To improve the efficiency of 3-D forward modeling in airborne electromagnetic (AEM) methods, we propose a novel high-fidelity surrogate modeling approach based on the hybrid deep operator network (DeepONet)-Fourier neural operator (FNO) (HDF). This method leverages the DeepONet's branch-trunk network to the input data, which is then processed in a higher dimensional Fourier space for enhanced information extraction and learning. The architecture preserves the deep neural network's (DNN) capacity to solve multiple partial differential equations (PDEs) while using Fourier transforms to improve generalization. The training dataset was generated using the Gaussian random field (GRF) method, which efficiently creates smooth, random geometric shapes across various scales, representing complex geological structures. The theoretical experiments demonstrate that the hybrid architecture outperforms conventional DeepONet and FNO models under the same training conditions, and it reduces the relative errors by nearly an order of magnitude. When applied to the real geological model of the Byneset region in Norway, the hybrid architecture achieves a prediction accuracy comparable to traditional numerical methods and outperforms DeepONet and FNO in terms of prediction errors. In addition, the proposed approach is approximately 1000x faster than the finite difference methods, making it a highly efficient solver for future data inversions.

Airborne electromagnetic (AEM) inversion is a key approach for reconstructing subsurface resistivity structures in geologically complex regions. Owing to the complexity of subsurface media, the conventional 1D and 2D inversion approaches are insufficient for resolving these geological structures. The development of fully 3D inversion methodologies is necessary. However, in large-scale 3D AEM inversions, the structured meshes impose severe limitations on local refinement, constraining mesh design and parameterization. Here, we present a 3D inversion framework for AEM data based on an adaptive octree discretization. The forward and adjoint modeling are performed using a vector finite-element formulation on octree meshes, enabling flexible local meshes guided by the system footprint and thereby reducing degrees of freedom while improving computational efficiency. An adaptive mesh-refinement strategy is further incorporated to dynamically balance inversion accuracy and computational cost. Synthetic experiments demonstrate that the adaptive octree approach outperforms the conventional uniform-mesh strategies in recovering anomaly geometry, delineating structural boundaries and reducing computational expenses. Application to an AEM field dataset acquired from Lofoten-Vesterålen region of Norway successfully resolves multiple conductive structures that are consistent with prior geological knowledge, confirming the robustness and suitability of the method for large-scale surveys. These results highlight the potential of octree-based adaptive inversion to substantially enhance both accuracy and efficiency in 3D AEM imaging.

Global demand for critical raw materials, including phosphorus (P) and rare earth elements (REEs), is on the rise. The south part of Norway, with a particular focus on the Southern Oslo Rift region, is a promising reservoir of Fe-Ti-P-REE resources associated with magmatic systems. Confronting challenges in mineral exploration within these systems, notably the absence of alteration haloes and distal footprints, we have explored alternative methodologies. In this study, we combine machine learning with geological expertise, aiming to identify prospective areas for critical metal prospecting. Our workflow involves processing over 400 rock samples to create training datasets for mineralization and non-mineralization, employing an intuitive sampling strategy to overcome an imbalanced sample ratio. Additionally, we convert airborne magnetic, radiometric, and topographic maps into machine learning-friendly features, with a keen focus on incorporating domain knowledge into these data preparations. Within a binary classification framework, we evaluate two commonly used classifiers: a random forest (RF) and support vector machine (SVM). Our analysis shows that the RF model outperforms the SVM model. The RF model generates a predictive map, identifying approximately 0.3% of the study area as promising for mineralization. These findings align with legacy data and field visits, supporting the map’s potential to guide future surveys.

Graphite is considered to be one of Europe’s most critical minerals. It is necessary for the transition from hydrocarbon fuel to electricity due to its use in batteries that power electronic devices and electric transport. In the past, high-quality exposed graphite was found in Norway without today’s advanced geophysical and geological methods. Norway is a key destination in Europe for graphite production. With an increasing demand for graphite, there have been efforts to systematically survey the country using modern geophysical and geological methods to find hidden graphite deposits. Among the various geophysical survey methods, electrical and electromagnetic (EM) methods are the first choice for the exploration of graphite due to the material’s high electrical conductivity. Airborne surveys are often used to cover a large area for a regional reconnaissance survey to locate the sites with potential mineral deposits before performing ground geophysical and geological surveys. Therefore, frequency-domain helicopter EM (HEM) and airborne magnetic surveys were performed in Northern Norway to locate interesting anomalies which were followed by ground surveys such as electrical resistivity tomography (ERT), charged-potential (CP), self-potential (SP), ground EM, and geological surveys. Some locations were also investigated with drilling and petrophysical core-sample analysis. In this paper, we present helicopter EM and magnetic data, 3D inversion of HEM data, and a successful ground follow-up survey result from the Vesterålen district in Northern Norway. The HEM survey identified previously known and new graphite occurrences, both partially exposed or buried, which were confirmed using ground surveys, drilling, and laboratory analysis of the samples.

Airborne electromagnetic (AEM) technology is an efficient geophysical exploration tool for investigating subsurface electrical structures. In recent years, 3-D inversion of AEM data has been developed rapidly, but it still faces challenges such as low resolution and computational efficiency. To solve these problems, we propose a multiscale shearlet-based regularization inversion algorithm by establishing the relationship between spatial resolution and shearlet coefficients in the inversion process. In the initial stage of inversion, the coarse grids and sparse measurement points data are used to recover the main subsurface structure. When the data misfit reaches a certain level, the previous results are used as the coarse scale model in the shearlet domain to recover the model with fine grids and dense measurements. By building this coarse-to-fine inversion scheme, we can well utilize the multiscale information in AEM data and effectively achieve high-resolution inversions. We demonstrate the effectiveness and practicality of our 3-D MS inversion algorithm using two synthetic examples and a field dataset from Norway. The numerical experiments show that our inversion method can effectively reduce the computational time and improve inversion resolution.

Airborne electromagnetic (AEM) surveys usually covers a large area and create a large amount of data. This has limited the application of three-dimensional (3D) AEM inversions. To make 3D AEM data inversion at a large scale possible, the local mesh method has been proposed to avoid solving large matrix equations in 3D AEM modeling. However, the local mesh only saves the computational cost and memory during forward modeling and Jacobian calculations. When the survey area is very large, the cost for storing and solving the inversion equations can be very high. This brings big challenges to practical 3D AEM inversions. To solve this problem, we develop a 3D scheme based on the block coordinate descent (BCD) method for inversions of large-scale AEM data. The BCD method divides the inversion for large models into series of small-local inversions, so that we can avoid solving the large matrix equations. Numerical experiments demonstrate that the BCD method can get very similar results to those from the existing inversion methods but saves huge amounts of memory.

Today, minerals are playing a critical role in the transition from fossil fuel-based energy systems to renewable and sustainable energy sources (Owen et al [...]

Methods for determining the radiation dose received by exposed biota require major improvements to reduce uncertainties and increase precision. We share our experiences in attempting to quantify external dose rates to free-ranging wildlife using GPS-coupled dosimetry methods. The manuscript is a primer on fundamental concepts in wildlife dosimetry in which the complexities of quantifying dose rates are highlighted, and lessons learned are presented based on research with wild boar and snakes at Fukushima, wolves at Chornobyl, and reindeer in Norway. GPS-coupled dosimeters produced empirical data to which numerical simulations of external dose using computer software were compared. Our data did not support a standing paradigm in risk analyses: Using averaged soil contaminant levels to model external dose rates conservatively overestimate the dose to individuals within a population. Following this paradigm will likely lead to misguided recommendations for risk management. The GPS-dosimetry data also demonstrated the critical importance of how modeled external dose rates are impacted by the scale at which contaminants are mapped. When contaminant mapping scales are coarse even detailed knowledge about each animal's home range was inadequate to accurately predict external dose rates. Importantly, modeled external dose rates based on a single measurement at a trap site did not correlate to actual dose rates measured on free ranging animals. These findings provide empirical data to support published concerns about inadequate dosimetry in much of the published Chernobyl and Fukushima dose-effects research. Our data indicate that a huge portion of that literature should be challenged, and that improper dosimetry remains a significant source of controversy in radiation dose-effect research.

The age and formation of the Scandinavian mountains and the Norwegian strandflat have long been the subject of dispute. Some researchers argue that the present-day mountains are remains of the Caledonian orogen while others claim that the Caledonian nappes after erosion were buried by Mesozoic sediments and subsequently exhumed. In order to clarify these issues, we have studied remains of chemically weathered rocks (saprolites) from the coast to the interior of central Norway. The multidisciplinary study includes digital topography, electrical resistivity tomography (ERT), XRD, XRF, palynological analyses and K–Ar dating of samples from outcrops, trenches and core drilling. The coastal areas are dominated by an outer strandflat and an inner joint-valley landscape, while the interior is characterised by smoother landscapes referred to as palaeo-surfaces. Remnants of pre–Tertiary weathering occur in the joint valley landscape as well as on the palaeo-surfaces. The saprolites are found within fault- and fracture-zones and at depths exceeding 50 m in drillholes. It is suggested that the old saprolites were strongly eroded along the coast and in the fjords and valleys such as in Orkdalen and Sunndalen. K–Ar dating of mainland clay alteration most frequently yielded Jurassic ages along a profile extending from the coast to the Dovrefjell mountains (c. 1400 m a.s.l.). The formation age of the smectite- and kaolinite-containing saprolites seems to be almost contemporaneous along this profile implying that the entire area was subject to weathering in a warm and humid climate, such as prevailed during the Late Triassic and Jurassic. Palynological residues containing thermally altered Triassic and Jurassic pollen and spores in the clay-infected bedrock lend support to the saprolite interpretation. The Mesozoic landscape in central Norway was consequently shaped by uplift and deep weathering in the Jurassic. The entire Trøndelag county was most likely covered by Mesozoic sedimentary rocks until Cenozoic exhumation. The landscape was modified by Cenozoic tectonic uplift and erosion, and finally reworked by Pleistocene glacial erosion. We therefore conclude that both the observed saprolites and the shape of the present-day landscape in central Norway give a strong impression of the original Jurassic weathering surface.

Adequate information on external exposure is often a limiting factor in ecological risk assessments because of a lack of exposure data for free-ranging animals as they interact with a heterogeneous distribution of contaminants. Instead, most wildlife exposure data are estimated from model simulations. However, empirical exposure data are rarely available to verify model results, or to test fundamental assumptions inherent in exposure assessments. We used novel, GPS-coupled radiation dosimeters on reindeer (Rangifer tarandus) to quantify their external exposure for five months in a Chernobyl fallout affected mountainous area of Norway. The exposure data were then used to test a fundamental assumption in screening-level risk assessments: Mean soil contaminant concentrations can be used to conservatively estimate chronic external exposures to representative animals. External exposure and GPS coordinates were obtained hourly and compared to model simulations of exposure based on airborne surveys of 137Cs soil contamination. Our objectives were to determine 1) if modelled dose estimates based on mean 137Cs soil concentrations were conservative, and 2) if modelled dose estimates could be improved by adjusting for spatial–temporal heterogeneity of contaminants using 137Cs concentrations within reindeers’ GPS-defined home ranges and core areas. We found that external exposure modelled from mean soil contaminant concentrations underestimated exposure by 70% compared to empirical measurements from GPS-dosimeter collars worn on individual animals. Using area-weighted mean contaminant levels within the animals’ home range improved the model estimates, but still underestimated the field dosimeter data by 53%. The best estimate of external exposure was obtained when high-use areas within their home range, along with spatial heterogeneity of the contaminant, was accounted for by using area-weighted mean soil contaminant levels within GPS-derived core areas. Accounting for temporal use of core areas within animals’ home range provided a 24% improvement. A comparison of our analyses to similar work performed on Chernobyl wolves found the two studies concur that risk assessors should be cautious in relying on the paradigm of using averaged soil contaminant levels to provide conservative estimates of external exposure to representative individuals. Results of modelled external exposure based on mean soil contaminant concentrations could misguide assessors and cause inappropriate management decisions.

The flight altitude has a large effect on airborne electromagnetic (AEM) responses. Due to the dynamic environment of the aircraft, the recorded sensor altitudes may contain errors. Research demonstrates that the AEM responses caused by several meters’ altitude errors can be larger than those caused by some anomalous body. Ignoring these errors will create erroneous results in AEM data interpretation. Considering that there is not yet a published 3-D AEM inversion method that considers the flight altitude, we develop in this article a 3-D inversion algorithm for AEM with the flight height treated as an inversion parameter. For the forward modeling, we use the finite-element method, while for the inversion, we use the Gauss–Newton (GN) optimization method. To make our inversion works for variable flight altitudes, we propose a scheme of 3-D Jacobean matrix calculation for both the resistivities and flight altitudes without much increasing the computational cost. The numerical simulation result confirms that the flight altitude really has a large effect on the AEM responses. The inversions of synthetic data show that our 3-D inversion method can both recover the resistivity distribution in the underground and decrease the altitude errors recorded, while the field data inversion demonstrates that our method can deliver a better inversion model with a smaller data misfit.

We compute the first probabilistic uranium concentration map of Norway. Such a map can support mineral exploration, geochemical mapping, or the assessment of the health risk to the human population. We employ multiple non-linear regression to fill the information gaps in sparse airborne and ground-borne uranium data sets. We mimic an expert elicitation by employing Random Forests and Multi-layer Perceptrons as digital agents equally qualified to find regression models. In addition to the regression, we use supervised classification to produce conservative and alarmistic classified maps outlining regions with different potential for the local occurrence of uranium concentration extremes. Embedding the introduced digital expert elicitation in a Monte Carlo approach we compute an ensemble of plausible uranium concentrations maps of Norway discretely quantifying the uncertainty resulting from the choice of the regression algorithm and the chosen parametrization of the used regression algorithms. We introduce digitated glyphs to visually integrate all computed maps and their associated uncertainties in a loss-free manner to fully communicate our probabilistic results to map perceivers. A strong correlation between mapped geology and uranium concentration is found, which could be used to optimize future sparse uranium concentration sampling to lower extrapolation components in future map updates.

Radon, a radioactive gas produced through the decay of uranium in the earth's crust, poses a significant health risk when it accumulates to high concentrations indoors. This study focuses on identifying areas at higher risk of radon accumulation in Norway by employing a data-driven approach based on geogenic factors, particularly the distribution of uranium on the ground surface. Utilizing two types of uranium measurements and employing a statistical methodology, we classify bedrock geology based on their average uranium content. The classification process integrates Self-organizing maps (SOM) with K-means clustering, facilitating the creation of a country-scale extrapolation. The resulting uranium map is merged from the high-resolution airborne uranium map and the extrapolated uranium map. While acknowledging the presence of uncertainties, our study offers valuable insights into geogenic radon risk, serving as a valuable resource for radon studies and mitigation efforts. Furthermore, the methodology employed in this study is characterized by its flexibility and scalability, enabling future updates and refinements to enhance radon risk assessment and management strategies.

Summary Quick-clay landslides are reported from different parts of the world, specially from Nordic countries, Canada, and Russia. Quick clay is mainly observed in marine clay areas. Various geophysical methods can help mapping of potential quick-clay deposits. NGU uses frequency-domain helicopter EM (HEM) and electrical resistivity tomography (ERT) to map potential quick-clay areas in Norway. Orkdal valley in Norway is characterized by thick deposits from the ice age and deglaciation period. In 2021 NGU, in collaboration with NVE, collected HEM, ERT and ground penetrating radar (GPR) data from Orkdal valley for quick-clay mapping. We present subsurface resistivity models obtained from full 3D inversion of HEM data and its comparison with ERT along one profile. There is a general good correlation between ERT and HEM data, and also with a geotechnical drilling profile from an earlier mapped quick-clay hazard zone.

Based on the spatial structure correlation in different geophysical parameters, we propose a new 3-D joint inversion method for frequency-domain airborne electromagnetic (AEM) and airborne magnetic (AirMag) data by incorporating a local Pearson correlation constraint (LPCC). For each iteration, the entire model is separated into multiple subdomains and the Pearson correlation coefficients of resistivity and magnetization in the subdomain are employed as the additional regularization term to do the joint constraint. This new regularization term is continuously updated in the inversion process to ensure that the resistivity and magnetization models in two separated inversions converge to a similar spatial structure. As a statistics technology, the LPCC-based joint inversion scheme not only has the advantages of the conventional joint inversions, but also can implement the structural constraints in different scales by selecting different sizes of the subdomain. This provides the flexibility for solving multiscale problems. Synthetic examples show that the joint inversion can improve the overall inversion resolution by combining the high vertical resolution of the EM method and large exploration depth and high horizontal resolution of the magnetic method. In the application to field survey datasets, the joint inversion delivers better results than those of separate inversions, which further verifies the effectiveness of our method.

The conventional, L2-norm-based, regularization term in electromagnetic (EM) inversions implements smooth constraints on model complexity in the space domain, which can smoothen the boundaries of complex underground structures. To improve the resolution of 3-D frequency-domain airborne EM (AEM) inversions, we propose a new algorithm for sparse-regularized inversion based on the shearlet transform. Unlike traditional methods that invert the model parameters in the space domain, we first transform the 3-D resistivity model into the frequency domain and then invert the sparse coefficients using an L1-norm measure to ensure the sparseness of the solution. Finally, we transform the shearlet coefficients back to the space domain to update the model. The shearlet transform has inherent multiscale and multidirectional properties, making it capable of effectively extracting complex geometries such as curved boundaries. We adopt the finite-difference method and the iteratively reweighted least-squares scheme for our 3-D AEM modeling and inversions and apply the “moving footprint” technique to speed up the inversion. Tests using synthetic data show that sparse-regularized inversion based on the shearlet transform can obtain more-focused inversion results than conventional smoothness-constrained inversions based on the L2-norm. Tests using field survey data also reveal that the new method can achieve more realistic underground structures.

Airborne electromagnetic (AEM) methods have been more and more widely used in mineral exploration, environmental and engineering studies, and ground water investigation. However, compared with ground-based electromagnetic (EM) methods, such as magnetotelluric or controlled-source EM, AEM methods generally produce large amounts of data, which leads to very costly 3D EM inversions. We have developed a new 3D AEM inversion scheme based on the finite-element method and unstructured tetrahedral local meshes. This is different from the traditional local mesh method in that the traditional method uses regular cuboids for 3D AEM inversions, whereas our scheme uses irregular tetrahedral meshes that can easily accommodate the topography and complex underground structure. Moreover, because we create our local mesh by extracting from part of the global model mesh, the relationship between the local and global meshes is straightforward, so we can easily create a projection of the Jacobian matrix between global and local meshes and rapidly construct the global Jacobian matrix for 3D EM inversions. After formulating the boundary value problem based on the finite-element method, we verify the accuracy of our modeling algorithm by checking against the semianalytical solution for a homogeneous half-space model, and we test our inversion algorithm by running inversions on synthetic and survey data collected over Vesterålen, Norway. The numerical experiments demonstrate that our method can model the AEM responses at high accuracy and recover the subsurface main resistivity structures from synthetic and field data.

From the first use of airborne electromagnetic (AEM) systems for remote sensing in the 1950s, AEM data acquisition, processing and inversion technology have rapidly developed. Once used extensively for mineral exploration in its early days, the technology is increasingly being applied in other industries alongside ground-based investigation techniques. This paper reviews the application of onshore AEM in Norway over the past decades. Norway’s rugged terrain and complex post-glacial sedimentary geology have contributed to the later adoption of AEM for widespread mapping compared to neighbouring Nordic countries. We illustrate AEM’s utility by using two detailed case studies, including time-domain and frequency domain AEM. In both cases, we combine AEM with other geophysical, geological and geotechnical drillings to enhance interpretation, including machine learning methods. The end results included bedrock surfaces predicted with an accuracy of 25% of depth, identification of hazardous quick clay deposits, and sedimentary basin mapping. These case studies illustrate that although today’s AEM systems do not have the resolution required for late-phase, detailed engineering design, AEM is a valuable tool for early-phase site investigations. Intrusive, ground-based methods are slower and more expensive, but when they are used to complement the weaknesses of AEM data, site investigations can become more efficient. With new developments of drone-borne (UAV) systems and increasing investment in AEM surveys, we see the potential for continued global adoption of this technology.