Groundwater is in many parts of the world an important source of fresh water for several purpose such as domestic and industrial use and irrigation. Pollution and bad management of groundwater are only two of the problems that affect the aquifers around the world. Detailed information about the spatial distribution of hydraulic properties in subsurface are of crucial importance for a proper management of groundwater and for the prediction of the solutes transport in aquifer and therefore for the design of effective remediation systems. Different methods have been used for characterizing aquifer hydraulic parameters but the most used are the interpretation of the pumping tests. They consist of measuring the drawdowns in an observation well due to the extraction of a constant rate of water from a different well. The data collected in this way are then fitted with analytical solutions that assume aquifer homogeneity so providing average values of the hydraulic parameters without considering any spatial distribution. In the last 15 years, to remove the homogeneity hypothesis and to investigate the spatial distribution of aquifer hydraulic properties, a technique called Hydraulic Tomography has been developed. It consists of sequential aquifer tests in which the stress location is sequentially moved and the hydraulic responses are monitored in other locations. The data collected are then used to solve an inverse problem and to obtain information about the spatial variability of the aquifer hydraulic parameters. In this work after a discussion of the traditional aquifer tests and an overview of the inverse methods applied to the hydraulic tomography, a Bayesian Geostatistical approach (conditioned on direct head data) is considered and tested with tomographic data in transient flow conditions and with both constant and non-stationary boundary conditions. Traditional analyses and the hydraulic tomography approach are then applied to a real case of the well field of the AIPO Boretto Research Site (Northern Italy) to test the methodologies on a field application. To date, the application of the Bayesian Geostatistical approach to inverse problems (in particular on real problems) is limited by the lack of tools available for the scientific and technical community. For this reason the USGS (United States Geological Survey) is sponsoring a project to incorporate the Bayesian approach as a module of the industry standard software package PEST for the parameters estimation. In this work the kernel of the Bayesian PEST developed by the Writer is described. This module is doubtless a good way to spread the Bayesian Geostatistical inverse procedure to the modelers community.
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