### References

Aanonsen, S.I., Nævdal, G., Oliver, D.S. et al. 2009. Review of Ensemble Kalman Filter in Petroleum Engineering. *SPE J.* **14 **(3): 393−412.

Abellan, A. and Noetinger, B. 2010. Optimizing Subsurface Field Data Acquisition Using Information Theory. *Mathematical Geosci.* **42:** 603−630. http://dx.doi.org/10.1007/s11004-010-9285-6.

Barker, J.W., Cuypers, M., and Holden, L. 2001. Quantifying Uncertainty in Production Forecasts: Another Look at the PUNQ-S3 Problem. *SPE J.* **6 **(4): 433−441.

Beirlant, J., Dudewicz, E.J., Györfi, L. et al. 1997. Nonparametric Entropy Estimation: An Overview. *International J. of the Mathematical Statistics Sci.* **6:** 17−39.

Cellucci, C.J., Albano, A.M., and Rapp, P.E. 2005. Statistical Validation of Mutual Information Calculations: Comparison of Alternative Numerical Algorithms. *Phys. Rev. E* **71:** 066,208.

Chapman, D. and Thomas, C.N. 2010. Think Big, Get Small. *Hart’s E&P* **83 **(2).

Coopersmith, E. and Cunningham, P. 2002. A Practical Approach To Evaluating the Value of Information and Real Option Decisions in the Upstream Petroleum Industry. In *Proceedings* *of the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, *Richardson, Texas: SPE.

Cover, T.M. and Thomas, J.A. 1991. *Elements of Information Theory,* New York, New York: Wiley-Interscience.

Darbellay, G. and Vajda, I. 1999. Estimation of the Information by an Adaptive Partitioning of the Observation Space. *Information Theory, IEEE Trans.* **45 **(4): 1315−1321.

Emerick, A.A. and Reynolds, A.C. 2011. Combining Sensitivities and Prior Information for Covariance Localization in the Ensemble Kalman Filter for Petroleum Reservoir Applications. *Computational Geosci.* **15 **(2): 251−269.

Emerick, A. and Reynolds, A. 2012a. History Matching Time-Lapse Seismic Data Using the Ensemble Kalman Filter With Multiple Data Assimilations. *Computational Geosci.* **16 **(3): 639−659.

Emerick, A.A. and Reynolds, A.C. 2012b. Combining the Ensemble Kalman Filter Markov-Chain Monte Carlo for Improved History Matching and Uncertainty Characterization. *SPE J.* **17 **(2): 418−440.

Emerick, A.A. and Reynolds, A.C. 2013a. Ensemble Smoother With Multiple Data Assimilations. *Computers & Geosci.* **55:** 3−15.

Emerick, A.A. and Reynolds, A.C. 2013b. Investigation of the Sampling Performance of Ensemble-Based Methods With a Simple Reservoir Model. *Computational Geosci.* **17 **(2): 325−350.

Evensen, G. 1997. Advanced Data Assimilation for Strongly Nonlinear Dynamics. *Monthly Weather Rev.* **125 **(6): 1342−1354.

Evensen, G. 2003. The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation. *Ocean Dynamics* **53:** 343−367.

Evensen, G. 2007. *Data Assimilation: The Ensemble Kalman Filter,* Berlin: Springer.

Floris, F.J.T., Bush, M.D., Cuypers, M. et al. 2001. Methods for Quantifying the Uncertainty of Production Forecasts: A Comparative Study. *Petroleum Geosci.* **7**(SUPP): 87−96.

Gao, G., Zafari, M. and Reynolds, A.C. 2006. Quantifying Uncertainty for the PUNQ-S3 Problem in a Bayesian Setting With RML and EnKF. *SPE J.* **11 **(4): 506−515.

Haskett, W.J. 2003. Optimal Appraisal Well Location Through Efficient Uncertainty Reduction and Value of Information Techniques. In *Proceedings* *of the SPE Annual Technical Conference and Exhibition, Denver, Colorado*, Richardson, Texas: SPE.

Kraskov, A., Stogbaurer, H., and Grassberger, P. 2004. Estimating Mutual Information. *Physical Rev. E* **69 **(066138): 1−15.

Le, D.H. and Reynolds, A.C. 2012. Optimal Choice of a Surveillance Operation Using Information Theory. In *Proceedings* *of the 13th European Conference of the Mathematics of Oil Recovery, ECMOR XIII, Biarritz, France*.

Oliver, D.S., He, N., and Reynolds, A.C. 1996. Conditioning Permeability Fields to Pressure Data. In *Proceedings of the European Conference for the Mathematics of Oil Recovery*.

Oliver, D.S., Reynolds, A.C., and Liu, N. 2008. *Inverse Theory for Petroleum Reservoir Characterization and History Matching,* Cambridge, UK: Cambridge University Press.

Quiroga, R.Q., Kraskov, A., and Grassberger, P. 2005. Reply to “Comment on ‘Performance of Different Synchronization Measures in Real Data: A Case Study on Electroencephalographic Signals.’” *Phys. Rev. E* **72:** 063,902.

Reynolds, A.C., He, N., and Oliver, D.S. 1999. Reducing Uncertainty in Geostatistical Description With Well Testing Pressure Data. In *Reservoir Characterization-Recent Advances,* ed. R.A. Schatzinger and J.F. Jordan, pp. 149−162, American Association of Petroleum Geologists.

Roulston, M.S. 1999. Estimating the Errors on Measured Entropy and Mutual Information. *Physica D: Nonlinear Phenomena* **125 **(34): 285−294.

Shannon, C.E. 1948. A Mathematical Theory of Communication. *Bell System Technical J.* **27**.

Tavakoli, R. and Reynolds, A.C. 2010. History Matching With Parameterization Based On the SVD of a Dimensionless Sensitivity Matrix. *SPE J.* **15 **(12): 495−508.

Ullo, J. 2008. Computational Challenges in the Search for the Production of Hydrocarbons. *Scientific Modeling and Simulation SMNS* **15 **(1−3): 313−337.