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The tidal flow of seawater across the Earth's magnetic field induces electric currents and magnetic fields within the ocean and solid Earth. The amplitude and phase of the induced fields depend on the electrical properties of both seawater and the solid Earth, and thus can be used as proxies to study the seabed properties or potentially for monitoring long-term trends in the global ocean climatology. This article presents new global oceanic tidal magnetic field models and their uncertainties for four tidal constituents, including M2,N2,O1 and even Q1 , which was not reliably retrieved previously. Models are obtained through a robust least-squares analysis of magnetic field observations from the Swarm and CHAMP satellites using a specially designed data selection scheme. We compare the retrieved magnetic signals with several alternative models reported in the literature. Additionally, we validate them using a series of high-resolution global three-dimensional (3D) electromagnetic simulations and place constraints on the conductivity of the sub-oceanic mantle for all tidal constituents, revealing an excellent agreement between all tidal constituents and the oceanic upper mantle structure. This article is part of the theme issue 'Magnetometric remote sensing of Earth and planetary oceans'. [ABSTRACT FROM AUTHOR]

Drone‐based geophysical surveying is an emerging measuring platform. High time‐cost efficiency and flexibility to survey over inaccessible areas make drones attractive or sometimes the only feasible option to carry geophysical measurements. This study presents a new drone‐towed electromagnetic induction and magnetic gradient sensor system used for near‐surface characterization and areal mapping. The system uses various datasets to enhance processing and interpretation. The system includes; an electromagnetic induction instrument; magnetic sensors; GNSS‐IMU system; photogrammetry; Lidar model data; and geoid model data. Robust data processing and stochastic inversion subsurface characterization for archaeological prospecting with drone‐towed electromagnetic induction and magnetic gradient sensor systems. Robust statistical methods were used to process the data. We conducted the fieldwork at one of the ancient Viking settlements in Denmark. The surveyed area was approximately 100×$\times$200 m. We then implemented and applied a one‐dimensional laterally constrained non‐linear stochastic inversion to image the subsurface electrical conductivity. The inversion results show a consistent conductive layer at 5–8 m depths, likely associated with the groundwater level. This conductive layer is disrupted under a prominent anomaly within a 2–4 m wide area. Our analysis showed that this conductivity disruption could be a flint mine extending 7 m deep. This anomaly also has a strong signature in magnetic gradient data. [ABSTRACT FROM AUTHOR]

Electric currents induced in conductive planetary interiors by time-varying magnetospheric and ionospheric current systems have a significant effect on electromagnetic (EM) field observations. Complete characterization of EM induction effects is difficult owing to nonlinear interactions between the three-dimensional electrical structure of a planet and spatial complexity of inducing current systems. We present, a general framework for time-domain modeling of three-dimensional EM induction effects in heterogeneous conducting planets. Our approach does not assume that the magnetic field is potential, allows for an arbitrary distribution of electrical conductivity within a planet, and can deal with spatially complex time-varying current systems. The method is applicable to both data measured at stationary observation sites and satellite platforms, and enables the calculation of three-dimensional EM induction effects in near real-time settings. [ABSTRACT FROM AUTHOR]

Geomagnetic storms, which are governed by the plasma magnetohydrodynamics of the solar-interplanetary-magnetosphere system, entail a formidable challenge for physical forward modeling. Yet, the abundance of high-quality observational data has been amenable to the application of datahungry neural networks to geomagnetic storm forecasting. Almost all applications of neural networks to storm forecasting have utilized solar wind observations from the Earth-Sun first Lagrangian point (L1) or closer and generated deterministic output without uncertainty estimates. Furthermore, forecasting work has focused on indices that are also sensitive to induced internal magnetic fields, complicating the forecasting problem with another layer of non-linearity. We address these points, presenting neural networks trained on observations from both the solar disk and the L1 point. Our architecture generates reliable probabilistic forecasts over Est, the external component of the disturbance storm time index, showing that neural networks can gauge confidence in their output. Plain Language Summary Geomagnetic storms are capable of damaging infrastructures like power grids and communication lines, motivating our need to forecast them. Solar phenomena produce geomagnetic storms, which occur when these phenomena reach Earth as bursts of the solar wind. Decades of satellite observations of both the solar wind near the Earth and of the Sun itself are promising for forecasting geomagnetic storms with algorithms known as neural networks. Several neural network architectures have been applied to geomagnetic storm forecasting, but their full potential remains unexplored. First, all existing neural networks have used measurements of the solar wind one hour upstream of the Earth or closer. While these observations are critical for understanding geomagnetic storm progression, from them it is nearly impossible to forecast more than an hour in advance. We include observations of the Sun itself, which reach Earth much faster than the solar wind, thereby including information for forecasting further in advance. Second, all existing neural networks have generated forecasts without uncertainty estimates, meaning that end-users (such as utilities or telecommunications companies) know little about forecast confidence. We present an architecture that generates estimates of uncertainty, and our results demonstrate that neural networks learn how confident to be in their forecasts. [ABSTRACT FROM AUTHOR]

We present electrical resistivity models, derived from magnetotelluric data, of the crust beneath the Bulnay region, Mongolia. They reveal that the lower crust contains a pattern of discrete zones (width of ~25 km) of low resistivity (<30 Ωm). Such features may be an effect of unaccounted‐for electrical anisotropy. However, when anisotropy is considered in the modeling, the features remain. We investigate an alternative explanation, based on a conceptual model of fluid localization and stagnation by thermally activated compaction, and demonstrate it is compatible with the observed low‐resistivity zones. The model explains the location, shape, and size of the zones, with plausible values of the activation energy for lower crustal creep (270–360 kJ/mol), and a viscous compaction length on the order of 10 km. The results imply tectonic deformation and compaction processes, rather than lithological‐structural heterogeneity, control the regional lower crustal fluid flow. Plain Language Summary: We collected magnetotelluric data in the Bulnay region, Mongolia, which is a compressive intracontinental region, by measuring electric and magnetic fields at the surface. Using these data, we generated high‐resolution electrical resistivity models. The models image the lower crust and show that it contains discrete zones of low resistivity that have a distinct pattern. Other studies have shown that such a pattern may be an effect of ignoring electrically anisotropy. But when anisotropy is considered in the modeling the features remain nearly the same. Because of this, we investigate whether an alternative explanation can cause these features. We find that a conceptual model of fluid localization and stagnation by hydromechanical compaction is compatible with the observed pattern of the low‐resistivity zones. In fact, it can explain their location, shape, and size. In addition, we use the conceptual model to determine which viscous rheology is consistent with the data. Finally, we find that estimates for hydraulic and rheological properties of the region are consistent with this explanation. This conceptual model has implications for fluid flow in the lower crust, showing that it is controlled by tectonic deformation and compaction processes, rather than lithological or structural features. Key Points: Electrical resistivity models across a compressive intracontinental region image a pattern of low‐resistivity zones in the lower crustThe pattern is consistent with hydrodynamic stagnation of crustal fluids due to thermally activated compactionThe results demonstrate that compaction processes, rather than lithological structure, control the regional lower crustal fluid flow [ABSTRACT FROM AUTHOR]

This paper provides an overview of the new features of the finite element library deal.II, version 9.2. [ABSTRACT FROM AUTHOR]

The article discusses a study which mapped the crust and upper mantle structure of central Mongolia to be able to understand the underlying mechanisms of intraplate processes and its implications for intraplate surface uplift and volcanism. Topics covered include the insights provided by thermo-mechanical numerical modeling, t potential explanations for intraplate surface uplift, and the results of the multi-scale magnetotelluric modeling.

This paper reports on new results in the determination of magnetic signals produced by oceanic tides as estimated from satellite magnetic measurements. We find that combining data from the past CHAMP (2000–2010) and the present Swarm (since 2013) satellite missions significantly improves the quality of the extracted tidal signals, in particular if along‐track and cross‐track magnetic "gradient" data are utilized. This allows us to determine the magnetic signature not only of the M2 tide but also of the much weaker N2 and O1 tidal constituents. To minimize disturbances from magnetospheric and ionospheric currents, we only use data from the nightside region during geomagnetic quiet conditions and remove core, crustal, and magnetospheric field contributions as given by the CHAOS geomagnetic field model. Despite their small magnitudes, all determined tidal constituents show sensitivity to the electrical conductivity profile of the underlying mantle, enabling imaging the upper mantle below the oceans. Key Points: Global models of the magnetic signals produced by the M2, N2, and O1 oceanic tides have been extracted from satellite magnetic measurementsCombining data from the Swarm and CHAMP missions as well as using field gradient plays key role in the robustness of the estimated modelsAll tidal constituents show significant sensitivity to the electrical conductivity of the oceanic mantle [ABSTRACT FROM AUTHOR]

This study aims at quantifying the influence of topographic distortions on magnetotelluric transfer functions, including the impedance tensor, tipper and phase tensor. To this end, we performed a series of numerical experiments using real topography. We utilized a high-order 3-D finite element modelling code combined with locally refined unstructured meshes to achieve an accurate representation of topography and low modelling errors. We calculated electromagnetic fields for a region in the Hangai Mountains (Mongolia) for a wide period range and showed that, depending on the period and size of topographic features, distortions due to both galvanic and inductive effects can become significant. In addition, we quantify the effect of the vertical electric field component for tilted electric dipoles located on slopes. For real topography examples considered here, we found that galvanic distortions dominate at periods >10 s, resulting in a static shift effect. At shorter periods (<1 s), inductive effects cause significant variations of the impedance, the phase tensor and the tipper. [ABSTRACT FROM AUTHOR]

This paper presents a methodology to sample equivalence domain (ED) in nonlinear partial differential equation (PDE)-constrained inverse problems. For this purpose, we first applied state-of-the-art stochastic optimization algorithm called Covariance Matrix Adaptation Evolution Strategy (CMAES) to identify low-misfit regions of the model space. These regions were then randomly sampled to create an ensemble of equivalent models and quantify uncertainty. CMAES is aimed at exploring model space globally and is robust on very ill-conditioned problems. We show that the number of iterations required to converge grows at a moderate rate with respect to number of unknowns and the algorithm is embarrassingly parallel. We formulated the problem by using the generalized Gaussian distribution. This enabled us to seamlessly use arbitrary norms for residual and regularization terms.We show that various regularization norms facilitate studying different classes of equivalent solutions. We further show how performance of the standard Metropolis-Hastings Markov chain Monte Carlo algorithm can be substantially improved by using information CMAES provides. This methodology was tested by using individual and joint inversions of magneotelluric, controlled-source electromagnetic (EM) and global EM induction data. [ABSTRACT FROM AUTHOR]

We have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, large conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM. [ABSTRACT FROM AUTHOR]

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finiteelement method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshes. [ABSTRACT FROM AUTHOR]

We present a robust and scalable solver for time-harmonic Maxwell's equations for problems with large conductivity contrasts, wide range of frequencies, stretched grids and locally refined meshes. The solver is part of the fully distributed adaptive 3-D electromagnetic modelling scheme which employs the finite element method and unstructured non-conforming hexahedral meshes for spatial discretization using the open-source software deal.II. We use the complex-valued electric field formulation and split it into two real-valued equations for which we utilize an optimal block-diagonal pre-conditioner. Application of this pre-conditioner requires the solution of two smaller real-valued symmetric problems. We solve them by using either a direct solver or the conjugate gradient method pre-conditioned with the recently introduced auxiliary space technique. The auxiliary space pre-conditioner reformulates the original problem in form of several simpler ones, which are then solved using highly efficient algebraic multigrid methods.In this paper, we consider the magnetotelluric case and verify our numerical scheme by using COMMEMI 3-D models. Afterwards, we run a series of numerical experiments and demonstrate that the solver converges in a small number of iterations for a wide frequency range and variable problem sizes. The number of iterations is independent of the problem size, but exhibits a mild dependency on frequency. To test the stability of the method on locally refined meshes, we have implemented a residual-based a posteriori error estimator and compared it with uniform mesh refinement for problems up to 200 million unknowns. We test the scalability of the most time consuming parts of our code and show that they fulfill the strong scaling assumption as long as each MPI process possesses enough degrees of freedom to alleviate communication overburden. Finally, we refer back to a direct solver-based pre-conditioner and analyse its complexity in time. The results show that for multiple right-hand sides the direct solver-based pre-conditioner can still be faster for problems of medium size. On the other hand, it also shows non-linear growth in memory, whereas the auxiliary space method increases only linearly. [ABSTRACT FROM PUBLISHER]

We evaluated 3D inversion of land controlled-source electromagnetic (CSEM) data collected across the Ketzin CO2 storage formation. A newly developed, parallel and distributed 3D inversion code, which is based on a direct forward solver, has been used. This inversion scheme allowed us to calculate the Jacobian matrix explicitly within a reasonable time and use it to calculate regularization parameters, inspect survey coverage, and carry out resolution analysis. After demonstrating that the magnetic field components are sensitive to conductors only, whereas the electric field components are sensitive to all features of interest, we continued to work with electric field data only. Estimates of data uncertainty obtained from robust processing were used for automated data preselection and weighting during inversion. We tested different regularization techniques and a range of starting models to explore the model space and assess the influence of regularization on the inversion images. We further demonstrated an approach for handling numerical singularities due to sources located inside the inversion domain. We estimated survey coverage, horizontal and vertical resolution, and depth penetration using cumulative sensitivity, point spread functions, and depth-resolution plots. Based on data fit analysis, we determined a preferred subsurface conductivity model, which we compared to an independent regional structural geologic model, and we provided an interpretation for the structures resolved. The inversion approach we used provides robust results in good agreement with known geology, offers new possibilities for model assessment, and should be transferable to other CSEM data sets. [ABSTRACT FROM AUTHOR]

Three-dimensional electrical conductivity distribution in the lower mantle can be estimated by inverting so-called matrix Q-responses. These responses relate spherical harmonic coefficients of external (inducing) and internal (induced) parts of the magnetic potential which describes the signals of magnetospheric origin. Currently, time series of these coefficients are estimated using potential method and both observatory as well as Swarm satellite data. However, the quality of the estimated induced coefficients containing information about 3-D conductivity remains insufficient, thus limiting recovery of lateral conductivity variations in the mantle. Here, we explore a feasibility of alternative approach for retrieving time series of inducing (and induced) coefficients. We utilize the fact that horizontal component of magnetic field is much less influenced by effects from 3-D inhomogeneities of the Earth when compared to the vertical component. Therefore, we first estimate time series of inducing coefficients by analysing only horizontal component assuming some prior Earth's background conductivity model. With the time series of inducing coefficients at hand, we determine induced coefficients by using radial component only. [ABSTRACT FROM AUTHOR]

The Hangai is an intra-continental mountain range in central Mongolia with unknown orogenesis. Previous seismic and gravitational studies revealed a low velocity/low density anomaly, but the understanding of the uplift process remains vague. Instead, detailed 2-D and 3-D conductivity models beneath the Hangai and surrounding areas can facilitate the understanding of the Hangai Mountain uplift. To obtain such models, we conducted a magnetotelluric survey in the Hangai region. During three field campaigns (2016-2018) a total of 328 stations were installed on a regular 50 x 50 km grid and along several profiles with a finer spacing. The grid covers a total area of 360 x 700 km, including the Hangai Dome, its surroundings and a part of the Gobi-Altai mountain range. The estimated transfer functions (impedance, tipper, and phase tensor, as well as intersite impedance/phase tensor) cover a wide frequency range (from 0.008s to 3000s at most and up to 16000s at some stations) and are of high quality due to low electromagnetic noise, although affected by galvanic distortions. We employ a 3-D FEM code (GoFEM) to obtain an image of the conductivity structure below the survey area. Locally refined unstructured meshes are used to ensure numerical accuracy with a sufficiently fine discretisation of the inversion domain, while keeping the computational cost feasible, and also allow for static shift correction. Models obtained by an inversion of the impedance tensor resolve the subsurface down to the Lithosphere-Asthenosphere boundary (LAB). The models show a strong subdivision, the northern part with the Hangai Dome is characterized by a predominantly layered structure and a shallow LAB, whereas the Gobi-Altai in the south is laterally more heterogeneous with a deeper LAB. The transition is rather abrupt and follows the previously known South Hangai Fault Zone. Additionally, we imaged two large anomalous vertical conductors in the lithosphere, which are likely related to the uplift process. [ABSTRACT FROM AUTHOR]