SUMMARY: We developed a 3-D forward modelling code, which simulates controlled source electromagnetic problems in frequency domain using edge-based finite elements and a total electric field approach. To evaluate electromagnetic data acquired across complex subsurface structures, software performing accurate 3-D modelling is required, especially for incorporation in inversion approaches. Our modelling code aims at finding a good compromise between the necessary solution accuracy at the points of interest and the general problem size by using a goal-oriented mesh refinement strategy designed for models of variable electric conductivity and magnetic permeability. To formulate an improved error estimator suitable for controlled source electromagnetic problems, we developed literature approaches of mesh refinement further targeting three aspects. First, to generate a roughly homogeneously fine mesh discretization around all receiver sites, our new error estimator weights the adjoint source term by the approximate decay of the electric field with increasing distance from the primal source using the expression for a homogeneous half-space. This causes almost no additional computational cost. Second, the error estimator employed in the refinement approach can be optimized for models with pronounced conductivity and magnetic permeability contrasts as often encountered in, for example, mineral prospecting scenarios by optionally including terms that measure the continuity of the normal component of current flow and the tangential component of the magnetic field across interfaces of abutting elements. Third, to avoid amplitude-dependent over-refining of the mesh, we formulate our element-wise error estimators relative to the local amplitude of the electromagnetic field. In this work, we evaluate the implemented adaptive mesh refinement approach and its solution accuracy comparing our solutions for simple 1-D models and a model with 3-D anomalies to semi-analytic 1-D solutions and a second-order finite-element code, respectively. Furthermore, a feasibility study for controlled-source electromagnetic measurements across ferrous mineral deposits is conducted. The numerical experiments demonstrate that our new refinement procedure generates problem-specific finite-element meshes and yields accurate solutions for both simple synthetic models and realistic survey scenarios. Especially for the latter, characteristics of our code, such as the possibility of modelling extended sources as well as including arbitrary receiver distributions and detailed subsurface anomalies, are beneficial.

In 3D geo-electromagnetic modeling, an adequate discretisation of the modeling domain is crucial to obtain accurate forward responses and reliable inversion results while reducing the computational cost. This paper investigates the mesh design for subsurface models, including steel-cased wells, which is relevant for many exploration settings but still remains a numerically challenging task. Applying a goal-oriented mesh refinement technique and subsequent calculations with the high-order edge finite element method, simulations of 3D controlled-source electromagnetic models in the presence of metallic infrastructure are performed. Two test models are considered, each needing a distinct version of approximation methods to incorporate the conductive steel casings of the included wells. The influence of mesh quality, goal-oriented meshing, and high-order approximations on problem sizes, computational cost, and accuracy of electromagnetic responses is investigated. The main insights of our work are: (a) the applied numerical schemes can mitigate the computational burden of geo-electromagnetic modeling in the presence of steel artifacts; (b) investigating the processes driving the meshing of models with embedded metallic infrastructures can lead to adequate strategies to deal with the inversion of such electromagnetic data sets. Based on the modeling results and analyses conducted, general recommendations for modeling strategies are proposed when performing simulations for challenging steel infrastructure scenarios.

Controlled‐source electromagnetic methods are applied to survey the electrical resistivity distribution of the subsurface. This work compares normalized electromagnetic field components and transfer functions such as impedance tensors and vertical magnetic transfer functions generated by two independent source polarizations as input data for three‐dimensional inversion. As most other available inversion codes allow for inverting only one of the mentioned input data types, it is unclear which data type is preferable for controlled‐source electromagnetic inversion. Our three‐dimensional non‐linear conjugate gradient inversion code can handle both input data types, facilitating a comparison of normalized electromagnetic field components and transfer functions inversion. Examining inversion results for a three‐dimensional synthetic model with two anomalies, we infer that the transfer functions inversion is favourable for recovering the overall resistivity distribution below the receiver sites in fewer iterations. The inversion of normalized electromagnetic field components produces a sharper image of the anomalies and may be capable of detecting the resistivity distribution below the extended sources, which comes at the price of introducing a more heterogeneous background resistivity in the model.

We develop a three‐dimensional inversion code to image the resistivity distribution of the subsurface from frequency‐domain controlled‐source electromagnetic data. Controlled‐source electromagnetic investigations play an important role in many different geophysical prospecting applications. To evaluate controlled‐source electromagnetic data collected with complex measurement setups, advanced three‐dimensional modelling and inversion tools are required.We adopt a preconditioned non‐linear conjugate gradient algorithm to enable three‐dimensional inversion of impedance tensor and vertical magnetic transfer function data produced by multiple sets of two independent active sources. Forward simulations are performed with a finite‐element solver. Increased sensitivities at source locations can optionally be counteracted with a weighting function in the regularization term to reduce source‐related anomalies in the resistivity model. We investigate the capabilities of the inversion code using one synthetic and one field example. The results demonstrate that we can produce reliable subsurface models, although data sets from single pairs of independent sources remain challenging.

The impacts of climate change, combined with population growth, necessitate practical and effective solutions for locating groundwater resources and ensuring drinking water quality. Our contribution explores recent advances in geoelectrical and electromagnetic imaging methods applied to investigate groundwater systems. Geoelectrical and electromagnetic imaging techniques are popular methods for characterising subsurface properties, such as electrical resistivity or dielectric permittivity. These electrical properties are strongly related to the hydrogeological characteristics of the subsurface. Therefore, geoelectrical and electromagnetic investigations can provide valuable insights into finding groundwater resources, assessing the water quality in terms of contaminations and conducting effective groundwater management.Our study examines state-of-the-art approaches in modelling and instrumentation of induced polarisation and electrical resistivity tomography, as well as time- and frequency-domain electromagnetics and ground-penetrating radar methods. We review recent impactful and innovative groundwater case studies where the above-mentioned methods were applied and further developed. Emphasising the combination of geoelectrical and electromagnetic methods, the studies provide insights into the variation of electrical subsurface properties at different scales, contributing to an improved understanding of the hydrological dynamics in the studied areas. Furthermore, we provide an outlook on the potential for applying geoelectrical and electromagnetic imaging techniques for large-scale groundwater investigations in the exascale computing area.