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Subsurface characterization with localized ensemble Kalman filter employing adaptive thresholding

Delijani, E. B ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.advwatres.2014.04.011
  3. Abstract:
  4. Ensemble Kalman filter, EnKF, as a Monte Carlo sequential data assimilation method has emerged promisingly for subsurface media characterization during past decade. Due to high computational cost of large ensemble size, EnKF is limited to small ensemble set in practice. This results in appearance of spurious correlation in covariance structure leading to incorrect or probable divergence of updated realizations. In this paper, a universal/adaptive thresholding method is presented to remove and/or mitigate spurious correlation problem in the forecast covariance matrix. This method is, then, extended to regularize Kalman gain directly. Four different thresholding functions have been considered to threshold forecast covariance and gain matrices. These include hard, soft, lasso and Smoothly Clipped Absolute Deviation (SCAD) functions. Three benchmarks are used to evaluate the performances of these methods. These benchmarks include a small 1D linear model and two 2D water flooding (in petroleum reservoirs) cases whose levels of heterogeneity/nonlinearity are different. It should be noted that beside the adaptive thresholding, the standard distance dependant localization and bootstrap Kalman gain are also implemented for comparison purposes. We assessed each setup with different ensemble sets to investigate the sensitivity of each method on ensemble size. The results indicate that thresholding of forecast covariance yields more reliable performance than Kalman gain. Among thresholding function, SCAD is more robust for both covariance and gain estimation. Our analyses emphasize that not all assimilation cycles do require thresholding and it should be performed wisely during the early assimilation cycles. The proposed scheme of adaptive thresholding outperforms other methods for subsurface characterization of underlying benchmarks
  5. Keywords:
  6. Thresholding functions ; Characterization ; Covariance matrix ; Forecasting ; Petroleum reservoirs ; Adaptive thresholding ; Covariance localization ; Ensemble Kalman Filter ; Kalman gain ; Subsurface characterizations ; Thresholding ; Monte Carlo methods ; Benchmarking ; Bootstrapping ; Correlation ; Covariance analysis ; Ensemble forecasting ; Flooding ; Kalman filter ; Matrix ; Monte Carlo analysis ; Numerical model
  7. Source: Advances in Water Resources ; Vol. 69, issue , 2014 , p. 181-196
  8. URL: http://www.sciencedirect.com/science/article/pii/S0309170814000785?np=y