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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.

2D electrical resistivity tomography has been applied within a mountain permafrost environment to assist in ice location. In the context of climate change, a warming process could partially thaw this permafrost and thereby increase the risk of slope instabilities. The extent and location of permafrost are therefore of considerable interest to civil engineers. The most challenging aspect of resistivity surveys on mountain permafrost concerns the surface layer, which mainly consists of large blocks with air voids. To overcome the very poor electrical contact, long steel stakes and sponges soaked in salt water are used as electrodes. Nevertheless, only a weak current can be injected. Another challenging aspect is the high resistivity contrast between frozen and unfrozen material, which makes inversion and interpretation difficult and problematic. In order to assess whether features at depth, indicated by the data, are real or are artefacts of the inversion process, a special inversion algorithm was applied to process depth of investigation (DOI) index maps. This method carries out two inversions of the same data set using different values of the reference resistivity. The two inversions give the same resistivity values in areas where the data contain information about the resistivity of the subsurface. On the other hand, the final result depends on the reference resistivity in areas where the data do not constrain the model. As can be deduced from field data from the Swiss Alps and the Jura Mountains, this methodology prevents over‐interpretations or misinterpretations of inversion results in mountain permafrost studies. From the DOI calculations, it is evident that little reliable information on the bedrock under the massive ice can be obtained and that the resistivity within the high resistivity zones cannot be determined accurately. The DOI map also helps to explain the occurrence of erratic and non‐geological structures at depth and indicates to what depth an inverted resistivity profile can provide results.