Abstract The lithospheric conductivity in the westernmost Fennoscandia has been studied using magnetotelluric (MT) data. The western margin of Fennoscandia was significantly affected in Paleozoic by the Caledonian orogeny and later by the rifting of Laurentia and the opening of the Atlantic Ocean c. 80 Ma ago. Magnetotelluric studies have been carried out in two target areas in southern Norway and in western Fennoscandia. The first study resulted in 2-D geoelectric models of two profiles stretching from Oslo to the Norwegian coast. The interpretation suggests that the basement is in general very resistive with a few conductive upper crustal layers, representing the alum shales, and middle crustal conductors possibly imaging the remnants of the closed ocean basins. A more extensive MT study was performed within the project "Magnetotellurics in the Scandes". Measurements were carried in summers of 2011 to 2013, resulting in an array of 279 MT sites. The data allowed us to derive 2-D geoelectric models for the crust and upper mantle as well as 3-D models for the crust. The inversions revealed a resistive upper crust and a conductive lower crust, two upper crustal conductors in the Skellefteå and Kittilä districts, highly conducting alum shales in the Caledonides and a conductive upper crust beneath the Lofoten peninsula. The thickness of the lithosphere is around 200 km in the north and 300 km in the south-west. The Palaeoproterozoic lithosphere is the thickest, not the Archaean, on contrary to a generally accepted hypothesis. A better image of the lithosphere will help to evaluate the proposed mechanisms of the exhumation of the Scandinavian Mountains. The theoretical part of this study is the development of a new multi-resolution approach to 3-D electromagnetic (EM) modelling. Three-dimensional modelling of MT data requires enormous computational resources because of the huge number of data and model parameters. The development of the multi-resolution forward solver is based on the fact that a finer grid resolution is often required near the surface. On the other hand, the EM fields propagate in a diffusive manner and can be sufficiently well described on a grid that becomes coarser with depth. Tests showed that the total run time can be reduced by five times and the memory requirements by three times compared with the standard staggered grid forward solver. / Tiivistelmä Olemme tutkineet litosfäärin sähkönjohtavuutta Fennoskandian länsiosassa magnetotelluurisen (MT) menetelmän avulla. Fennoskandian länsireuna muokkautui merkittävästi paleotsooisena aikana Kaledonidien vuorijonopoimutuksessa sekä myöhemmin mesotsooisena aikana Laurentia-mantereen repeytyessä ja Atlantin valtameren syntyessä noin 80 miljoonaa vuotta sitten. MT-tutkimukset tehtiin Etelä-Norjassa ja Fennoskandian luoteisosassa. Ensimmäisessä tutkimuksessa kallioperän sähkönjohtavuutta kuvattiin kaksiulotteisilla (2-D) johtavuusmalleilla, jotka ulottuvat Oslosta Norjan rannikolle. Mallien tulkinta viittaa siihen, että maan kuori on pääosin hyvin eristävä lukuun ottamatta muutamaa kuoren ylä- ja keskiosassa olevaa johdekerrosta. Yläkuoren johteet edustavat alunaliuskeita ja keskikuoren johteet todennäköisesti suljetuissa merialtaissa syntyneitä hiilipitoisia sedimenttikerrostumia. Laajempi MT-tutkimus tehtiin ”Magnetotellurics in the Scandes” -hankkeessa. Mittauksia tehtiin 279 mittauspisteessä kesinä 2011–2013. Saadun aineiston avulla voitiin laatia 2-D inversiomallit kuoresta ja ylävaipasta sekä 3-D inversiomalli kuoresta. Tulosten mukaan täällä kuoren yläosa on eristävä kun taas kuoren alaosa on sähköä hyvin johtava. Edellisen lisäksi malleissa näkyy yläkuoren johtavat muodostumat Skellefteån ja Kittilän alueilla, korkean johtavuuden alunaliuskeet Kaledonidien alueella sekä johde Lofoottien alla. Litosfäärin paksuus on noin 200 km mittausverkon pohjoisosassa ja noin 300 km lounaassa. Tämän mukaan litosfääri on paksuin varhaisproterotsooisen litosfäärin alueella, ei arkeeisen litosfäärin alueella vastoin yleistä hypoteesia. Tutkimuksen teoreettisessa osassa kehitettiin sähkömagneettiseen mallinnukseen uusi monitasoiseen diskretisointiin perustuva menetelmä. MT-aineiston 3-D käänteisongelman ratkaisu ja siihen liittyvä suora mallintaminen vaativat suuren laskennallisen kapasiteetin, koska havaintojen ja mallin kuvaamiseen tarvittavien parametrien määrä on erittäin suuri. Moniresoluutio-algoritmi perustuu siihen, että mallin hienojakoisempaa diskretisointia tarvitaan yleensä lähellä maan pintaa kun taas syvemmälle edettäessä, sähkömagneettisen aallon diffuusin etenemisen vuoksi, malli voi olla karkeampi. Tietokonesimulaatioiden mukaan suoritusaika on viidennes ja muistitarve kolmannes verrattuna tavanomaiseen suoran laskennan ”staggered grid” -diskretisointiin.

The Northern Norrbotten ore district hosts a multitude of Sweden’s mineral deposits including world class deposits such as the Malmberget and Kirunavaara Iron oxide apatite deposits, the Aitik Iron oxide copper gold deposit, and a multitude of smaller deposits. Northern Norrbotten has been shaped by tectonothermal events related to the evolution of the Fennoscandian Shield and is a geologically complex environment. Without extensive rock outcropping and with most drilling localized to known deposits the regional to local scale of mineralization is not fully understood. To better understand the evolution and extent of the mineralization’s cross-disciplinary geosciences must be applied, where geophysical methods allow for interpretations of the deep and non-outcropping subsurface. Common earth modelling is a term describing a joint model derived from all available geoscientific data in an area, where geophysical models provide the framework.This study describes the geophysical modeling of two IOA deposits in Norrbotten, the Malmberget deposit in Gällivare and the Per-Geijer deposit in Kiruna. To better put these two deposits into a semi-regional setting magnetotelluric (MT) measurements have been conducted together with LKAB. LTU and LKAB have measured more than 200 MT stations in the two areas from 2016-2023. These measurements have then been robustly processed into magnetic transfer functions (impedances) for the broadband MT frequency spectrum (1000Hz,1000s). Then, all processed data judged to be of sufficient quality have been used for 3D inversion modelling using the ModEM code. The resulting conductivity/resistivity models reveals the local conductivity structure of the area, believed to be closely tied to the mineralization due to the conductive properties of the iron bearing minerals. Both areas yielded believable models which pinpointed known mineralization’s at surface as conductive anomalies and their connections to deeper regional anomalies.During modelling a robust iteratively re-weighted least square (IRLS) scheme has been implemented in the inversion algorithms. This scheme allows for objective re-weighting of data errors based on the ability for a given model discretization to predict individual datums. This, to better identify measurements which have been contaminated by local electromagnetic noise due to anthropogenic sources (mainly the power grid and railway). Due to the mathematical properties of the scheme, it allows for models which minimizes the L1 data error-norm instead of usual L2 minimization. This has yielded models whit sharper contrasts in resistivity and successfully emphasizes data believed to be reliable. Results indicate that the scheme was implemented successfully and the tradeoffs in data-fit are deemed acceptable.In addition, in the Kiruna study potential field data (magnetic total field and gravimetry) have been 3D modelled for the same area. These data sets have been inversion modelled in 3D using the MR3D-code developed at LTU with partners. Resulting 3D models have then been interpreted collectively both traditionally and with the use of machine learning methods. To guide interpretations more than 100 rock samples have been collected in the area and their petrophysical properties (density, magnetic susceptibility, electrical resistivity) have been measured at LTU. These petrophysical properties have been used to guide the machine learning methods for the 3D models by first using K-mean clustering on normalized petrophysical data and then using the resulting centroid vectors as input for a Gaussian mixture model of the similarly normalized 3D models. Resulting clusters show potential in being able to pick up sharp geological boundaries but expectedly is unable to fully capture geological structures one to one.

Nesta tese, dados gravimétricos terrestres e de satélite foram combinados revelando que as bordas oeste e sul da Bacia do Paraná são caracterizadas por um forte gradiente que se estende por 2000 km, desde o cráton Rio Apa até a margem continental Atlântica na latitude do Sinclinal de Torres. Enquanto a Bacia do Paraná é caracterizada por anomalias Bouguer negativas (~-80 mGal), os crátons Rio de la Plata, Rio Tebicuary e Rio Apa e a Bacia do Chaco-Paraná são marcados por anomalias Bouguer positivas (~10 mGal). Dados sismológicos e de compensação isostática permitiram correlacionar a variação regional da amplitude das anomalias Bouguer à espessura crustal, de ~40 km na Bacia do Paraná para 30-35 km nos crátons. Essas observações geofísicas e a ocorrência de granitos cálcio-alcalinos de idade Neoproterozoica-Cambriana ao longo do gradiente gravimétrico indicam um ambiente tectônico de colisão e zona de subducção. A essa descontinuidade de escala litosférica denominamos Zona de Sutura do Oeste do Paraná (WPS Western Paraná Suture shear/zone). Dois perfis magnetotelúricos (MT) foram coletados para estudar a natureza e a estrutura elétrica da crosta e do manto litosférico através da WPS. O primeiro perfil se estende por 830 km desde o cráton Rio de la Plata, no Uruguai, até a parte sul da Bacia do Paraná. Modelagem inversa 2-D desses dados mostra que o manto superior no cráton Rio de la Plata é bastante resistivo (~2000 m) até 250 km de profundidade, enquanto o manto superior na Bacia do Paraná é geralmente mais condutivo e heterogêneo. Com base numa descontinuidade lateral de escala litosférica bem definida no modelo de resistividade, o limite nordeste do cráton Rio de la Plata é redefinido no norte do bloco Valentines. O segundo perfil se estende por 450 km na Argentina, entre o cráton Rio Tebicuary e a Bacia do Paraná. No modelo MT o cráton Rio Tebicuary é caracterizado por um manto superior resistivo (2000 m) até 150 km de profundidade. A litosfera na Bacia do Paraná é menos resistiva (~500 m) e provavelmente menos espessa (~80 km). Um perfil MT entre o cráton Rio Apa e a Bacia do Paraná mostra estrutura geoelétrica similar. As estruturas elétricas observadas, juntamente com dados geocronológicos, geoquímicos, sismológicos e densidade, sugerem processos de refertilização na litosfera da Bacia do Paraná. Sucessões de anomalias condutivas em antigas zonas de sutura e resistivas em blocos e terrenos juvenis nos modelos geoelétricos, integradas a dados geológicos, indicam um processo de acresção horizontal e uma progressão de subducções de placas litosféricas oceânicas, sendo a mais jovem sob a litosfera continental da Bacia do Paraná. Os resultados obtidos mostram que a WPS é uma descontinuidade litosférica de primeira ordem que marca o fechamento de um oceano durante os estágios finais da formação do Gondwana Sul-Ocidental no Neoproterozoico-Cambriano. / In this thesis, terrestrial and satellite gravity data were integrated revealing a steep gravity gradient at the western and southern borders of the Paraná Basin. This gradient extends for 2,000 km from the Rio Apa craton to the Brazilian Atlantic margin at Torres Syncline latitude. Negative Bouguer anomalies (~-80 mGal) occur over the Paraná Basin, whereas positive anomalies are observed at Rio de la Plata, Rio Tebicuary and Rio Apa cratons, as well as Chaco-Paraná Basin. Seismological data and isostasy correlate the gravity gradient with crustal thickness variation, being thicker in the Paraná Basin (~40 km) and shallower in the cratons (~35 km). These geophysical observations and the presence of Neoproterozoic calc-alkaline granites along the gravity gradient suggest a collisional and subduction tectonic setting. This lithospheric discontinuity is hereafter referred to as Western Paraná Suture/shear zone (WPS). Two magnetotelluric (MT) profiles perpendicular to WPS were set up to study the electrical structure and nature of the crust and lithospheric mantle across the suture zone. The first profile, 830 km long, extends northward from Rio de la Plata craton, in Uruguay, to Paraná Basin southern border. 2-D inversion of this MT profile shows that the Rio de la Plata craton upper mantle is highly resistive (~2000 m) down to 250 km depth, whereas the Paraná Basin lithosphere is conductive and heterogeneous. Based on a lithospheric-scale lateral discontinuity in the resistivity model, the Rio de la Plata craton northern limit is redefined to the Valentines block northern limit. The second profile is 450 km long and extends from Rio Tebicuary craton to the Paraná Basin, and all stations are in Argentina. The MT model shows that Rio Tebicuary craton is characterized by a resistive lithosphere (2000 m) down to 150 km depth. The Paraná Basin lithosphere is less resistive (~500 m) and probably thinner (~80 km). Previous MT study between the Rio Apa craton and the Paraná basin, to the north, shows a similar electrical structure. These electrical characteristics, integrated with geochronological, geochemical, seismological and density data, suggest that Paraná Basin lithosphere underwent refertilization episodes. In the geoelectrical models, a series of resistive blocks and juvenile terrains and conductive anomalies in suture zone relics, integrated with geological data, suggest a horizontal accretionary process by means of progressive oceanic lithospheres subductions, the youngest one occurring below the Paraná Basin continental lithosphere. Altogether, these results show that the WPS is a first order lithosphere discontinuity, a site of an ocean closure during the South-Western Gondwana late stages of amalgamation in Neoproterozoic/Cambrian times.

Nesta tese, dados gravimétricos terrestres e de satélite foram combinados revelando que as bordas oeste e sul da Bacia do Paraná são caracterizadas por um forte gradiente que se estende por 2000 km, desde o cráton Rio Apa até a margem continental Atlântica na latitude do Sinclinal de Torres. Enquanto a Bacia do Paraná é caracterizada por anomalias Bouguer negativas (~-80 mGal), os crátons Rio de la Plata, Rio Tebicuary e Rio Apa e a Bacia do Chaco-Paraná são marcados por anomalias Bouguer positivas (~10 mGal). Dados sismológicos e de compensação isostática permitiram correlacionar a variação regional da amplitude das anomalias Bouguer à espessura crustal, de ~40 km na Bacia do Paraná para 30-35 km nos crátons. Essas observações geofísicas e a ocorrência de granitos cálcio-alcalinos de idade Neoproterozoica-Cambriana ao longo do gradiente gravimétrico indicam um ambiente tectônico de colisão e zona de subducção. A essa descontinuidade de escala litosférica denominamos Zona de Sutura do Oeste do Paraná (WPS Western Paraná Suture shear/zone). Dois perfis magnetotelúricos (MT) foram coletados para estudar a natureza e a estrutura elétrica da crosta e do manto litosférico através da WPS. O primeiro perfil se estende por 830 km desde o cráton Rio de la Plata, no Uruguai, até a parte sul da Bacia do Paraná. Modelagem inversa 2-D desses dados mostra que o manto superior no cráton Rio de la Plata é bastante resistivo (~2000 m) até 250 km de profundidade, enquanto o manto superior na Bacia do Paraná é geralmente mais condutivo e heterogêneo. Com base numa descontinuidade lateral de escala litosférica bem definida no modelo de resistividade, o limite nordeste do cráton Rio de la Plata é redefinido no norte do bloco Valentines. O segundo perfil se estende por 450 km na Argentina, entre o cráton Rio Tebicuary e a Bacia do Paraná. No modelo MT o cráton Rio Tebicuary é caracterizado por um manto superior resistivo (2000 m) até 150 km de profundidade. A litosfera na Bacia do Paraná é menos resistiva (~500 m) e provavelmente menos espessa (~80 km). Um perfil MT entre o cráton Rio Apa e a Bacia do Paraná mostra estrutura geoelétrica similar. As estruturas elétricas observadas, juntamente com dados geocronológicos, geoquímicos, sismológicos e densidade, sugerem processos de refertilização na litosfera da Bacia do Paraná. Sucessões de anomalias condutivas em antigas zonas de sutura e resistivas em blocos e terrenos juvenis nos modelos geoelétricos, integradas a dados geológicos, indicam um processo de acresção horizontal e uma progressão de subducções de placas litosféricas oceânicas, sendo a mais jovem sob a litosfera continental da Bacia do Paraná. Os resultados obtidos mostram que a WPS é uma descontinuidade litosférica de primeira ordem que marca o fechamento de um oceano durante os estágios finais da formação do Gondwana Sul-Ocidental no Neoproterozoico-Cambriano. / In this thesis, terrestrial and satellite gravity data were integrated revealing a steep gravity gradient at the western and southern borders of the Paraná Basin. This gradient extends for 2,000 km from the Rio Apa craton to the Brazilian Atlantic margin at Torres Syncline latitude. Negative Bouguer anomalies (~-80 mGal) occur over the Paraná Basin, whereas positive anomalies are observed at Rio de la Plata, Rio Tebicuary and Rio Apa cratons, as well as Chaco-Paraná Basin. Seismological data and isostasy correlate the gravity gradient with crustal thickness variation, being thicker in the Paraná Basin (~40 km) and shallower in the cratons (~35 km). These geophysical observations and the presence of Neoproterozoic calc-alkaline granites along the gravity gradient suggest a collisional and subduction tectonic setting. This lithospheric discontinuity is hereafter referred to as Western Paraná Suture/shear zone (WPS). Two magnetotelluric (MT) profiles perpendicular to WPS were set up to study the electrical structure and nature of the crust and lithospheric mantle across the suture zone. The first profile, 830 km long, extends northward from Rio de la Plata craton, in Uruguay, to Paraná Basin southern border. 2-D inversion of this MT profile shows that the Rio de la Plata craton upper mantle is highly resistive (~2000 m) down to 250 km depth, whereas the Paraná Basin lithosphere is conductive and heterogeneous. Based on a lithospheric-scale lateral discontinuity in the resistivity model, the Rio de la Plata craton northern limit is redefined to the Valentines block northern limit. The second profile is 450 km long and extends from Rio Tebicuary craton to the Paraná Basin, and all stations are in Argentina. The MT model shows that Rio Tebicuary craton is characterized by a resistive lithosphere (2000 m) down to 150 km depth. The Paraná Basin lithosphere is less resistive (~500 m) and probably thinner (~80 km). Previous MT study between the Rio Apa craton and the Paraná basin, to the north, shows a similar electrical structure. These electrical characteristics, integrated with geochronological, geochemical, seismological and density data, suggest that Paraná Basin lithosphere underwent refertilization episodes. In the geoelectrical models, a series of resistive blocks and juvenile terrains and conductive anomalies in suture zone relics, integrated with geological data, suggest a horizontal accretionary process by means of progressive oceanic lithospheres subductions, the youngest one occurring below the Paraná Basin continental lithosphere. Altogether, these results show that the WPS is a first order lithosphere discontinuity, a site of an ocean closure during the South-Western Gondwana late stages of amalgamation in Neoproterozoic/Cambrian times.

Ein transversales Störungssystem im Nahen Osten, die Dead Sea Transform (DST), trennt die Arabische Platte von der Sinai-Mikroplatte und erstreckt sich von Süden nach Norden vom Extensionsgebiet im Roten Meer über das Tote Meer bis zur Taurus-Zagros Kollisionszone. Die sinistrale DST bildete sich im Miozän vor etwa 17 Ma und steht mit dem Aufbrechen des Afro-Arabischen Kontinents in Verbindung. Das Untersuchungsgebiet liegt im Arava Tal zwischen Totem und Rotem Meer, mittig über der Arava Störung (Arava Fault, AF), die hier den Hauptast der DST bildet.<br /> <br /> Eine Reihe seismischer Experimente, aufgebaut aus künstlichen Quellen, linearen Profilen über die Störung und entsprechend entworfenen Empfänger-Arrays, zeigt die Untergrundstruktur in der Umgebung der AF und der Verwerfungszone selbst bis in eine Tiefe von 3-4 km. Ein tomographisch bestimmtes Modell der seismischen Geschwindigkeiten von P-Wellen zeigt einen starken Kontrast nahe der AF mit niedrigeren Geschwindigkeiten auf der westlichen Seite als im Osten. Scherwellen lokaler Erdbeben liefern ein mittleres P-zu-S Geschwindigkeitsverhältnis und es gibt Anzeichen für Änderungen über die Störung hinweg. Hoch aufgelöste tomographische Geschwindigkeitsmodelle bestätigen der Verlauf der AF und stimmen gut mit der Oberflächengeologie überein. <br /> <br /> Modelle des elektrischen Widerstands aus magnetotellurischen Messungen im selben Gebiet zeigen eine leitfähige Schicht westlich der AF, schlecht leitendes Material östlich davon und einen starken Kontrast nahe der AF, die den Fluss von Fluiden von einer Seite zur anderen zu verhindern scheint. Die Korrelation seismischer Geschwindigkeiten und elektrischer Widerstände erlaubt eine Charakterisierung verschiedener Lithologien im Untergrund aus deren physikalischen Eigenschaften. Die westliche Seite lässt sich durch eine geschichtete Struktur beschreiben, wogegen die östliche Seite eher einheitlich erscheint. Die senkrechte Grenze zwischen den westlichen Einheiten und der östlichen scheint gegenüber der Oberflächenausprägung der AF nach Osten verschoben zu sein.<br /> <br /> Eine Modellierung von seismischen Reflexionen an einer Störung deutet an, dass die Grenze zwischen niedrigen und hohen Geschwindigkeiten eher scharf ist, sich aber durch eine raue Oberfläche auf der Längenskala einiger hundert Meter auszeichnen kann, was die Streuung seismischer Wellen begünstigte. Das verwendete Abbildungsverfahren (Migrationsverfahren) für seismische Streukörper basiert auf Array Beamforming und der Kohärenzanalyse P-zu-P gestreuter seismischer Phasen. Eine sorgfältige Bestimmung der Auflösung sichert zuverlässige Abbildungsergebnisse.<br /> <br /> Die niedrigen Geschwindigkeiten im Westen entsprechen der jungen sedimentären Füllung im Arava Tal, und die hohen Geschwindigkeiten stehen mit den dortigen präkambrischen Magmatiten in Verbindung. Eine 7 km lange Zone seismischer Streuung (Reflektor) ist gegenüber der an der Oberfläche sichtbaren AF um 1 km nach Osten verschoben und lässt sich im Tiefenbereich von 1 km bis 4 km abbilden. Dieser Reflektor markiert die Grenze zwischen zwei lithologischen Blöcken, die vermutlich wegen des horizontalen Versatzes entlang der DST nebeneinander zu liegen kamen. Diese Interpretation als lithologische Grenze wird durch die gemeinsame Auswertung der seismischen und magnetotellurischen Modelle gestützt. Die Grenze ist möglicherweise ein Ast der AF, der versetzt gegenüber des heutigen, aktiven Asts verläuft. Der Gesamtversatz der DST könnte räumlich und zeitlich auf diese beiden Äste und möglicherweise auch auf andere Störungen in dem Gebiet verteilt sein. / The Dead Sea Transform (DST) is a prominent shear zone in the Middle East. It separates the Arabian plate from the Sinai microplate and stretches from the Red Sea rift in the south via the Dead Sea to the Taurus-Zagros collision zone in the north. Formed in the Miocene about 17 Ma ago and related to the breakup of the Afro-Arabian continent, the DST accommodates the left-lateral movement between the two plates. The study area is located in the Arava Valley between the Dead Sea and the Red Sea, centered across the Arava Fault (AF), which constitutes the major branch of the transform in this region.<br /> <br /> A set of seismic experiments comprising controlled sources, linear profiles across the fault, and specifically designed receiver arrays reveals the subsurface structure in the vicinity of the AF and of the fault zone itself down to about 3-4 km depth. A tomographically determined seismic P velocity model shows a pronounced velocity contrast near the fault with lower velocities on the western side than east of it. Additionally, S waves from local earthquakes provide an average P-to-S velocity ratio in the study area, and there are indications for a variations across the fault. High-resolution tomographic velocity sections and seismic reflection profiles confirm the surface trace of the AF, and observed features correlate well with fault-related geological observations.<br /> <br /> Coincident electrical resistivity sections from magnetotelluric measurements across the AF show a conductive layer west of the fault, resistive regions east of it, and a marked contrast near the trace of the AF, which seems to act as an impermeable barrier for fluid flow. The correlation of seismic velocities and electrical resistivities lead to a characterisation of subsurface lithologies from their physical properties. Whereas the western side of the fault is characterised by a layered structure, the eastern side is rather uniform. The vertical boundary between the western and the eastern units seems to be offset to the east of the AF surface trace.<br /> <br /> A modelling of fault-zone reflected waves indicates that the boundary between low and high velocities is possibly rather sharp but exhibits a rough surface on the length scale a few hundreds of metres. This gives rise to scattering of seismic waves at this boundary. The imaging (migration) method used is based on array beamforming and coherency analysis of P-to-P scattered seismic phases. Careful assessment of the resolution ensures reliable imaging results.<br /> <br /> The western low velocities correspond to the young sedimentary fill in the Arava Valley, and the high velocities in the east reflect mainly Precambrian igneous rocks. A 7 km long subvertical scattering zone reflector is offset about 1 km east of the AF surface trace and can be imaged from 1 km to about 4 km depth. The reflector marks the boundary between two lithological blocks juxtaposed most probably by displacement along the DST. This interpretation as a lithological boundary is supported by the combined seismic and magnetotelluric analysis. The boundary may be a strand of the AF, which is offset from the current, recently active surface trace. The total slip of the DST may be distributed spatially and in time over these two strands and possibly other faults in the area.

In der vorliegenden Arbeit werden verschiedene Randwertprobleme zur Beschreibung der Ausbreitung magnetotellurischer Felder mit Hilfe der Finite-Elemente-Methode numerisch gelöst. Die zwei- und dreidimensionalen Randwertprobleme zur Simulation des elektrischen oder des magnetischen Feldes, des magnetischen Vektorpotentials und des elektrischen Skalarpotentials, des magnetischen Vektorpotentials allein oder des anomalen magnetischen Vektorpotentials werden aus den Maxwell-Gleichungen hergeleitet. Auf Grundlage von Anwendung der Konvergenztheorie auf die Finite-Elemente-Lösung werden Konvergenzstudien für zweidimensionale Modelle des homogenen und des geschichteten Halbraums sowie für das dreidimensionale COMMEMI 3-D-2-Modell durchgeführt. Diese werden genutzt, um die Randwertprobleme hinsichtlich ihrer Effizienz zu bewerten. Außerdem liefern Konvergenzstudien eine Abschätzung des lokalen Fehlers der numerischen Lösung für ein realitätsnahes Modell des Vulkans Stromboli und seiner Umgebung, welches digitale Geländedaten enthält. / This thesis presents the numerical finite-element solution of different formulations of the magnetotelluric boundary value problem. Based on Maxwell\'s equations, the two-dimensional and three-dimensional boundary value problems are derived in terms of the electric or the magnetic field, the magnetic vector and the electric scalar potential, the magnetic vector potential only, or the anomalous magnetic vector potential. To evaluate their efficiency, convergence studies are performed for the two-dimensional models of the homogeneous and the layered halfspace as well as for the COMMEMI-3-D-2 model. Moreover, convergence studies yield estimates of the local error of the numerical solution for a close-to-reality model of Stromboli volcano incorporating digital terrain data.

No description available.

In der vorliegenden Arbeit werden verschiedene Randwertprobleme zur Beschreibung der Ausbreitung magnetotellurischer Felder mit Hilfe der Finite-Elemente-Methode numerisch gelöst. Die zwei- und dreidimensionalen Randwertprobleme zur Simulation des elektrischen oder des magnetischen Feldes, des magnetischen Vektorpotentials und des elektrischen Skalarpotentials, des magnetischen Vektorpotentials allein oder des anomalen magnetischen Vektorpotentials werden aus den Maxwell-Gleichungen hergeleitet. Auf Grundlage von Anwendung der Konvergenztheorie auf die Finite-Elemente-Lösung werden Konvergenzstudien für zweidimensionale Modelle des homogenen und des geschichteten Halbraums sowie für das dreidimensionale COMMEMI 3-D-2-Modell durchgeführt. Diese werden genutzt, um die Randwertprobleme hinsichtlich ihrer Effizienz zu bewerten. Außerdem liefern Konvergenzstudien eine Abschätzung des lokalen Fehlers der numerischen Lösung für ein realitätsnahes Modell des Vulkans Stromboli und seiner Umgebung, welches digitale Geländedaten enthält. / This thesis presents the numerical finite-element solution of different formulations of the magnetotelluric boundary value problem. Based on Maxwell\'s equations, the two-dimensional and three-dimensional boundary value problems are derived in terms of the electric or the magnetic field, the magnetic vector and the electric scalar potential, the magnetic vector potential only, or the anomalous magnetic vector potential. To evaluate their efficiency, convergence studies are performed for the two-dimensional models of the homogeneous and the layered halfspace as well as for the COMMEMI-3-D-2 model. Moreover, convergence studies yield estimates of the local error of the numerical solution for a close-to-reality model of Stromboli volcano incorporating digital terrain data.

A three-dimensional inversion was implemented for magnetotellurics, which is a passive electromagnetic method in geophysics. It exploits natural electromagnetic fields of the Earth, which function as sources. Their interaction with the conductive parts of the subsurface are registered when components of the electric and the magnetic field are measured and evaluated. The all-at-once approach is an inversion scheme that is relatively new to geophysics. In this approach, the objective function – the basis of each inversion – is called the Lagrangian. It consists of three parts: (i) the data residual norm, (ii) the regularisation part, and (iii) the forward problem. The latter is the significant difference to conventional inversion approaches that are built up of a forward calculation part and an inversion part. In the case of all-at-once, the forward problem is incorporated in the objective function and is therefore already taken into account in each inversion iteration. Thus, an explicit forward calculation is obsolete. As an objective function, the Lagrangian shall reach a minimum and therefore its first and second derivatives are evaluated. Hence, the gradient of the Lagrangian and its Hessian are constituent parts of the KKT system – the Newton-type system that is set up in the all-at-once inversion. Conventional inversion approaches avoid the Hessian because it is a large, dense, not positive definite matrix that is challenging to handle. However, it provides additional information to the inversion, which raises hope for a high quality inversion result. As a first step, the inversion was programmed for the more straightforward one-dimensional magnetotelluric case. This was particularly suitable to become familiar with sQMR – a Krylov subspace method which is essential for the three-dimensional case to be able to work with the Hessian and the resulting KKT system. After the implementation and validation of the one-dimensional forward operator, the Lagrangian and its derivatives were set up to complete the inversion, which successfully solved the KKT system. Accordingly, the three-dimensional forward operator also needed to be implemented and validated, which was done using published data from the 3D-2 COMMEMI model. To realise the inversion, the Lagrangian was assembled and its first and second derivatives were validated with a test that exploits the Taylor expansion. Then, the inversion was initially programmed for the Gauss-Newton approximation where second order information is neglected. Since the system matrix of the Gauss-Newton approximation is positive definite, the solution of this system of equations could be carried out by the conventional solver pcg. Based on that, the complete KKT system (Newton\\\'s method) was set up and preconditioned sQMR solved this system of equations.

No description available.