2012
DOI: 10.1007/s00477-012-0613-x
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Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

Abstract: A new parameter estimation algorithm based on ensemble Kalman filter (EnKF) is developed. The developed algorithm combined with the proposed problem parametrization offers an efficient parameter estimation method that converges using very small ensembles and without any tuning parameters. The inverse problem is formulated as a sequential data integration problem. Gaussian Process Regression (GRP) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Lo… Show more

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Cited by 32 publications
(28 citation statements)
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References 67 publications
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“…An approximation with an overfitted resolution will greatly increase the dimension of the search space and deteriorate computational efficiency. Even with a proper discretization, Downloaded by [Florida International University] at 04:23 20 December 2014 the typical techniques for inverse problems, such as Bayesian inference [2,4,18,30] and ensemble Kalman filter (EnKF) [7,9,24], still need to evaluate a massive number of solution ensembles in a relatively high-dimensional parameter space, resulting in slow convergence. Furthermore, the situation is even worse because we lack prior knowledge concerning the behaviour of the unknown field.…”
Section: Introductionmentioning
confidence: 99%
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“…An approximation with an overfitted resolution will greatly increase the dimension of the search space and deteriorate computational efficiency. Even with a proper discretization, Downloaded by [Florida International University] at 04:23 20 December 2014 the typical techniques for inverse problems, such as Bayesian inference [2,4,18,30] and ensemble Kalman filter (EnKF) [7,9,24], still need to evaluate a massive number of solution ensembles in a relatively high-dimensional parameter space, resulting in slow convergence. Furthermore, the situation is even worse because we lack prior knowledge concerning the behaviour of the unknown field.…”
Section: Introductionmentioning
confidence: 99%
“…In this work, we propose an adaptive sparse-grid (SG) iterative ensemble Kalman filter (IEnKF) approach to both discretize and estimate spatially varying parameters. We use the IEnKF technique developed in [7,28] to estimate the parameter values. Unlike the conventional EnKF [9] approach, the state vector of the IEnKF only consists of model parameters and the EnKF update is applied iteratively in a batch mode for parameter estimation.…”
Section: Introductionmentioning
confidence: 99%
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“…These techniques can be classified into Bayesian methods based on Markov chain Monte Carlo (MCMC) [Oliver et al, 1997;Efendiev et al, 2005;Elsheikh et al, 2012], gradient-based optimization methods [McLaughlin and Townley, 1996;Carrera et al, 2005;Altaf et al, 2013], stochastic search algorithms [Li and Reynolds, 2011;Elsheikh et al, 2013aElsheikh et al, , 2013bElsheikh et al, , 2013cElsheikh et al, , 2013d, and ensemble Kalman filter methods [Moradkhani et al, 2005;Naevdal et al, 2005;Oliver et al, 2008;Luo et al, 2012;Elsheikh et al, 2013e]. It is evident from these studies (among others) that Bayesian statistics provide a general framework for estimating the probability distribution functions of the unknown parameters (i.e., inverse uncertainty quantification).…”
Section: Introductionmentioning
confidence: 99%
“…It is known that the KF is computationally efficient; however, it is limited by the non-universal linear and Gaussian modeling assumptions. To relax these assumptions, the extended Kalman filter (EKF) [7,8,16,17,18] and the unscented Kalman filter (UKF) [7,8,19,20,21] are developed and the ensemble kalman filter (EnKF) [22,23]. In extended Kalman filtering, the model describing the system is linearized at every time sample (in order to estimate the mean and covariance matrix of the state vector), and thus the model is assumed to be differentiable.…”
mentioning
confidence: 99%