Novel hydrogeologic characterization methods: utilizing the analytic element method in hydrogeophysical studies

Abstract

An accurate conceptualization of groundwater-surface water connectivity is critical for quantification of fluxes between rivers and aquifers. Point based hydrologic data provides a useful indicator to delineate an aquifers response to changes in streamflow; however, supplementary hydrogeologic information is often needed to fully constrain connectivity patterns due to the presence of focused recharge pathways. Electrical resistivity tomography (ERT) is a near surface geophysical method that determines the electrical resistivity distribution within the earth. Electrical resistivity is an intrinsic material property that is strongly correlated to hydrogeologic properties (e.g., water content, porosity, pore fluid salinity, clay content). The spatial and temporal distribution of electrical resistivity provides insight into the hydrologic state of sediments. Ultimately, changes in electrical resistivity across space and time provide of level of understanding about hydrogeologic processes that is unmatched by the analysis of point based hydrologic measurements alone. ERT surveys were conducted along the Arkansas River in Western Kansas to depict the hydrologic state of riverbed sediments, and to gain insight on the hydrologic response of the sediments across changes in streamflow and the hydrogeologic landscape. The electrical resistivity profiles revealed large contrasts in resistivity beneath portions of the inundated riverbed, indicating different regimes of groundwater-surface water (gw-sw) connectivity persist both spatially and temporally. Although the initial results of the study indicated that ERT can be used to observe differences in gw-sw connectivity through time and space, a more rigorous hydrogeologic interpretation of ERT surveys is needed to bridge the gap between quantitative groundwater models and the information provided by geophysical earth models. This motivated the inclusion of the Analytic Element Method (AEM) into geophysical inversion and ERT survey design to further advance the ability of near surface geophysics to fully exploit the hydrogeologic information inherent geophysical data. Electrical conduction through soil was modelled using the AEM. Soil was represented using interconnected rectangular elements, each with a constant electrical resistivity. The forward response of an ERT array was generated over layered resistivity models. The AEM model matched electrostatic boundary an interface conditions to high accuracy for lowly and highly resistivity layers, as well as for isolated inclusions within uniform backgrounds. The implementation of a particle swarm optimization scheme was used to reconstruct resistivity models from synthetic data, which were in good agreement with the known model within the theoretical depths investigation of the simulated array. Resistivity models constructed from field data were highly dependent on the norm used. Simulations that used the root mean square percentage error as the norm significantly underestimated the voltage potentials measured near the source pair. This is attributed to the fact that voltage potentials measured at large dipole separations can potentially be given a higher weight as the residual is normalized by the true value, which can be small for large arrays. Simulations using the root mean square error (RMSE) as the norm produced 1D resistivity models whose response better matched the voltage potentials derived from low dipole separations. The RMSE heavily penalizes larger residuals, thus, the RMSE simulations provided solutions whose responses better match observations calculated at small dipole separations (larger voltage potentials) as more importance was placed on matching larger voltage measurements. The significance of this research in regards to advancing geophysical inversion techniques is two fold. The first significant contribution is that the numerical accuracy of AEM solutions are not dependent upon the discretization of a computational grid, thus, a complex discretization is not required to achieve a sound hydrogeologic interpretation of ERT data unless necessitated by the data. Although the earth is inherently complex, a finely discretized model leads to a large number of parameters that need to be estimated. An equally good explanation of the subsurface may be provided by analytic elements, removing the requirement of finely discretized regions to achieve numerical stability. The second major contribution is that the RMSE or MAE should be used as the norm for models using a single objective function to provide the most realistic representation of earth models. Ultimately, the AEM-PSO scheme improves the hydrogeologic information that can be inferred from ERT data, and furthers the ability of ERT to serve as an effective in situ hydrogeologic characterization method.