Talk on Measure-Theoretic Stochastic Inversion of Groundwater Contamination Problems

The movement of contaminant plumes in underground aquifers is highly dependent on many hydrogeological parameters. Some of these parameters include porosity, flow direction, flow speed dispersivities, and effects of geochemical reactions. It is often prohibitively expensive or impossible to make accurate and reliable measurements of these parameters in the field. It is also difficult to know the position and shape of a contaminant plume at a given time or the exact details of the source of the contamination, e.g. size, location, origin time, and magnitude. If decisions are to be made regarding contaminant remediation strategies or predictions of future contaminant concentrations in and near water-supply wells, then these uncertain hydrogeological and source parameters need to be analyzed and estimated. We utilize a measure-theoretic inverse framework to perform uncertainty quantification and estimation for these parameters. We also analyze the error in the solution. There are two main sources of error in the solution of the stochastic inverse problem: error introduced from using a finite number of samples to approximate a set of uncertain parameters and error introduced from numerically solving the forward model. We show a posteriori error estimates for both of these types of error and the total error in the solution to the stochastic inverse problems.