The Characterization Of Non-Gaussian Hydraulic Conductivity Fields Using Inverse Sequential Simulation And Correlated Probability Field Method

Ensemble kalman filter(EnKF) has proven to be a powerful inverse method for the characterization of hydraulic conductivities, which works well for non-linear state equation and Gaussian-distributed parameters. However, it fails to deal with non-Gaussinity. The main issue addressed in this thesis is how to properly address the problem of characterizing non-Gaussian hydraulic conductivity fields.First, we proposes a new stochastic inverse method named inverse sequential simulation(iSS). The iSS is a breed of sequential simulation and the normal-score ensemble Kalman filter. The new approach applies the ensemble concept to generate realizations by sequential simulation using the experimental non-stationary cross-covariance between conductivities and piezometric heads computed on an ensemble of realizations. We use the normal-score transformation to ensure marginal Gaussian distribution. And then, we apply standard multivariate sequential Gaussian conditional simulation to generate conductivity realizations conditioned to both conductivity and piezometric data. The benchmark against the NS-EnKF shows that the iSS is capable of generating inverse-conditioned non-Gaussian realizations with similar quality for both approaches.Then, we investigates the inverse method proposed by(Hu et al.,2013) and proposes an improved version. Unlike the idea of(Hu et al., 2013), which uses the EnKF to directly update uncorrelated uniform random fields(those used to draw from the local conditional marginal distributions in sequential simulation), the new version propose working on correlated uniform random fields, more precisely the same uniform random field used in probability field simulation(Froidevaux, 1993). The comparison of both versions shows that the new proposed one is much better than the original in order to capture the main patterns of conductivity and in reducing uncertainty.