Localization and regularization for iterative ensemble smoothers

Annan, J. D., Hargreaves, J. C., Edwards, N. R., Marsh, R.: Parameter estimation in an intermediate complexity earth system model using an ensemble Kalman filter. Ocean Model. 8(1–2), 135–154 (2005). doi: 10.1016/j.ocemod.2003.12.004 . ISSN 1463– 5003

Chen, Y., Oliver, D. S.: Ensemble-based closed-loop optimization applied to Brugge Field. SPE Reserv. Eval. Eng. 13(1), 56–71 (2010a). doi: 10.2118/118926-PA

Chen, Y., Oliver, D. S.: Cross-covariances and localization for EnKF in multiphase flow data assimilation. Comput. Geosci. 14, 579–601 (2010b). doi: 10.1007/s10596-009-9174-6 . ISSN 1420-0597

Chen, Y., Oliver, D. S.: Ensemble randomized maximum likelihood method as an iterative ensemble smoother. Math. Geosci. 44(1), 1–26 (2012). doi: 10.1007/s11004-011-9376-z . ISSN 1874-8961

Chen, Y., Oliver, D. S.: Levenberg-Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification. Comput. Geosci. 17(4), 689–703 (2013). doi: 10.1007/s10596-013-9351-5 . ISSN 1420–0597

Chen, Y., Oliver, D. S.: History matching of the Norne full-field model with an iterative ensemble smoother. SPE Reserv. Eval. Eng. 17(2), 244–256 (2014). doi: 10.2118/164902-PA

Emerick, A., Reynolds, A.: Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications. Comput. Geosci. 15(2), 251–269 (2011). doi: 10.1007/s10596-010-9198-y . ISSN 1420-0597

Emerick, A. A.: Analysis of the performance of ensemble-based assimilation of production and seismic data. J. Petrol. Sci. Eng. Online first (2016)

Emerick, A. A., Reynolds, A. C.: Ensemble smoother with multiple data assimilation. Comput. Geosci. 55, 3–15 (2013a). doi: 10.1016/j.cageo.2012.03.011 . ISSN 0098-3004

Emerick, A. A., Reynolds, A. C.: History-matching production and seismic data in a real field case using the ensemble smoother with multiple data assimilation, SPE-164902. In: Proc of SPE RSS. The Woodlands (2013b)

Evensen, G: Data Assimilation: The Ensemble Kalman Filter, 2n edn.. Springer Verlag (2009)

Fahimuddin, A., Aanonsen, S. I., Skjervheim, J.-A.: 4D seismic history matching of a real field case with EnKF: Use of local analysis for model updating. In: SPE Annual Technical Conference and Exhibition, 19-22 September 2010. Florence (2010)

Fertig, E. J., Hunt, B. R., Ott, E., Szunyogh, I.: Assimilating non-local observations with a local ensemble Kalman filter. Tellus A 59(5), 719–730 (2007). doi: 10.1111/j.1600-0870.2007.00260.x

Furrer, R., Bengtsson, T.: Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants. J. Multivar. Anal. 98(2), 227–255 (2007). doi: 10.1016/j.jmva.2006.08.003 . ISSN 0047-259X

Gaspari, G., Cohn, S. E.: Construction of correlation functions in two and three dimensions. Q. J. R. Meteorol. Soc. 125(554), 723–757 (1999)

Greybush, S. J., Kalnay, E., Miyoshi, T., Ide, K., Hunt, B. R.: Balance and ensemble Kalman filter localization techniques. Mon. Weather Rev. 139(2), 511–522 (2011). doi: 10.1175/2010MWR3328.1 . ISSN 0027-0644

Hamill, T. M., Whitaker, J. S., Snyder, C.: Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Weather Rev. 129(11), 2776–2790 (2001)

Houtekamer, P. L., Mitchell, H. L.: A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Weather Rev. 129(1), 123–137 (2001)

Houtekamer, P. L., Mitchell, H. L.: Data assimilation using an ensemble Kalman filter technique. Mon. Weather Rev. 126(3), 796–811 (1998)

Hunt, B. R., Kostelich, E. J., Szunyogh, I.: Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter. Physica D: Nonlin. Phenom. 230(1–2), 112–126 (2007)

Li, R., Reynolds, A. C., Oliver, D. S.: History matching of three-phase flow production data. SPE J. 8 (4), 328–340 (2003). doi: 10.2118/87336-PA

Miyoshi, T., Yamane, S.: Local ensemble transform Kalman filtering with an AGCM at a T159/L48 resolution. Mon. Weather Rev. 135(11), 3841–3861 (2007). doi: 10.1175/2007MWR1873.1

Nerger, L., Janjić, T., Schrȯter, J., Hiller, W.: A regulated localization scheme for ensemble-based Kalman filters. Q. J. R. Meteorol. Soc. 138(664), 802–812 (2012). doi: 10.1002/qj.945

Oliver, D. S.: Calculation of the inverse of the covariance. Math. Geol. 30(7), 911–933 (1998)

Oliver, D. S., Reynolds, A. C., Liu, N.: Inverse Theory for Petroleum Reservoir Characterization and History Matching, 1st edn. Cambridge University Press, Cambridge (2008)

Ott, E., Hunt, B. R., Szunyogh, I., Zimin, A. V., Kostelich, E. J., Corazza, M., Kalnay, E., Patil, D. J., Yorke, J. A.: A local ensemble Kalman filter for atmospheric data assimilation. Tellus A 56(5), 415–428 (2004)

Peters, L., Arts, R. J., Brouwer, G. K., Geel, C. R., Cullick, S., Lorentzen, R. J., Chen, Y., Dunlop, K. N. B., Vossepoel, F. C., Xu, R., Sarma, P., Alhutali, A. H., Reynolds, A. C.: Results of the Brugge benchmark study for flooding optimization and history matching. SPE Reserv. Evalu. Eng. 13(3), 391–405 (2010). doi: 10.2118/119094-PA

Sætrom, J., Hove, J., Skjervheim, J.-A., Vabø, J. G.: Improved uncertainty quantification in the ensemble Kalman filter using statistical model-selection techniques. SPE J. 17, 152–162 (2012). doi: 10.2118/145192-PA

Sakov, P., Bertino, L.: Relation between two common localisation methods for the EnKF. Comput. Geosci. 15(2), 225–237 (2011). doi: 10.1007/s10596-010-9202-6 . ISSN 1420-0597

Skjervheim, J.-A., Evensen, G.: An ensemble smoother for assisted history matching. In: SPE Reservoir Simulation Symposium, 21–23 February. The Woodlands, 10.2118/141929-MS (2011)

Weaver, A. T., Mirouze, I.: On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation. Q. J. R. Meteorol. Soc. 139(670), 242–260 (2013). doi: 10.1002/qj.1955 . ISSN 1477-870X

Zhao, Y., Reynolds, A. C., Li, G.: Generating facies maps by assimilating production data and seismic data with the ensemble Kalman filter, SPE-113990. In: Proc of SPE IOR Symp. Tulsa, doi: 10.2118/113990-MS (2008)