Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

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. 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-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative regularized ensemble Kalman filter algorithm. The filter is converted to an optimization algorithm by using a pseudo time-stepping technique such that the model output matches the time dependent data. The EnKF Kalman gain matrix is regularized using truncated SVD to filter out noisy correlations. Numerical results show that the proposed algorithm is a promising approach for parameter estimation of subsurface flow models. A.H. Elsheikh Department of Earth Science and Engineering, Imperial College London, E-mail: [email protected] Current address: Center for Subsurface Modeling (CSM), Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, TX, USA E-mail: [email protected] C.C. Pain · F. Fang · J.L.M.A. Gomes Department of Earth Science and Engineering, Imperial College London, SW7 2BP, UK I.M. Navon Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306-4120, USA