Identifying effective solutions for locating groundwater resources and ensuring the quality of drinking water is increasingly urgent, given the challenges posed by climate change and population growth. This review investigates electromagnetic geophysical imaging techniques, in both time- and frequency-domain, that can provide valuable insights for groundwater assessment. We explore computational electromagnetic methods used to evaluate electromagnetic data and several recent hydrogeophysical case studies.As open-source frameworks for modeling electromagnetic geophysical problems become available, a broader range of researchers can interpret their data with computationally advanced software. We provide an overview of documented open-source codes for evaluating electromagnetic data and analyze various hydrological targets in relation to their electromagnetic surveying technique and the computational method applied. Furthermore, we evaluate the potential of advanced computational techniques, including three-dimensional modeling, non-deterministic inversion and machine learning, to couple geophysical with numerical groundwater modeling and apply it in groundwater system studies. Despite obstacles such as complexity and resource demands, our findings indicate that the quantification and integration of predictive uncertainties from both electromagnetic and hydrological data and simulations would significantly improve the reliability of hydrogeophysical models. This can lead to a deeper understanding of groundwater systems and improved management practices.

Subsurface electrical conductivity models from frequency-domain electromagnetic (FDEM) induction measurements are often derived using computationally efficient one-dimensional piecewise inversion (PWI) approaches. However, PWI does not account for lateral conductivity variations or the measurement overlap between adjacent soundings, which can limit model estimation accuracy. Laterally constrained inversion (LCI) introduces smoothness constraints to reduce lateral variability between neighbouring models, potentially improving continuity. In this study, both PWI and LCI use a 1D forward function, assuming a horizontally layered earth, and a horizontally laying rigid boom instrument, to perform the estimations This study presents a detailed analysis of how various 2.5D and 3D conductivity distributions, including topographic variations and instrument pitch angle, affect FDEM measurements. We examine how these measurement distortions propagate into PWI and LCI inversion results. Under ideal conditions, such as flat terrain, no instrument tilt, and simple two-layer models, both methods recover accurate conductivity structures, with LCI offering little advantage in accuracy. When topography is introduced, however, distortions occur even at slopes as small as 2°, and both methods show degraded performance, particularly in 3D scenarios. In the field example, LCI produces smoother and more stable results than PWI in the presence of noise, but its assumption of lateral smoothness can be restrictive in geologically complex settings. Our findings show that both inversion strategies are sensitive to topographic and 3D effects, and that error propagation significantly influences inversion reliability. These results highlight the need for improved methodologies capable of handling realistic acquisition conditions and measurement uncertainties in FDEM surveys.

Electromagnetic induction measurements from multi-coil configuration instruments are used to obtain information about the electrical conductivity distribution in the subsurface. The resulting inverse problem might not have a unique and stable solution. In that case, a local inversion method can be trapped in a local minimum and lead to an incorrect solution. In this study, we evaluate the well-posedness of the inverse problem for two and three-layered electrical conductivity models. We show that for a two-layered model, uniqueness is ensured only when both in-phase and quadrature data are available from the measurements. Results from a Gauss–Newton inversion and a lookup table demonstrate that the solution space is convex. Furthermore, we demonstrate that for even a simple three-layered model, the data contained in such measurements are insufficient to reach a correct or stable solution. For models with more than 2 layers, independent prior information is necessary to solve the inverse problem. The insights from the numerical examples are applied in a field case.