Efficient estimation of hydraulic conductivity heterogeneity with non-redundant measurement information

Abstract

Solving the inverse problem of identifying groundwater model parameters with measurements is a computationally intensive task. Although model reduction methods provide computational relief, the performance of many inversion methods depends on the amount of often highly correlated measurements. We propose a measurement reduction method that only incorporates essential measurement information in the inversion process. The method decomposes the covariance matrix of the model output and projects both measurements and model response on the eigenvector space corresponding to the largest eigenvalues. We combine this measurement reduction technique with two inversion methods, the Iterated Extended Kalman Filter (IEKF) and the Sequential Monte Carlo (SMC) methods. The IEKF method linearizes the relationship between measurements and parameters, and the cost of the required gradient calculation increases with increase of the number of measurements. SMC is a Bayesian updating approach that samples the posterior distribution through sequentially sampling a set of intermediate measures and the number of sampling steps increases with increase of the information content. We propose modified versions of both algorithms that identify the underlying eigenspace and incorporate the reduced information content in the inversion process. The performance of the modified IEKF and SMC methods with measurement reduction is tested on a numerical example that illustrates the computational benefit of the proposed approach as compared to the standard IEKF and SMC methods with full measurement sets.