Abstract. This paper presents the results of the 2022 groundwater time series modeling challenge, where 15 teams from different institutes applied various data-driven models to simulate hydraulic head time series at four monitoring wells. Three of the wells were located in Europe and one in the USA, in different hydrogeological settings but all in temperate or continental climates. Participants were provided with approximately 15 years of measured heads at (almost) regular time intervals and daily measurements of weather data starting some 10 years prior to the first head measurements and extending around 5 years after the last head measurement. The participants were asked to simulate the measured heads (the calibration period), provide a forecast for around 5 years after the last measurement (the validation period for which weather data was provided but not head measurements), and to include an uncertainty estimate. Three different groups of models were identified among the submissions: lumped-parameter models (3 teams), machine learning models (4 teams), and deep learning models (8 teams). Lumped-parameter models apply relatively simple response functions with few parameters, while the artificial intelligence models used models of varying complexity, generally with more parameters and more input, including input engineered from the provided data (e.g., multi-day averages). The models were evaluated on their performance to simulate the heads in the calibration period and the validation period. Different metrics were used to assess performance including metrics for average relative fit, average absolute fit, fit of extreme (high or low) heads, and the coverage of the uncertainty interval. For all wells, reasonable performance was obtained by at least one team from each of the three groups. However, the performance was not consistent across submissions within each groups, which implies that application of each method to individual sites requires significant effort and experience. Especially estimates of the uncertainty interval varied widely between teams, although some teams submitted confidence intervals rather than prediction intervals. There was not one team, let alone one method, that performed best for all wells and all performance metrics. Lumped-parameter models generally performed as well as artificial intelligence models, except for the well in the USA, where the lumped-parameter models did not use (or use to the full benefit) the provided river stage data, which was crucial for obtaining a good model. In conclusion, the challenge was a successful initiative to compare different models and learn from each other. Future challenges are needed to investigate, e.g., the performance of models in more variable climatic settings, to simulate head series with significant gaps, or to estimate the effect of drought periods.
A 3D tomography algorithm of self‐potential (SP) signals is applied for the first time to the localization of subsurface cavities. A specific application is made to a marl‐pit in Normandy (North‐West of France). A SP map with a total of 221 (5 m‐spaced) measurements shows a negative anomaly with an amplitude of −8 mV associated with the position of the marl pit. To explain these data, we solved the boundary‐value problem for the coupled hydro‐electric problem associated with the presence of the cavity using a finite‐element code. The numerical simulations point out the role of open conduits in electrical charge accumulation near the roof of the cavity and the resistivity contrast between the cavity and the surrounding formation. We applied successfully a SP tomography algorithm showing that the roof of the cavity was associated with a monopole charge accumulation due to the entrance of the ground water flow in a network of open cracks.
The seismoelectric method is based on the interpretation of the electrical field associated with the conversion of mechanical to electromagnetic energy during the propagation of seismic waves in heterogeneous porous media. We propose an extension of a poroacoustic model that takes into account fluid flow and the effect of saturation. This model is coupled with an electrokinetic model accounting for the effect of saturation and in agreement with available experimental data in sands and carbonate rocks. We also developed new scaling laws for the permeability, the streaming potential coupling coefficient and the capillary entry pressure of porous media. The theory is developed for frequencies much below the critical frequency at which inertial effects starts to dominate in the Navier–Stokes equation (>10 kHz). The equations used to compute the propagation of the P waves and the seismoelectric effect in unsaturated condition are solved with finite elements using triangular meshing. We demonstrate the usefulness of a recently developed technique, seismoelectric beamforming, to localize saturation fronts by focusing seismic waves and looking at the resulting seismoelectric conversions. This method is applied to a cross-hole problem showing how a saturation front characterized by a drop in the electrical conductivity and compressibility is responsible for seismoelectric conversions. These conversions can be used, in turn, to determine the position of the front over time.
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Seismoelectric beamforming/focusing allows for the enhancement of the electrical field associated with seismoelectric conversions over the spurious coseismic signals. This chapter presents the basic ideas of this method, followed by numerical tests in piecewise constant and heterogeneous materials. It demonstrates how this method can be used to improve cross-well electrical resistivity tomography (ERT) through a technique called "image-guided inversion". The basic idea of image-guided inversion is to use information from an image to impose the structure in a way that shapes the model covariance smoothness matrix that imposes this structural information in the inversion of the geophysical data. The chapter demonstrates that the method is applicable to heterogeneous geological structures with a contrast in the water saturation. The spectral beamforming method could be used to detect and characterize fractures in a reservoir.
Fractures and conduits existing in the vadose zone can significantly affect the groundwater-surface runoff interaction, however information regarding location, hydrodynamic properties and the water saturation distribution in the fractured vadose zone is challenging. Electrical resistivity tomography, as a non-invasive hydrogeophysical method, has the potential to deliver vast information regarding some of the characteristics of fractures and conduits as well as water saturation distribution in the fractured vadose zone. Numerical simulation of the flow in variably saturated fractured media can be coupled to field investigations of resistivity methods as an invaluable tool to improve the data acquired and as a tool for parameter estimation. In this study we develop and present an advanced method for coupled simulation of variably saturated fluid flow and electrical current distribution in an explicitly fractured porous media. In this model, the fractures are simulated with the 1D/2D hybrid dimension (i.e. 1D fracture elements and 2D matrix elements) discrete fracture matrix model. Mixed hybrid finite element method has been used as the numerical method of discretization for both fluid flow and electrical current. The steps of discretization for electrical current for triangular elements of porous matrix and piecewise linear elements of fractures are presented in the mathematical development section. The results of the numerical solution are validated by comparing against the results obtained by a finite element based package for three synthetic configurations. The developed tool is then used to investigate the effect of some geometric characteristics (i.e. angle and length) of the fracture on the normalized apparent resistivity in the top midpoint of the domain. Finally, the effect of electrical dipole location on the simulated normalized apparent resistivity is investigated numerically. The results show that the location and the orientation of the fracture and the electrical dipole play important roles in the accuracy and resolution of the simulated apparent resistivity and consequently the measured response attributed to the fracture. The present work can be used as a new tool for the coupled simulation of electrical current and variably saturated flow in highly heterogeneous porous media.
