... a measurement K ^ ∈ ℝ m of permeability (or some other quantity of interest) at m locations in Ω, and we also denote θ ^ = log ( K ^ ) . For mathematical purposes we assume these are noisy measurements from a Gaussian random field distributed with covariance [1...

..., for preserving higher-moments of non-Gaussian random fields, Kernel Principal Component Analysis (KPCA) was used by Sarma et al. (2008). It was shown in their work that complex geological structures can be effectively decomposed into lower dimension by mapping the random field into feature space. History...

... collapse, which is particularly evident for small ensembles. Further, EnKF is theoretically appropriate only if all ensemble members belong to the same multi-Gaussian random field. This is an important issue because for most real fields, we have more than one geological scenario, and ideally, we would...

... reservoir simulation polynomial chaos expansion enkf modeling & simulation random field pckf history matching prediction probabilistic collocation method expansion ensemble kalman filter state variable kalman filter artificial intelligence upstream oil & gas coefficient...

... and efficient tool for data assimilation. Although the EnKF has many advantages such as ease of implementation and efficient uncertainty quantification, it is technically appropriate only for random fields (e.g., permeability) characterized by two-point geostatistics (multi-Gaussian random fields). Realistic...

... approach receiving the most attention to date is the ensemble Kalman filter (EnKF). Although the EnKF has many advantages such as ease of implementation and efficient uncertainty quantification, it is technically appropriate only for random fields (e.g., permeability) characterized by two-point...