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.

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.

In this report, the effect of external torque injection of a particular phase and frequency was analyzed using an induction motor assembly consisting of a prototype of an induction motor and a flexible mounting arrangement. The eigenfrequencies of the several components that make up the construction of the induction machine assembly are found out both by analytical and FEM methods. The electromagnetics of the Induction machine is simulated utilizing COMSOL Finite Element Analysis (FEA) software. The single direction coupling is set up to synchronize the parameters between the Rotating Machinery, Magnetic (RMM) and Multi Body Dynamics (MBD) models in COMSOL. / I denna rapport analyserades effekten av extern momentinsprutning av särskild fas och frekvens med hjälp av en induktionsmotor som består av en prototyp av induktionsmotor och ett flexibelt monteringsarrangemang. Egenfrekvenserna för de flera komponenterna som utgör konstruktionen av induktions maskin aggregatet upptäcks både med analytiska metoder och metoder. Induktions maskinens elektromagnetik simuleras med COMSOL FEA programvara. En enkelriktad koppling är konfigurerad för att synkronisera parametrarna mellan RMM och MBD modellerna i COMSOL.

The mitigation of greenhouse gases, like CO2 is a challenging aspect for our society. A strategy to hamper the constant emission of CO2 is utilizing carbon capture and storage technologies. CO2 is sequestrated in subsurface reservoirs. However, these reservoirs harbor the risk of leakage and appropriate geophysical monitoring methods are needed. A crucial aspect of monitoring is the assignment of measured data to certain events occurring. Especially if changes in the measured data are small, suitable statistical methods are needed. In this thesis, a new statistical workflow based on cluster analysis is proposed to detect similar transient electromagnetic signals. The similarity criteria dynamic time warping, the autoregressive distance, and the normalized root-mean-square distance are investigated and evaluated with respect to the classic Euclidean norm. The optimal number of clusters is determined using the gap statistic and visualized with multidimensional scaling. To validate the clustering results, silhouette values are used. The statistical workflow is applied to a synthetic data set, a long-term monitoring data set and a repeat measurement at a pilot CO2-sequestration site in Brooks, Alberta.

Geophysical methods are essential for exploration and monitoring of subsurface formations, e.g. in carbon dioxide sequestration or enhanced geothermal energy. One of the keys to their successful application is the knowledge of how the measured physical quantities are related to the desired reservoir parameters. The work presented in this thesis shows that the presence of carbon dioxide (CO2) in pore space gives rise to multiple processes all of which contribute to the electrical rock conductivity variation. Basically, three mechanisms take place: (1) CO2 partially replaces the pore water, which is equivalent to a decrease in water saturation. (2) CO2 chemically interacts with the pore water by dissolution and dissociation. These processes change both the chemical composition and the pH of the pore filling fluid. (3) The low-pH environment can give rise to mineral dissolution and/or precipitation processes and changes the properties of the grain-water interface. Investigations on the pore water phase show that the reactive nature of CO2 in all physical states significantly acts on the electrical conductivity of saline pore waters. The physico-chemical interaction appears in different manifestations depending mainly on the pore water composition (salinity, ion types) but also on both temperature and pressure. The complex behaviour includes a low- and a high-salinity regime originating from the conductivity increasing effect of CO2 dissociation, which is opposed by the conductivity decreasing effect of reduced ion activity caused by the enhanced mutual impediment of all solutes. These results are fundamental since the properties of the water phase significantly act on all conduction mechanisms in porous media. In order to predict the variation of pore water conductivity, both a semi-analytical formulation and an empirical relationship for correcting the pore water conductivity, which depends on salinity, pressure and temperature, are derived. The central part of the laboratory experiments covers the spectral complex conductivity of water-bearing sand during exposure to and flow-through by CO2 at pressures up to 30MPa and temperatures up to 80°C. It is shown that the impact of CO2 on the real part of conductivity of a clean quartz sand is dominated by the low- and high-salinity regime of the pore water. The obtained data further show that chemical interaction causes a reduction of interface conductivity, which could be related to the low pH in the acidic environment. This effect is described by a correction term, which is a constant value as a first approximation. When the impact of CO2 is taken into account, a correct reconstruction of fluid saturation from electrical measurements is possible. In addition, changes of the inner surface area, which are related to mineral dissolution or precipitation processes, can be quantified. Both the knowledge gained from the laboratory experiments and a new workflow for the description and incorporation of geological geometry models enable realistic finite element simulations. Those were conducted for three different electromagnetic methods applied in the geological scenario of a fictitious carbon dioxide sequestration site. The results show that electromagnetic methods can play an important role in monitoring CO2 sequestration. Compared to other geophysical methods, electromagnetic techniques are generally very sensitive to pore fluids. The proper configuration of sources and receivers for a suitable electromagnetic method that generates the appropriate current systems is essential. Its reactive nature causes CO2 to interact with a water-bearing porous rock in a much more complex manner than non-reactive gases. Without knowledge of the specific interactions between CO2 and rock, a determination of saturation and, consequently, a successful monitoring are possible only to a limited extend. The presented work provides fundamental laboratory investigations for the understanding of the electrical properties of rocks when the reactive gas CO2 enters the rock-water system. All laboratory results are put in the context of potential monitoring applications. The transfer from petrophysical investigations to the planning of an operational monitoring design by means of close-to-reality 3D FE simulations is accomplished.

The objective of our studies is the combination of electromagnetic and direct current (DC) resistivity methods in a joint inversion approach to improve the reconstruction of a given conductivity distribution. We utilize the distinct sensitivity patterns of different methods to enhance the overall resolution power and ensure a more reliable imaging result. In order to simplify the work with more than one electromagnetic method and establish a flexible and state-of-the-art software basis, we developed new DC resistivity and electromagnetic forward modeling and inversion codes based on finite elements of second order on unstructured grids. The forward operators are verified using analytical solutions and convergence studies before we apply a regularized Gauss-Newton scheme and successfully invert synthetic data sets. Finally, we link both codes with each other in a joint inversion. In contrast to most widely used joint inversion strategies, where different data sets are combined in a single least-squares problem resulting in a large system of equations, we introduce a sequential approach that cycles through the different methods iteratively. This way, we avoid several difficulties such as the determination of the full set of regularization parameters or a weighting of the distinct data sets. The sequential approach makes use of a smoothness regularization operator which penalizes the deviation of the model parameters from a given reference model. In our sequential strategy, we use the result of the preceding individual inversion scheme as reference model for the following one. We successfully apply this approach to synthetic data sets and show that the combination of at least two methods yields a significantly improved parameter model compared to the individual inversion results. / Ziel der vorliegenden Arbeit ist die gemeinsame Inversion (\"joint inversion\") elektromagnetischer und geoelektrischer Daten zur Verbesserung des rekonstruierten Leitfähigkeitsmodells. Dabei nutzen wir die verschiedenartigen Sensitivitäten der Methoden aus, um die Auflösung zu erhöhen und ein zuverlässigeres Ergebnis zu erhalten. Um die Arbeit mit mehr als einer Methode zu vereinfachen und eine flexible Softwarebasis auf dem neuesten Stand der Forschung zu etablieren, wurden zwei Codes zur Modellierung und Inversion geoelektrischer als auch elektromagnetischer Daten neu entwickelt, die mit finiten Elementen zweiter Ordnung auf unstrukturierten Gittern arbeiten. Die Vorwärtsoperatoren werden mithilfe analytischer Lösungen und Konvergenzstudien verifiziert, bevor wir ein regularisiertes Gauß-Newton-Verfahren zur Inversion synthetischer Datensätze anwenden. Im Gegensatz zur meistgenutzten \"joint inversion\"-Strategie, bei der verschiedene Daten in einem einzigen Minimierungsproblem kombiniert werden, was in einem großen Gleichungssystem resultiert, stellen wir schließlich einen sequentiellen Ansatz vor, der zyklisch durch die einzelnen Methoden iteriert. So vermeiden wir u.a. eine komplizierte Wichtung der verschiedenen Daten und die Bestimmung aller Regularisierungsparameter in einem Schritt. Der sequentielle Ansatz wird über die Anwendung einer Glättungsregularisierung umgesetzt, bei der die Abweichung der Modellparameter zu einem gegebenen Referenzmodell bestraft wird. Wir nutzen das Ergebnis der vorangegangenen Einzelinversion als Referenzmodell für die folgende Inversion. Der Ansatz wird erfolgreich auf synthetische Datensätze angewendet und wir zeigen, dass die Kombination von mehreren Methoden eine erhebliche Verbesserung des Inversionsergebnisses im Vergleich zu den Einzelinversionen liefert.

Geophysical methods are essential for exploration and monitoring of subsurface formations, e.g. in carbon dioxide sequestration or enhanced geothermal energy. One of the keys to their successful application is the knowledge of how the measured physical quantities are related to the desired reservoir parameters. The work presented in this thesis shows that the presence of carbon dioxide (CO2) in pore space gives rise to multiple processes all of which contribute to the electrical rock conductivity variation. Basically, three mechanisms take place: (1) CO2 partially replaces the pore water, which is equivalent to a decrease in water saturation. (2) CO2 chemically interacts with the pore water by dissolution and dissociation. These processes change both the chemical composition and the pH of the pore filling fluid. (3) The low-pH environment can give rise to mineral dissolution and/or precipitation processes and changes the properties of the grain-water interface. Investigations on the pore water phase show that the reactive nature of CO2 in all physical states significantly acts on the electrical conductivity of saline pore waters. The physico-chemical interaction appears in different manifestations depending mainly on the pore water composition (salinity, ion types) but also on both temperature and pressure. The complex behaviour includes a low- and a high-salinity regime originating from the conductivity increasing effect of CO2 dissociation, which is opposed by the conductivity decreasing effect of reduced ion activity caused by the enhanced mutual impediment of all solutes. These results are fundamental since the properties of the water phase significantly act on all conduction mechanisms in porous media. In order to predict the variation of pore water conductivity, both a semi-analytical formulation and an empirical relationship for correcting the pore water conductivity, which depends on salinity, pressure and temperature, are derived. The central part of the laboratory experiments covers the spectral complex conductivity of water-bearing sand during exposure to and flow-through by CO2 at pressures up to 30MPa and temperatures up to 80°C. It is shown that the impact of CO2 on the real part of conductivity of a clean quartz sand is dominated by the low- and high-salinity regime of the pore water. The obtained data further show that chemical interaction causes a reduction of interface conductivity, which could be related to the low pH in the acidic environment. This effect is described by a correction term, which is a constant value as a first approximation. When the impact of CO2 is taken into account, a correct reconstruction of fluid saturation from electrical measurements is possible. In addition, changes of the inner surface area, which are related to mineral dissolution or precipitation processes, can be quantified. Both the knowledge gained from the laboratory experiments and a new workflow for the description and incorporation of geological geometry models enable realistic finite element simulations. Those were conducted for three different electromagnetic methods applied in the geological scenario of a fictitious carbon dioxide sequestration site. The results show that electromagnetic methods can play an important role in monitoring CO2 sequestration. Compared to other geophysical methods, electromagnetic techniques are generally very sensitive to pore fluids. The proper configuration of sources and receivers for a suitable electromagnetic method that generates the appropriate current systems is essential. Its reactive nature causes CO2 to interact with a water-bearing porous rock in a much more complex manner than non-reactive gases. Without knowledge of the specific interactions between CO2 and rock, a determination of saturation and, consequently, a successful monitoring are possible only to a limited extend. The presented work provides fundamental laboratory investigations for the understanding of the electrical properties of rocks when the reactive gas CO2 enters the rock-water system. All laboratory results are put in the context of potential monitoring applications. The transfer from petrophysical investigations to the planning of an operational monitoring design by means of close-to-reality 3D FE simulations is accomplished.

The objective of our studies is the combination of electromagnetic and direct current (DC) resistivity methods in a joint inversion approach to improve the reconstruction of a given conductivity distribution. We utilize the distinct sensitivity patterns of different methods to enhance the overall resolution power and ensure a more reliable imaging result. In order to simplify the work with more than one electromagnetic method and establish a flexible and state-of-the-art software basis, we developed new DC resistivity and electromagnetic forward modeling and inversion codes based on finite elements of second order on unstructured grids. The forward operators are verified using analytical solutions and convergence studies before we apply a regularized Gauss-Newton scheme and successfully invert synthetic data sets. Finally, we link both codes with each other in a joint inversion. In contrast to most widely used joint inversion strategies, where different data sets are combined in a single least-squares problem resulting in a large system of equations, we introduce a sequential approach that cycles through the different methods iteratively. This way, we avoid several difficulties such as the determination of the full set of regularization parameters or a weighting of the distinct data sets. The sequential approach makes use of a smoothness regularization operator which penalizes the deviation of the model parameters from a given reference model. In our sequential strategy, we use the result of the preceding individual inversion scheme as reference model for the following one. We successfully apply this approach to synthetic data sets and show that the combination of at least two methods yields a significantly improved parameter model compared to the individual inversion results. / Ziel der vorliegenden Arbeit ist die gemeinsame Inversion (\"joint inversion\") elektromagnetischer und geoelektrischer Daten zur Verbesserung des rekonstruierten Leitfähigkeitsmodells. Dabei nutzen wir die verschiedenartigen Sensitivitäten der Methoden aus, um die Auflösung zu erhöhen und ein zuverlässigeres Ergebnis zu erhalten. Um die Arbeit mit mehr als einer Methode zu vereinfachen und eine flexible Softwarebasis auf dem neuesten Stand der Forschung zu etablieren, wurden zwei Codes zur Modellierung und Inversion geoelektrischer als auch elektromagnetischer Daten neu entwickelt, die mit finiten Elementen zweiter Ordnung auf unstrukturierten Gittern arbeiten. Die Vorwärtsoperatoren werden mithilfe analytischer Lösungen und Konvergenzstudien verifiziert, bevor wir ein regularisiertes Gauß-Newton-Verfahren zur Inversion synthetischer Datensätze anwenden. Im Gegensatz zur meistgenutzten \"joint inversion\"-Strategie, bei der verschiedene Daten in einem einzigen Minimierungsproblem kombiniert werden, was in einem großen Gleichungssystem resultiert, stellen wir schließlich einen sequentiellen Ansatz vor, der zyklisch durch die einzelnen Methoden iteriert. So vermeiden wir u.a. eine komplizierte Wichtung der verschiedenen Daten und die Bestimmung aller Regularisierungsparameter in einem Schritt. Der sequentielle Ansatz wird über die Anwendung einer Glättungsregularisierung umgesetzt, bei der die Abweichung der Modellparameter zu einem gegebenen Referenzmodell bestraft wird. Wir nutzen das Ergebnis der vorangegangenen Einzelinversion als Referenzmodell für die folgende Inversion. Der Ansatz wird erfolgreich auf synthetische Datensätze angewendet und wir zeigen, dass die Kombination von mehreren Methoden eine erhebliche Verbesserung des Inversionsergebnisses im Vergleich zu den Einzelinversionen liefert.