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.

In an effort to improve the accuracy of common 1-D analysis for frequency domain helicopter-borne electromagnetic data at reasonable computing costs, a 3-D inversion approach is developed. The strategy is based on the prior localization of an entire helicopter-borne electromagnetic survey to parts which are actually affected by expected local 3-D anomalies and a separate inversion of those sections of the surveys (cut-&-paste strategy). The discrete forward problem, adapted from the complete Helmholtz equation, is formulated in terms of the secondary electric field employing the finite difference method. The analytical primary field calculation incorporates an interpolation strategy that allows to effectively handle the enormous number of transmitters. For solving the inverse problem, a straightforward Gauss-Newton method and a Tikhonov-type regularization scheme are applied. In addition, different strategies for the restriction of the domain where the inverse problem is solved are used as an implicit regularization. The derived linear least squares problem is solved with Krylov-subspace methods, such as the LSQR algorithm, that are able to deal with the inherent ill-conditioning. As the helicopter-borne electromagnetic problem is characterized by a unique transmitter-receiver relation, an explicit representation of the Jacobian matrix is used. It is shown that this ansatz is the crucial component of the 3-D HEM inversion. Furthermore, a tensor-based formulation is introduced that provides a fast update of the linear system of the forward problem and an effective handling of the sensitivity related algebraic quantities. Based on a synthetic data set of a predefined model problem, different application examples are used to demonstrate the principal functionality of the presented algorithm. Finally, the algorithm is applied to a data set obtained from a real field survey in the Northern German Lowlands. / Die vorliegende Arbeit beschäftigt sich mit der 3-D Inversion von Hubschrauberelektromagnetikdaten im Frequenzbereich. Das vorgestellte Verfahren basiert auf einer vorhergehenden Eingrenzung des Messgebiets auf diejenigen Bereiche, in denen tatsächliche 3-D Strukturen im Untergrund vermutet werden. Die Resultate der 3-D Inversion dieser Teilbereiche können im Anschluss wieder in die Ergebnisse der Auswertung des komplementären Gesamtdatensatzes integriert werden, welche auf herkömmlichen 1-D Verfahren beruht (sog. Cut-&-Paste-Strategie). Die Diskretisierung des Vorwärtsproblems, abgeleitet von einer Sekundärfeldformulierung der vollständigen Helmholtzgleichung, erfolgt mithilfe der Methode der Finiten Differenzen. Zur analytischen Berechnung der zugehörigen Primärfelder wird ein Interpolationsansatz verwendet, welcher den Umgang mit der enorm hohen Anzahl an Quellen ermöglicht. Die Lösung des inversen Problems basiert auf dem Gauß-Newton-Verfahren und dem Tichonow-Regularisierungsansatz. Als Mittel der zusätzlichen impliziten Regularisierung dient eine räumliche Eingrenzung des Gebiets, auf welchem das inverse Problem gelöst wird. Zur iterativen Lösung des zugrundeliegenden Kleinste-Quadrate-Problems werden Krylov-Unterraum-Verfahren, wie der LSQR Algorithmus, verwendet. Aufgrund der charakteristischen Sender-Empfänger-Beziehung wird eine explizit berechnete Jakobimatrix genutzt. Ferner wird eine tensorbasierte Problemformulierung vorgestellt, welche die schnelle Assemblierung leitfähigkeitsabhängiger Systemmatrizen und die effektive Handhabung der zur Berechnung der Jakobimatrix notwendigen algebraischen Größen ermöglicht. Die Funktionalität des beschriebenen Ansatzes wird anhand eines synthetischen Datensatzes zu einem definierten Testproblem überprüft. Abschließend werden Inversionsergebnisse zu Felddaten gezeigt, welche im Norddeutschen Tiefland erhoben worden.

In an effort to improve the accuracy of common 1-D analysis for frequency domain helicopter-borne electromagnetic data at reasonable computing costs, a 3-D inversion approach is developed. The strategy is based on the prior localization of an entire helicopter-borne electromagnetic survey to parts which are actually affected by expected local 3-D anomalies and a separate inversion of those sections of the surveys (cut-&-paste strategy). The discrete forward problem, adapted from the complete Helmholtz equation, is formulated in terms of the secondary electric field employing the finite difference method. The analytical primary field calculation incorporates an interpolation strategy that allows to effectively handle the enormous number of transmitters. For solving the inverse problem, a straightforward Gauss-Newton method and a Tikhonov-type regularization scheme are applied. In addition, different strategies for the restriction of the domain where the inverse problem is solved are used as an implicit regularization. The derived linear least squares problem is solved with Krylov-subspace methods, such as the LSQR algorithm, that are able to deal with the inherent ill-conditioning. As the helicopter-borne electromagnetic problem is characterized by a unique transmitter-receiver relation, an explicit representation of the Jacobian matrix is used. It is shown that this ansatz is the crucial component of the 3-D HEM inversion. Furthermore, a tensor-based formulation is introduced that provides a fast update of the linear system of the forward problem and an effective handling of the sensitivity related algebraic quantities. Based on a synthetic data set of a predefined model problem, different application examples are used to demonstrate the principal functionality of the presented algorithm. Finally, the algorithm is applied to a data set obtained from a real field survey in the Northern German Lowlands. / Die vorliegende Arbeit beschäftigt sich mit der 3-D Inversion von Hubschrauberelektromagnetikdaten im Frequenzbereich. Das vorgestellte Verfahren basiert auf einer vorhergehenden Eingrenzung des Messgebiets auf diejenigen Bereiche, in denen tatsächliche 3-D Strukturen im Untergrund vermutet werden. Die Resultate der 3-D Inversion dieser Teilbereiche können im Anschluss wieder in die Ergebnisse der Auswertung des komplementären Gesamtdatensatzes integriert werden, welche auf herkömmlichen 1-D Verfahren beruht (sog. Cut-&-Paste-Strategie). Die Diskretisierung des Vorwärtsproblems, abgeleitet von einer Sekundärfeldformulierung der vollständigen Helmholtzgleichung, erfolgt mithilfe der Methode der Finiten Differenzen. Zur analytischen Berechnung der zugehörigen Primärfelder wird ein Interpolationsansatz verwendet, welcher den Umgang mit der enorm hohen Anzahl an Quellen ermöglicht. Die Lösung des inversen Problems basiert auf dem Gauß-Newton-Verfahren und dem Tichonow-Regularisierungsansatz. Als Mittel der zusätzlichen impliziten Regularisierung dient eine räumliche Eingrenzung des Gebiets, auf welchem das inverse Problem gelöst wird. Zur iterativen Lösung des zugrundeliegenden Kleinste-Quadrate-Problems werden Krylov-Unterraum-Verfahren, wie der LSQR Algorithmus, verwendet. Aufgrund der charakteristischen Sender-Empfänger-Beziehung wird eine explizit berechnete Jakobimatrix genutzt. Ferner wird eine tensorbasierte Problemformulierung vorgestellt, welche die schnelle Assemblierung leitfähigkeitsabhängiger Systemmatrizen und die effektive Handhabung der zur Berechnung der Jakobimatrix notwendigen algebraischen Größen ermöglicht. Die Funktionalität des beschriebenen Ansatzes wird anhand eines synthetischen Datensatzes zu einem definierten Testproblem überprüft. Abschließend werden Inversionsergebnisse zu Felddaten gezeigt, welche im Norddeutschen Tiefland erhoben worden.

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.