral thesis