Characterization of parameters for a spatially heterogenous aquifer from pumping test data

This study considers the estimation of aquifer parameters for a spatially heterogenous aquifer from pumping test data. An approach is proposed that is based on modeling the unknown parameters as smooth Markov random fields. The associated inverse problem is formulated using the Bayesian framework and the posterior probability distribution of parameters is explored using Markov chain Monte Carlo. The method is evaluated by a numerical simulation in which measurements are taken in four observation wells. Even such a minimalist example presents significant computational challenges. Therefore, to obtain a computationally feasible solution, a model reduction is carried out and the estimation problem is reduced from over 1,000 parameters to 40 parameters. The approximate posterior distribution is then sampled using an adaptive Markov chain Monte Carlo sampler in order to quantify parameter uncertainty. This paper compares the parameter with predictive uncertainty and discusses the consequences of the model reduction.