A sequential inverse approach for hydraulic tomography and electrical resistivity tomography: An effective method for site characterization

Hydraulic tomography (i.e., a sequential aquifer test) has recently been proposed as a method for characterizing aquifer heterogeneity. In this study a sequential inverse approach is developed to interpret results of hydraulic tomography. The approach uses an iterative geostatistical inverse method to yield the effective hydraulic conductivity of an aquifer, conditioned on each set of head/discharge data. To efficiently include all the head/discharge data sets, a sequential conditioning method is employed. Two-dimensional numerical experiments were conducted to investigate the optimal sampling scheme for the hydraulic tomography. The effects of measurement errors and uncertainties in statistical parameters required by the inverse model were also investigated. The robustness of this inverse approach was demonstrated through its application to a hypothetical, three-dimensional, heterogeneous aquifer. Two sandbox experiments were conducted to evaluate the performance of the sequential geostatistical inverse approach under realistic conditions. One sandbox was packed with layered sands to represent a stratified aquifer while the other with discontinuous sand bodies of different shapes and sizes to represent a more complex and realistic heterogeneous aquifer. The tomography was found ineffective if abundant head measurements were collected at closely spaced intervals in a highly stratified aquifer. While it was found beneficial when head measurements were limited and the geological structure was discontinuous. The sequential inverse approach for hydraulic tomography was extended for electrical resistivity tomography. Numerical experiments were conducted to demonstrate the robustness of this approach for delineating the resistivity distribution in the subsurface and to investigate effectiveness of different sampling arrays of the ERT: the surface, the down-hole, and the combination of the surface and down-hole array. Orientation of bedding was found to dictate the effectiveness of the ERT layout. Samples were collected to quantify spatial variability of the resistivity-moisture relationship in the field. Numerical experiments then illustrated how the spatially varying relationship exacerbated the level of uncertainty in the interpretation of change of moisture content based on the estimated change in resistivity. A sequential inverse approach was then developed to estimate water content with less uncertainty by considering the spatial variability of the resistivity-moisture relationship and incorporating point moisture measurements and ERT data sets.