A Markov random field model of contamination source identification in porous media flow

A contamination source identification problem in constant porous media flow is addressed by solving the advection–dispersion equation (ADE) with a hierarchical Bayesian computation method backward through time. The contaminant concentration is modeled as a pair-wise Markov random field (MRF) and the distribution is updated using current concentration measurements at finite 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 modified single-component Gibbs algorithm. The methodology is first tested via examples of contaminant identification in a homogeneous porous medium using both diffusion-dominated and convection-dominated conditions. A heterogeneous porous media flow case is also examined. In all the numerical studies reported, the anisotropic dispersion effect is considered. It is verified that the MRF model can effectively model the spatial correlation of the concentration field, and the presented approach can provide accurate solutions to the ill-posed inverse problem.