Bayesian Approach for the Estimation of the Transmissivity Spatial Structure from Hydraulic Tomography Data

Groundwater flow and contaminant transport are strongly influenced by the spatial variability of subsurface flow parameters. However, the interpretation of pumping test data used for subsurface characterization is normally performed using conventional methods that are based on the assumption of aquifer homogeneity. In recent years, hydraulic tomography has been proposed by some researchers to address the limitations of conventional site characterization methods. Hydraulic tomography involves the sequential pumping at one of a series of wells and observing the drawdown due to pumping at adjacent wells. The interpretation of the drawdown data from hydraulic tomography has been mostly performed using formal inverse procedures for the estimation of the spatial variability of the flow parameters. The purpose of this study is to develop a method for the estimation of the statistical spatial structure of the transmissivity from hydraulic tomography data. The method relies on the pumping test interpretation procedure of Copty et al. (2011), which uses the time-drawdown data and its time derivative at each observation well to estimate the spatially averaged transmissivity as a function of radial distance from the pumping well. A Bayesian approach is then used to identify the statistical parameters of the transmissivity field (i.e. variance and integral scale). The approach compares the estimated transmissivity as a function of radial distance from the pumping well to the probability density function of the spatially-averaged transmissivity. The method is evaluated using synthetically-generated pumping test data for a range of input parameters. This application demonstrates that, through a relatively simple procedure, additional information of the spatial structure of the transmissivity may be inferred from pumping tests data. Results indicate that as the number of available pumping tests increases, the reliability of the estimated transmissivity statistical parameters also increases. The implications of the proposed procedure on the interpretation of time-drawdown data are discussed.