A geostatistical approach to the conditional estimation of spatially distributed solute concentration and notes on the use of tracer data in the inverse problem

This paper presents a theoretical framework for deriving the moments of the concentration, based on the Lagrangian approach and using a stochastic framework, conditional to measurements of conductivity and hydraulic head. The method consists of deriving the spatial correlations between concentration and travel time and hydrologic variables such as the conductivity and the hydraulic head. These correlations allow the conditioning of the moments of the concentration on measurements. By conditioning the concentration the uncertainty associated with its estimation can be reduced substantially. Consequently, difficulties associated with estimation of the extent of contamination can be alleviated. The theoretical framework and derivations may also be used to condition the moments of the conductivity on tracer data such as concentrations, travel times, and displacements. An application of such an approach would require a configuration of sources and samplers. We show that measured concentration is inferior to travel time and displacements in terms of efficient conditioning.