Contaminant source estimation in a two-layers porous environment using a Bayesian approach

Pollution source estimation based on groundwater concentration measurements is an ill-posed inverse problem in that several different sources can supply similar observations. Consequently, constraints on the source must be added. Most of the works in the literature regularize the problem either by introducing parametric source models or by penalizing undesirable solutions. In our work, we use both strategies. In this paper, we focus on point and instantaneous pollution source. Since the source depends on a small number of parameters, the inverse problem becomes over-determined. In addition, the use of prior probability on parameters is a way of dealing with difficult situations in which few observations are available. Information from observations and prior information are combined in a Bayesian framework. The approach leads to a posterior probability given the data that summarizes all the available information about the source. We explore the posterior law with a Markov Chain Monte Carlo sampling method and estimate the source characteristics by posterior mean. The proposed method is applied to a simulated case of pollution.