Markov random field models for quantifying uncertainty in subsurface remediation

Remediation of subsurface contamination by volatile organic compounds requires knowledge of the distribution of the contamination within the formation. To avoid the need for extensive sampling of the subsurface, here we present a Markov random field modeling approach where organic phase saturation is conditioned on the heterogeneous permeability of the domain. Estimation of the model parameters is accomplished using a Newton-type method in the context of a tractable pseudo-likelihood approximation to the true maximum likelihood objective function. Monte-Carlo analysis of samples drawn from this model indicate the potential utility of the approach for quantification of uncertainty for remediation design and assessment.