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.
Highlights
Aquifer parameters governing groundwater flow, such as the hydraulic conductivity, are highly variable and heterogeneous
We demonstrate how to incorporate this approach within an approximation and a sampling method, namely the Iterated Extended Kalman Filter (IEKF) and Sequential Monte Carlo (SMC) methods
In order to focus the investigation on the influence of the number of samples, instead of obtaining the observation covariance through sampling, SMC was run with constant model output eigenmodes obtained from the IEKF solution
Summary
Aquifer parameters governing groundwater flow, such as the hydraulic conductivity, are highly variable and heterogeneous. An extension of analytical solutions to nonlinear inversion models with Gaussian prior fields is given by the Successive Linear Estimator (SLE) method (Yeh and Zhang 1996) This approach iteratively linearizes the nonlinear relationship between hydraulic pressure head and the spatial distribution of hydraulic. The linearization assumption in SLE and IEKF, which renders the methods effective in problems where the hydraulic conductivity variance is small, leads to convergence issues in inversion problems with large variance This can be circumvented through the application of sampling-based methods, which generate samples that follow the true posterior distribution of the sought parameters and use the actual forward simulation model without linearization.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.