Simultaneous Estimation of Transmissivity Values and Zonation

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Abstract
The extended Kalman filter (EKF) has long been recognized as a powerful, yet computationally intensive, methodology for stochastic parameter estimation. Three improvements to traditional algorithms are presented and applied to heterogeneous transmissivity estimation. First, the costly EKF covariance updates are replaced by more efficient approximations. Second, the zonation structure of the distributed parameter field being estimated is dynamically determined and refined using a partitional clustering algorithm. Third, a new method of merging first and second moments of random fields that have heterogeneous statistics is introduced. We apply this method, called random field union, as an alternative to conventional random field averaging for the systematic shrinking of covariance matrices as the dimensionality of the parameter space is reduced. The effects of these three improvements are examined. In applications to steady state groundwater flow test problems, we show that the first and second improvements reduce the computational time requirements dramatically, while the second and third can improve the accuracy and stability of the results. The resulting integrated method is successfully applied to a larger, more realistic calibration test case under steady and cyclostationary flow conditions (similar to regular seasonal fluctuations). When flow is steady, the method can be viewed as iterative; when flow is transient, the method is fully recursive.