ORIGINAL PAPER 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. The inverse problem is formulated as a sequential data inte-gration problem. Gaussian process regression 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 func-tions are estimated by an iterative regularized EnKF algorithm. The filter is converted to an optimization algo-rithm 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. Keywords ensemble Kalman filter inverse problems regularization Gaussian process regression Karhunen–Loève expansion