In inverse problems, investigating uncertainty in the posterior distribution of model parameters is as important as matching data. In recent years, most efforts have focused on techniques to sample the posterior distribution with reasonable computational costs. Within a Bayesian context, this posterior depends on the prior distribution. However, most of the studies ignore modeling the prior with realistic geological uncertainty. In this paper, we propose a workflow inspired by a Popper-Bayes philosophy that data should first be used to falsify models, then only be considered for matching. We propose a workflow consisting of three steps: (1) in defining the prior, we interpret multiple alternative geological scenarios from literature (architecture of facies) and site-specific data (proportions of facies). Prior spatial uncertainty is modeled using multiplepoint geostatistics, where each scenario is defined using a training image. (2) We validate these prior geological scenarios by simulating electrical resistivity tomography (ERT) data on realizations of each scenario and comparing them to field ERT in a lower dimensional space. In this second step, the idea is to probabilistically falsify scenarios with ERT, meaning that scenarios which are incompatible receive an updated probability of zero while compatible scenarios receive a nonzero updated belief. (3) We constrain the hydrogeological model with hydraulic head and ERT using a stochastic search method. The workflow is applied to a synthetic and a field case studies in an alluvial aquifer. This study highlights the importance of considering and estimating prior uncertainty (without data) through a process of probabilistic falsification.

Abstract. We have investigated the potential of 2D electrical imaging for the characterization of seawater intrusion using field data from a site in Almeria, SE Spain. Numerical simulations have been run for several scenarios, with a hydrogeological model reflecting the local site conditions. The simulations showed that only the lower salt concentrations of the seawater-freshwater transition zone could be recovered, due to the loss of resolution with depth. We quantified this capability in terms of the cumulative sensitivity associated with the measurement setup and showed that the mismatch between the targeted and imaged parameter values occurs from a certain sensitivity threshold. Similarly, heterogeneity may only be determined accurately if located in an adequately sensitive area. At the field site, we identified seawater intrusion at the scale of a few kilometres down to a hundred metres. Borehole logs show a remarkable correlation with the image obtained from surface data but indicate that the electrically derived mass fraction of pure seawater could not be recovered due to the discrepancy between the in-situ and laboratory-derived petrophysical relationships.Surface-to-hole inversion results suggest that the laterally varying resolution pattern associated with such a setup dominates the image characteristics compared to the laterally more homogeneous resolution pattern of surface only inversion results, and hence surface-to-hole images are not easily interpretable in terms of larger-scale features. Our results indicate that electrical imaging can be used to constrain seawater intrusion models if image appraisal tools are appropriately used to quantify the spatial variation of sensitivity and resolution. The most crucial limitation is probably the apparent non stationarity of the petrophysical relationship during the imaging process.

The growing demand for renewable energy leads to an increase in the development of 1 geothermal energy projects and heat has become a common tracer in hydrology and 2 hydrogeology. Designing geothermal systems requires a multidisciplinary approach including 3 geological and hydrogeological aspects. In this context, electrical resistivity tomography 4 (ERT) can bring relevant, qualitative and quantitative information on the temperature 5 distribution in operating shallow geothermal systems or during heat tracing experiments. We 6 followed a heat tracing experiment in an alluvial aquifer using cross-borehole time-lapse 7 ERT. Heated water was injected in a well while water of the aquifer was extracted at another 8well. An ERT section was set up across the main flow direction. The results of ERT were 9 transformed into temperature using calibrated petrophysical relationships. These ERT-derived 10 temperatures were then compared to direct temperature measurements in control piezometers 11 collected with distributed temperature sensing (DTS) and groundwater temperature loggers.

In theory, aquifer thermal energy storage (ATES) systems can recover in winter the heat stored in the aquifer during summer to increase the energy efficiency of the system. In practice, the energy efficiency is often lower than expected from simulations due to spatial heterogeneity of hydraulic properties or non‐favorable hydrogeological conditions. A proper design of ATES systems should therefore consider the uncertainty of the prediction related to those parameters. We use a novel framework called Bayesian Evidential Learning (BEL) to estimate the heat storage capacity of an alluvial aquifer using a heat tracing experiment. BEL is based on two main stages: pre‐ and postfield data acquisition. Before data acquisition, Monte Carlo simulations and global sensitivity analysis are used to assess the information content of the data to reduce the uncertainty of the prediction. After data acquisition, prior falsification and machine learning based on the same Monte Carlo are used to directly assess uncertainty on key prediction variables from observations. The result is a full quantification of the posterior distribution of the prediction conditioned to observed data, without any explicit full model inversion. We demonstrate the methodology in field conditions and validate the framework using independent measurements.

In hard-rock aquifers, fractured zones constitute adequate drinking water exploitation areas but also potential contamination paths. One critical issue in hydrogeological research is to identify, characterize, and monitor such fractured zones at a representative scale. A tracer test monitored with surface electrical resistivity tomography (ERT) could help by delineating such preferential flow paths and estimating dynamic properties of the aquifer. However, multiple challenges exist including the lower resolution of surface ERT compared with crosshole ERT, the finite time that is needed to complete an entire data acquisition, and the strong dilution effects. We conducted a natural gradient salt tracer test in fractured limestones. To account for the high transport velocity, we injected the salt tracer continuously for four hours at a depth of 18 m. We monitored its propagation with two parallel ERT profiles perpendicular to the groundwater flow direction. Concerning the data acquisition, we always focused on data quality over temporal resolution. We performed the experiment twice to prove its reproducibility by increasing the salt concentration in the injected solution (from 38 to [Formula: see text]). Our research focused on how we faced every challenge to delineate a preferential flow and solute transport path in a typical calcareous valley of southern Belgium and on the estimation of the transport velocity (more than [Formula: see text]). In this complex environment, we imaged a clear tracer arrival in both ERT profiles and for both tests. Applying filters (with a cutoff on the relative sensitivity matrix and on the background-resistivity changes) was helpful to isolate the preferential flow path from artifacts. Regarding our findings, our approach could be improved to perform a more quantitative experiment. With a higher temporal resolution, the estimated value of the transport velocity could be narrowed, allowing estimation of the percentage of tracer recovery.