Preserving spatial structure for inverse stochastic simulation using blocking Markov chain Monte Carlo method

Abstract

State data (piezometric head) provides valuable information for identifying the spatial pattern of aquifer parameters (hydraulic conductivity) and to reduce the uncertainty of aquifer models. To extract such spatial information from the measurements and accurately quantify the uncertainty, a Monte Carlo method typically calls for a large number of realizations that are conditional to hard data and inverse-conditional to state data. However, inverse stochastic simulation is extremely computationally intensive, since a non-linear inverse problem is involved. In contrast to some classical non-linear optimizers, a blocking Markov chain Monte Carlo scheme is presented to generate independent, identically distributed realizations by sampling directly from a posterior distribution that incorporates a priori information and a posteriori observations in a Bayesian framework. The realizations are not only conditioned to hard data and inverse-conditioned to state data, but also preserve expected spatial structures. A synthetic example demonstrates the effectiveness of the proposed method.