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Three-dimensional resistivity surveys and their associated inversion models are required to accurately resolve structures exhibiting very complex geology. In the same light, 3D resistivity surveys collected at multiple times are required to resolve temporally varying conditions. In this work we present 3D data sets, both synthetic and real, collected at different times. The large spatio-temporal data sets are then inverted simultaneously using a least-squares methodology that incorporates roughness filters in both the space and time domains. The spatial roughness filter constrains the model resistivity to vary smoothly in the x-, y-and z-directions. A temporal roughness filter is also applied that minimizes changes in the resistivity between successive temporal inversion models and the L-curve method is used to determine the optimum weights for both spatial and temporal roughness filters. We show that the use of the temporal roughness filter can accurately resolve changes in the resistivity even in the presence of noise. The L1-and L2-norm constraints for the temporal roughness filter are first examined using a synthetic model. The synthetic data test shows that the L1-norm temporal constraint produces significantly more accurate results when the resistivity changes abruptly with time. The model obtained with the L1-norm temporal constraint is also less sensitive to random noise compared with independent inversions (i.e., without any temporal constraint) and the L2-norm temporal constraint. Anomalies that are common in models using independent inversions and the L2-norm and L1-norm temporal constraints are likely to be real. In contrast, anomalies present in a model using independent inversions but that are significantly reduced with the L2-norm and L1-norm constraints are likely artefacts. For field data sets, the method successfully recovered temporal changes in the subsurface resistivity from a landfill monitoring survey due to rainwater infiltration, as well as from an experiment to map the migration of sodium cyanide solution from an injection well using surface and borehole electrodes in an area with significant topography.

An electrical-resistivity survey was completed at the T tank farm at the Hanford nuclear site in Washington State, U.S.A. The purpose of the survey was to define the lateral extent of waste plumes in the vadose zone in and around the tank farm. The T tank farm consists of single-shell tanks that historically have leaked and many liquid-waste-disposal facilities that provide a good target for resistivity mapping. Given that the site is highly industrialized with near-surface metallic infrastructure that potentially could mask any interpretable waste plume, it was necessary to use the many wells around the site as long electrodes. To accommodate the long electrodes and to simulate the effects of a linear conductor, the resistivity inversion code was modified to assign low-resistivity values to the well’s location. The forward model within the resistivity code was benchmarked for accuracy against an analytic solution, and the inverse model was tested for its ability to recreate images of a hypothetical target. The results of the tank-farm field survey showed large, low-resistivity targets beneath the disposal areas that coincided with the conceptual hydrogeologic models developed regarding the releases. Additionally, in areas of minimal infrastructure, the long-electrode method matched the lateral footprint of a 3D surface-resistivity survey with reasonable fidelity. Based on these results, the long-electrode resistivity method may provide a new strategy for environmental characterization at highly industrialized sites, provided a sufficient number and density of wells exist.

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A surface resistivity survey was conducted on the Hanford Site over a waste disposal trench that received a large volume of liquid inorganic waste. The objective of the survey was to map the extent of the plume that resulted from the disposal activities approximately 50 yr earlier. The survey included six resistivity transects of at least 200 m, where each transect provided two‐dimensional profile information of subsurface electrical properties. The results of the survey indicated that a low resistivity plume resides at a depth of approximately 25 to 44 m below ground surface. The target depth was calibrated with borehole data of pore‐water electrical conductivity. Due to the high correlation of the pore‐water electrical conductivity to nitrate concentration and the high correlation of measured apparent resistivity to pore‐water electrical conductivity, inferences were made that proposed the spatial distribution of the apparent resistivity was due to the distribution of nitrate. Therefore, apparent resistivities were related to nitrate, which was subsequently rendered in three dimensions to show that the nitrate likely did not reach the water table and the bounds of the highest concentrations are directly beneath the collection of waste sites.