Theoretical development of the history matching method for subsurface characterizations based on simulated annealing algorithm

Two history matching methods for subsurface characterization are proposed based on the simulated annealing (SA) algorithm with 1) an unconditional geostatistical simulation (i.e., SA-US) and 2) a radial basis function network (i.e., SA-RBFN) as random-walk transition kernels. For the validations, the proposed methods and an ensemble Kalman filter (EnKF) method are applied to a synthetic hydraulic conductivity field, and the results are compared based on two hypothetical cases. In Case 1, the statistics of the target field (i.e., mean, variance, and spatial correlation lengths of a hydraulic conductivity field) are well known, whereas in Case 2, the statistics are inaccurately known. According to each method, 10 predictions are made per case to evaluate the consistency of predictions. Although the estimated mean fields by the proposed methods in Case 1 show relatively lower prediction accuracies than that by the EnKF method, the individual prediction accuracy values of the SA-RBFN method are almost comparable. In Case 2, majority of the results of the proposed methods show higher prediction accuracy than those of the EnKF method. Overall, the results show more consistent prediction performance by the proposed methods than that by the EnKF method regardless of the level of field information, which indicates less susceptibility of the developed methods to prior statistics. The study includes the MethodsX companion paper as a complement to the main paper (this study).