An iterative stochastic ensemble method for parameter estimation of subsurface flow models

Authors:
Ahmed H. Elsheikh;Mary F. Wheeler;Ibrahim Hoteit
Affiliations:
Center for Subsurface Modeling (CSM), Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, TX, USA and Dept. of Earth Sciences and Engineering, King Abdullah ...;Center for Subsurface Modeling (CSM), Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, TX, USA;Dept. of Earth Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia and Dept. of Applied Mathematics and Computational Sciences, King Abdullah ...
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss-Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates.