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Assessing the risk posed by Geomagnetically Induced Currents (GICs) to the regular operation of power grids requires a hazard specification in terms of the induced geoelectric field (GEF). In order to specify the GIC hazard posed to the German high-voltage transmission grid, we model the GEF within Germany for geomagnetically disturbed conditions using magnetic field measurements from INTERMAGNET observatories and a predefined electrical conductivity model of the subsurface as input. This contribution focuses on a comparison of GEFs modeled assuming electromagnetic (EM) induction scenarios of different complexity, which are imposed through the specification of the inducing EM field on the one hand and the dimensionality of the conductivity model on the other. The former is specified either as a plane wave or a laterally varying field obtained by fitting Spherical Elementary Current Systems basis functions to the magnetic field observations. The conductivity distribution is given either by the “EURHOM” model or our new dedicated 3D model for Germany obtained from legacy magnetotelluric data. The latter also includes realistic 3D conductivity variations due to the ocean/sea and marine sediments, which are known to affect magnetotelluric impedance tensors at GIC-relevant frequencies near coastlines. Based on the modeled GEFs, we calculate GICs exemplarily at selected substations and geomagnetic disturbance events. The results indicate the level of complexity needed in the GEF modeling in order to derive meaningful GIC hazard maps for Germany down the line., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

A major source of time-varying magnetic fields are external ionosphere-magnetosphere currents and associated fields induced in subsurface and oceans. Induced fields may bias external and core field models if not accounted for in a physically consistent manner. In addition, induced fields contain unique information on the subsurface conductivity distribution. Yet, induced fields are often considered noise (and neglected) or at best treated peripherally as a nuisance parameter. The outstanding accuracy of Swarm magnetic field data and increasing demand for fast-track magnetic field products has pushed the frontier of the field to a point where sophisticated core and external magnetic field models are hindered by improper modelling of induced fields. We propose a versatile and efficient way of modelling induced fields in ground and satellite measurements, which also enables modelling in near real-time settings as is required by many present Space Weather products. The proposed approach also offers a more consistent way to assimilate geomagnetic data from ground observatories and satellites into physics-based magnetic field models., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

Understanding the geological setting of nonvolcanic geothermal systems is vital to explaining the formation of geothermal reservoirs and their observable surface manifestations. The magnetotelluric method, used to determine the subsurface electrical conductivity distribution, is a common tool in geothermal exploration. In this study, we present an integrated interpretation of an electrical conductivity subsurface model, together with geological analyses and geochemical probes from a nonvolcanic, intermediate-temperature geothermal system in Mongolia. We conducted magnetotelluric (MT) and telluric-magnetotelluric (TMT) measurements at the Tsenkher geothermal area in the Mongolian Khangai dome during the summers of 2019 and 2020. The 20km*20km large area is characterized by three major hot springs with water temperatures up to 87°C. From a total of 196 MT and TMT stations, we obtained a 3-D electrical conductivity model of the subsurface. To interpret the data, we used a high-order finite-element electromagnetic modelling code (GOFEM) with locally refined hexahedral meshes that allows including accurate topography while ensuring high numerical accuracy with a sufficiently fine discretization of the inversion domain. The best-fitting model provides essential insights into the subsurface structure of the Tsenkher geothermal area. The model is characterized by a strong vertical crustal conductor that appears south of the hot springs area and rises from depths of more than 10 km to the surface. We interpret this conductor as a remnant of past local volcanism and a zone of former magma ascent, indicating the potential source for the observed enhanced surface heat flow in the hot springs area around Tsenkher. Additionally, the model includes a prominent striking conductor beneath the hot springs at depths down to more than 3 km below the surface. The conductor is spatially aligned with a major fault that intersects the survey area, and is accompanied by several basaltic dyke intrusions. We interpret the fault-aligned conductor as the major area of deep fluid circulation and an accumulation zone for heated fluids. The interpretation agrees with theoretical concepts of topography-driven deep fluid circulation and local fault zones playing a major role in the transport of hot water from a reservoir to the surface. Inferred reservoir temperatures from geochemical fluid analyses are inagreement with interpretations of the maximum depth of fluid circulation inferred from the MT model. Our MT subsurface model serves to better understand the formation of the Tsenkher hot springs in particular and intermediate-temperature geothermal systems in general, 25th EM Induction Workshop

Intraplate processes, such as continental surface uplift and intraplate volcanism, are enigmatic and the underlying mechanisms responsible are not fully understood. Central Mongolia is an ideal natural laboratory for studying such processes because of its location in the continental interior far from tectonic plate boundaries, its high-elevation plateau, and its widespread, low-volume, basaltic volcanism. The processes responsible for developing this region remain largely unexplained — due in part to a lack of high-resolution geophysical studies — and thus are open questions. A recent project undertaken to map the crust and upper mantle structure of central Mongolia has collected a large magnetotelluric array (~700 km x ~450 km).

Magnetotelluric measurements are a powerful tool to image the subsurface under active volcanic regions. 3-D models, computed from magnetotelluric data, nowadays provide detailed multi-scale images of the electrical conductivity distribution. Since electrical conductivity is predominantly controlled by the presence of melt and fluid phases, conductivity models proved to be highly suitable for mapping the distribution of melt and for constraining melt fractions. Melt fractions can be estimated by combining laboratory models for melt electrical conductivity and mixing laws to derive the bulk electrical conductivity of multiphase systems. Melt electrical conductivity depends on the composition of the melt, the amount of dissolved water as well as temperature and pressure conditions. However, estimates of melt fractions are often based on arbitrary combinations of these parameters, and they do not consider the dependance of melt interconnectedness on melt fraction. Here we present an interdisciplinary approach to interpret electric conductivity models from three volcanoes in the Main Ethiopian Rift. We use rhyolite-MELTS to model magma crystallization and storage conditions constrained by petrological analyses of on-site erupted products. To derive the electrical conductivity of melt during fractional crystallization we derive an expanded melt electrical conductivity model by interpolating between existing models for rhyolite, dacite and andesite melt. Thereby we obtain a generalized model that describes the electrical conductivity of melt in dependence on the SiO2 and H2O content, pressure and temperature. These parameters are given by rhyolite-MELTS. Decreasing melt connectedness with diminishing melt fraction is considered by varying the cementation exponent, m, in the generalized Archie’s law whilst taking into account conservation of connectedness. Furthermore, we describe the magma reservoirs as three-phase systems consisting of crystals, melt and magmatic volatiles. The results show that this approach enables us to constrain the current state of magma reservoirs in terms of melt fraction, temperature and free volatile abundance. The latter is of eminent importance when discriminating between the two major mechanisms that drive volcanic unrest: magma on the move or increased degassing of a crystallizing magmatic system, so-called second boiling. With this study we demonstrate the great capability of the presented interdisciplinary solution approach that combines geophysical observations, petrological probes and laboratory models to capture the current state of volcanoes. The outcome is of major importance when it comes to realistic volcanic hazard assessment and geothermal energy applications that require a detailed understanding of magmatic heat sources that sustain geothermal reservoirs., 25th EM Induction Workshop

Galvanic distortions represent one of the greatest challenges when dealing with magnetotelluric datasets. Several methods exist that try to mitigate the effect of distortions on inversion. One solution to avoid this major issue was provided with the introduction of the phase tensor, a transfer function that is free of galvanic distortion. However, the nature of the phase tensor makes it predominantly sensitive to relative changes of resistivity and its ability to constrain absolute resistivities is still under debate. So far, case studies have shown that phase tensor inversion works effectively if (i) the subsurface resistivity distribution has significant 3-D heterogeneities, (ii) MT site spacing is sufficiently dense, and (iii) data-constrained starting models are employed. There is presently a lack of systematic investigations to what extent phase tensors constrain absolute resistivity values in 3-D subsurface models. To shed light on this discussion we systematically analyse to what degree variations of absolute resistivities influence the fit of phase tensor data. We use a dataset with measurements from 127 MT stations in an area of about 340 km2 covering a volcanic geothermal field in the Main Ethiopian Rift. To ensure the eligibility of the dataset for 3-D phase tensor inversion we introduce a quantitative criterion for “sufficiently” dense station spacing. Using a homogenous starting model derived from the average apparent resistivity we retrieve a model with a good data fit, that acts as a reference model. In a first test the fit of the reference model is compared to models obtained from inversion using arbitrary (i.e. not data-constrained) starting models consisting of homogenous halfspace models of 20, 50, 100 and 1000 Wm. This results in poorer data fit and less geologically plausible models, thereby demonstrating the importance of using starting models that are constrained by data. In a second test we use the reference model and vary the resistivity values using algorithms from image processing such as contrast adjustment and linear stretching. Detailed analysis of the modelled responses and residuals reveals significant changes in the misfit relative to the reference model. We conclude that in a realistic 3-D settings with sufficiently dense MT site spacing phase tensor inversion can be considered as a reliable method to recover true subsurface resistivities. If performed properly, phase tensor inversion is an elegant and straight-forward method to obtain models not affected by galvanic distortion., 25th EM Induction Workshop

Aluto-Langano in the Main Ethiopian Rift Valley is currently the only producing geothermal field in Ethiopia and probably the best studied prospect in the Ethiopian Rift. Geoscientific exploration began in 1973 and led to the siting of an exploration well LA3 on top of the volcanic complex. The well was drilled in 1983 to a depth of 2144m and encountered temperatures of 320°C. Since 1990 Aluto has produced electricity, albeit with interruptions. Currently it is undergoing a major expansion phase with the plan to generate about 70MWe from eight new wells, until now two of them have been drilled successfully. Geophysical exploration at Aluto involved magnetotelluric (MT) soundings, which helped delineate the clay cap atop of the hydrothermal reservoir. However, until now geophysical studies did not succeed in imaging the proposed magmatic heat source that would drive the observed hydrothermal convection. For this study, we inverted 165 of a total of 208 MT stations that were measured over the entire volcanic complex in three independent surveys by the Geological Survey of Ethiopia and ETH Zurich, Switzerland. For the inversion, we used a novel 3-D inverse solver that employs adaptive finite element techniques, which allowed us to accurately model topography and account for varying lateral and vertical resolution. We inverted MT phase tensors. This transfer function is free of galvanic distortions that have long been recognized as an obstacle in MT inversion. Our recovered model shows, for the first time, the entire magmatic-hydrothermal system under the geothermal field. The up-flow of melt is structurally controlled by extensional rift faults and sourced by a lower crustal basaltic mush reservoir. Productive wells were all drilled into a weak fault zone below the clay cap. The productive reservoir is underlain by an electrically conductive upper-crustal feature, which we interpret as a highly crystalline rhyolitic mush zone, acting as the main heat source. Our results demonstrate the importance of a dense MT site distribution and state-of-the-art inversion tools in order to obtain reliable and complete subsurface models of high enthalpy systems below volcanic geothermal prospects.

Experiments in Fluids, 61, ISSN:0723-4864, ISSN:1432-1114

Geophysical Research Abstracts, 21, ISSN:1029-7006, ISSN:1607-7962

Geophysical Journal International, 217 (1), ISSN:0956-540X, ISSN:1365-246X

Geophysical Research Abstracts, 21, ISSN:1029-7006, ISSN:1607-7962

Geophysical Research Abstracts, 20, ISSN:1029-7006, ISSN:1607-7962

The solar quiet (Sq) source morphology changes on a daily basis and becomes disturbed during periods of increased magnetic activity. Therefore, it may be preferable to use single-day magnetic field recordings for the analysis of Sq variations. However, in short recordings, Sq and ocean tidal magnetic signals are often indistinguishable because of the close periods. As a result, the tidal magnetic signals can be erroneously attributed to signals of Sq origin, which can potentially lead to wrong interpretations, especially when small signals, such as those induced by the 3-D heterogeneities in the mantle, are sought. In this work, we quantitatively estimate the effect of ocean tidal signals in daily variations by performing rigorous 3-D modeling and comparing the results with real measurements from ground and sea floor observatories. We found that the vertical magnetic field component, Z, is affected the most such that at some locations the tidal signals explain the majority of the observed daily variation. Further, horizontal tidal magnetic fields at the sea floor are larger in amplitude and exhibit different spatial structures compared to signals estimated at the sea level. We propose a scheme aimed at correcting data for the ocean tidal signals and show that such correction suppresses the tidal signals in the observed field variations., Earth, Planets and Space, 70 (1), ISSN:1343-8832, ISSN:1880-5981

GEOPHYSICS, 79 (2)

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., Geophysical Journal International, 198 (1), ISSN:0956-540X, ISSN:1365-246X

Earth materials can be characterized by their electrical resistivity. Geophysicists use electromagnetic methods to decipher the electrical structure of earth, to determine chemical and physical properties of rocks and to investigate associated dynamic processes within earth. Measured data, typically observed at earth’s surface, cannot be directly converted into a comprehensive image of the subsurface. To achieve this goal geophysicists use mathematical and numerical techniques which require significant computational resources. We discuss application of electromagnetic sounding methods, show depth sections derived from 3D inversion, discuss field configuration simulations and resolution tests, introduce the concept and potential of joint inversion and give an outlook on monitoring to decipher temporal changes of the subsurface.

The main goals of this thesis are: (i) developing a 3D inversion scheme for controlled-source electromagnetic (CSEM) data in frequency-domain using modern computational concepts; (ii) creating a methodology to invert real datasets including those collected using a three-phase transmitter configuration developed within the research group I have been working with. Three- dimensional inversion of non-stationary electromagnetic fields is a challenging task that, given problems of practical interest, can only be handled through using massively parallel platforms. Therefore, I developed a parallel distributed inversion scheme that runs on modern supercomputers and clusters. Since memory that is required to store vectors, matrices and arrays, as well as workload are distributed evenly among processes, good scalability of the numerical scheme is achieved. A number of technical and numerical challenges were addressed in the implementation. First, I use a direct solver for 3D forward modeling. Since direct solvers have not been widely used for 3D inversions, analysis of advantages and drawbacks of this decision from both technical and numerical points of view is presented. Second, in inversion I calculate and store the Jacobian matrix explicitly. Analysis of memory and time complexities shows that, if a direct solver is used for forward modeling, the calculation of the full Jacobian is feasible for a large amount of practical cases. Advantages of this approach are demonstrated in the following chapters. For the first time in 3D CSEM inversion I study the implicit regularization effect resulting from incomplete solutions of linear least- squares problems using Krylov subspace techniques. This study gives an insight into sources of inverse problem instability. Moreover, several explicit stabilizing functionals have been implemented. In addition to well-known smoothing regularization, this work includes minimum-norm and focusing stabilizers. The application of different regularization techniques helps explore the model space and estimate the bias of individual regularization techniques. Finally, the algorithm developed is applied to the land-based CSEM data collected across the Ketzin CO$_2$ storage formation. I start with data preparation and aim to extract a representable subset of data that permits many inversion runs within reasonable computational time and effectively contains most of subsurface information. Then, the design of inversion and forward modeling grids is presented. A proper discretization of the domain has to (i) minimize negative boundary effects, (ii) provide accurate model responses and (iii) be able to adequately capture subsurface structures resolved during inversion. Different regularization techniques, starting models and several approaches to avoid numerical singularities arising in land-based CSEM studies are studied and compared. The preferred model is selected based on overall misfit. I provide the analysis of data fit, resolution and depth penetration for the preferred model. Finally, it is compared with a regional geological model and shows a good agreement with respect to both structure and lithology. The methodology devised in this work can be generally followed when dealing with real CSEM datasets., Hauptziele der vorliegenden Doktorarbeit sind: (i) Entwicklung eines 3D- Inversions-schemas für CSEM-Daten im Frequenzbereich (CSEM: Controlled Source Electromagnetic); (ii) Schaffung einer Methodik für die Arbeit mit realen Datensätzen, darunter auch solchen, die unter Verwendung einer in unserer Forschungsgruppe neu entwickelten Dreiphasen-Transmitterkonfiguration aufgenommen wurden. Die dreidimensionale Inversion nicht stationärer elektromagnetischer Felder ist eine Herausforderung, die angesichts der in Praxis gegebenen Probleme nur mit Einsatz umfangreicher paralleler Plattformen zu bewältigen ist. Daher habe ich ein vollständig parallel verteiltes Inversionsschema entwickelt, das auf modernen Supercomputern und Clustern verwendet werden kann. Da der für Vektoren, Matrizen und Felder benötigter Speicherplatz sowie die Rechnerauslastung gleichmäßig zwischen verschiedenen Prozessen verteilt werden, wird eine gute Skalierbarkeit des numerischen Schemas erreicht. Bei der Implementierung der Inversion war eine Reihe technischer und numerischer Herausforderungen zu meistern. Erstens verwende ich direkte Löser für die 3D-Vorwärts-modellierung. Da diese nicht häufig für 3D-Inversionen eingesetzt werden, habe ich die Vor- und Nachteile dieser Wahl sowohl in technischer als auch in numerischer Hinsicht analysiert. Zweitens berechne und speichere ich bei der Inversion explizit die Jacobi-Matrix. Die Analyse von Speicher- und Zeitbedarf zeigt, dass die Berechnung der voll- ständigen Jacobi-Matrix für eine große Anzahl praktischer Anwendungen durchgeführt werden kann, wenn direkte Löser für 3D-Vorwärtsmodellierung verwendet wurden. Die Vorzüge dieses Ansatzes werden in den folgenden Kapiteln diskutiert. Erstmals bei der 3D-CSEM-Inversion untersuche ich mithilfe des Krylovraum Verfahrens den impliziten Regularisierungseffekt, der sich aus der Unvollständigkeit der Lösungen bei der Methode der linearen kleinsten Quadrate ergibt. Diese Untersuchung beleuchtet die Ursachen der Instabilität von inversen Problemen. Zusätzlich zur bekannten Regularisierung durch Glättung wurden mehrere Stabilisatoren, wie z.B. minimale Norm oder Fokussierung, implementiert und getestet. Die Anwendung unterschiedlicher Regularisierungstechniken ermöglicht eine umfassende Erforschung des Modellraums sowie die Abschätzung der Verzerrung bei den einzelnen Regularisierungstechniken. Schließlich wird der entwickelte Algorithmus auf die CSEM-Daten angewandt, welche über der CO2-Speicherungsformation in Ketzin aufgenommen wurden. Beginnend mit der Aufbereitung der Daten ist das Ziel eine repräsentative Teilmenge der Daten auszuwählen, welche eine Vielzahl von Inversionsdurchläufen in einer angemessenen Zeit erlaubt und dabei die Mehrzahl der Untergrundinformationen enthält. Danach wird das Design der Inversion und des Modelgrids vorgestellt. Eine saubere Diskretisierung des Inversionsbereichs muss (i) negative Randeffekte minimieren, (ii) genaue Modelantworten liefern und (iii) in der Lage sein, die durch Inversion aufgelöste Untergrundstrukturen ausreichend zu erfassen. Weiterhin werden unterschiedliche Regularisierungstechniken und Ausgangsmodelle sowie verschiedene Ansätze zur Vermeidung von numerischen Singularitäten untersucht, die für landbasierte CSEM-Studien typisch sind. Das bevorzugte Model wird anhand des Gesamt-Misfits ausgewählt und durch Analyse der Datenanpassung, Auflösung und Eindringtiefe überprüft. Schließlich wird das Model mit dem regionalen geologischen Modell verglichen, mit dem es in Bezug auf die Struktur wie auch Lithologie eine gute Übereinstimmung zeigt. Die in dieser Arbeit entwickelte Inversionsmethodik ist nicht nur für den untersuchten Datensatz gültig, sondern kann allgemein für die Auswertung der landbasierten CSEM-Daten eingesetzt werden.