J. M. Lewis, S. Lakshmivarahan and S. Dhall, “Dynamic Data Assimilation: A Least Squares Approach (Encyclopedia of Mathematics and its Applications),” Cambridge University Press, Cambridge, 2006. doi:10.1017/CBO 9780511526480

has been cited by the following article:

• TITLE: Reservoir Multiscale Data Assimilation Using the Ensemble Kalman Filter

  AUTHORS: Santha R. Akella

  KEYWORDS: Kalman Filter, Reservoir Engineering, Uncertainty Quantification, Multiscale Data

  JOURNAL NAME: Applied Mathematics, Vol.2 No.2, February 25, 2011

  ABSTRACT: In this paper we propose a way to integrate data at different spatial scales using the ensemble Kalman filter (EnKF), such that the finest scale data is sequentially estimated, subject to the available data at the coarse scale (s), as an additional constraint. Relationship between various scales has been modeled via upscaling techniques. The proposed coarse-scale EnKF algorithm is recursive and easily implementable. Our numerical results with the coarse-scale data provide improved fine-scale field estimates when compared to the results with regular EnKF (which did not incorporate the coarse-scale data). We also tested our algorithm with various precisions of the coarse-scale data to account for the inexact relationship between the fine and coarse scale data. As expected, the results show that higher precision in the coarse-scale data, yielded improved estimates.