View article

Kalman filter-based methods have been widely applied for assimilating new measurements to continuously update the estimate of state variables, such as reservoir properties and responses. The standard Kalman filtering scheme requires computing and storing the covariance matrix of state variables, which is computationally expensive for large-scale problems with millions of gridblocks. In the ensemble Kalman filter (EnKF), this problem is alleviated with sampling from a limited number of realizations and computing the required subset of the covariance matrix at each update. However, the goodness of the (ensemble) covariance approximated from the limited ensemble depends on the number of realizations used and the representativity of a given ensemble. In this study, we propose an efficient, dimension-reduced Kalman filtering scheme based on Karhunen-Loeve (KL) and other orthogonal polynomial …