Reconstructing the release history of underground containment by applying the adaptive bayesian backward estimation

Abstract

The problem of contamination source identification in porous medial is addressed by solving the inverse model with a hierarchical Bayesian computation method backward through time. The contaminant concentration is modelled as a pair-wise Markov random field and the distribution is updated using current contamination measurements at a finite set of locations. Hierarchical Bayesian analysis is used to derive the posterior distribution of the contaminant concentration at past time points. The posterior mean estimate is computed using a Gibbs algorithm. The release history of contaminant is estimated using adaptive collecting of samples. First a limited number of samples is collected to estimate the history of contamination and related uncertainties. This allows to determine if and where additional samples are necessary to achieve a greater accuracy of the history estimation. This approach can be useful in cases where the location and the rate of contaminant release are not known quite well.