In this thesis, four inversion problems of different scale and difficulty are solved. Two of them are electromagnetic inverse problems. Two more are joint inversion problems of potential field data and other types of data. First, a linear approximation, which is a generalization of the low-induction-number approximation standard in slingram dual-loop interpretation is developed and used for rapid two and three dimensional inversion. The approximation takes induction within a background half-space into account and can thus be applied in conductive scenarios, where otherwise a rigorous electromagnetic modeling would be required. Second, a three-dimensional inversion of airborne tensor very-low-frequency data with a rigorous forward modeling at its core is developed. For dealing with the large scale of the forward problem, a nested fast-Fourier-transform-based integral equation method is introduced, wherein electromagnetic interactions are arranged according to their range and larger ranges are treated with less accuracy and effort. The inversion improves the traditional interpretation through data derived maps by providing a conductivity model, thus constraining the upper few hundred meters of the crust down to the shallowest conductor and allowing the study of its top in three dimensions. The third inversion problem is the the joint inversion of refraction and geoelectric data. By requiring the velocity and resistivity models to share a common, laterally variable layered geometry, easily interpretable models, which are reasonable in many geological near surface situations (e.g., groundwater exploration in Quaternary sediments), are produced directly from the joint inversion. Finally, a joint inversion of large scale potential field data from a gabbro intrusion is presented. Gravity and magnetic data are required to abide to a petrophysical constraint, which is derived from extensive field sampling. The impact of the constraint is maximized under the provision that both data sets are explained equally well as they would be through individual inversions. This leads to a simple and clearly defined intrusion geometry, consistent for both the density and magnetic susceptibility distribution. In all presented inversion problems, field data sets are successfully inverted, the results are appraised through synthetic tests and, if available, through comparison with independent data. / Diese Arbeit hat die Lösung von vier geophysikalischen Umkehraufgaben, sogenannten Inversionsproblemen, zum Gegenstand. Zwei dieser Aufgaben befassen sich mit der Inversion elektromagnetischer Daten, zwei weitere sind Probleme der kombinierten Inversion von Datensätzen aus unterschiedlichen geophysikalischen Messverfahren. Im ersten Problem wird die für die Auswertung elektromagnetischer Zweispulensystemdaten typische lineare Näherung der kleinen Induktionszahlen als Bornsche Näherung verallgemeinert, ihre Anwendbarkeit durch exakte Berücksichtigung der Induktionsvorgänge in einem beliebigen homogenen Halbraum von schlechtleitenden auf gutleitende Untergründe ausgedehnt und schließlich zur zwei- und dreidimensionalen Inversion eingesetzt. Dadurch kann auch im leitfähigen Untergrund eine aufwändige exakte Modellierung vermieden werden. Im zweiten Problem wird eine dreidimensionale Inversion von flugzeuggestützten Längstwellenmessungen entwickelt und als ihre Grundlage eine exakte elektromagnetische Rechnung erdacht. Damit wird traditionelle kartengestützte Dateninterpretation durch ein dreidimensionales Leitfähigkeitsmodell ergänzt, welches die oberen hundert bis dreihundert Meter der Erdkruste bis hin zur Tiefe des obersten Leiters abbildet, so dass dessen Oberflächenform erkundet werden kann. Die enorme Problemgröße wird durch eine Fouriertransformationsmethode bewältigt, welche die elektromagnetischen Wechselwirkungen nach ihrer Reichweite einteilt, die Fernwirkungen mit entsprechend verringerter Genauigkeit behandelt und dadurch eine erhebliche Anzahl an Rechnungen einspart. Im dritten Problem werden refraktionsseismische und geoelektrische Messungen kombiniert, indem sowohl das Geschwindigkeits- als auch das Widerstandsmodell mit einer gemeinsamen, lateral veränderlichen und durch beide Datensätze bestimmten Schichtstruktur versehen werden. Ein solches, durch Schichten definiertes Inversionsergebnis, stellt in vielen oberflächennahen Anwendungen, beispielsweise im Grundwasserbereich, ein sinnvolles Abbild der Erde dar. Im vierten Problem werden Schweremessungen und Magnetfeldmessungen, die über einer Gabbrointrusion aufgenommen wurden, mittels einer empirischen petrophysikalischen Beziehung vereinigt, welche aus Labormessungen an einer großen Anzahl von Gesteinsproben abgeleitet wurde. Hierbei wird der Einfluss dieser Modellkopplung solange maximiert, wie beide Datensätze mit derjenigen Genauigkeit angepasst werden können, welche vorher in Einzelinversionen erreicht wurde. Das Ergebnis ist ein einfaches, geometrisch konsistentes Modell der Verteilungen von Dichte und magnetischer Suszeptibilität. In allen vier Aufgaben wurden erfolgreich reale Felddaten invertiert. Die Güte der Ergebnisse wurde mittels synthetischer Experimente untersucht und, so vorhanden, mit unabhängigen Informationen verglichen.

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Abstract This work is devoted to the theory of joint interpretation of multimethod geophysical data and its application to the solution of real geophysical inverse problems. The targets of such joint interpretation can be geological bodies with an established dependence between various physical properties that cause anomalies in several geophysical fields (geophysical multiresponse). The establishing of the relationship connecting the various physical properties is therefore a necessary first step in any joint interpretation procedure. Bodies for which the established relationship between physical properties is violated (single-response bodies) can be targets of separate interpretations. The probabilistic (Bayesian) approach provides the necessary formalism for addressing the problem of the joint inversion of multimethod geophysical data, which can be non-linear and have a non-unique solution. Analysis of the lower limit of resolution of the non-linear problem of joint inversion using the definition of e-entropy demonstrates that joint inversion of multimethod geophysical data can reduce non-uniqueness in real geophysical inverse problems. The question can be formulated as a multiobjective optimisation problem (MOP), enabling the numerical methods of this theory to be employed for the purpose of geophysical data inversion and for developing computer algorithms capable of solving highly non-linear problems. An example of such a problem is magnetotelluric impedance tensor inversion with the aim of obtaining a 3-D resistivity distribution. An additional area of application for multiobjective optimisation can be the combination of various types of uncertain information (probabilistic and non-probabilistic) in a common inversion scheme applicable to geophysical inverse problems. It is demonstrated how the relationship between seismic velocity and density can be used to construct an algorithm for the joint interpretation of gravity and seismic wide-angle reflection and refraction data. The relationship between the elastic and electrical properties of rocks, which is a necessary condition for the joint inversion of data obtained by seismic and electromagnetic methods, can be established for solid- liquid rock mixtures using theoretical modelling of the elastic and electrical properties of rocks with a fractal microstructure and from analyses of petrophysical data and borehole log data.

Geophysical methods are non-invasive and allow an effective way of understanding subsurface structures and their physical properties. One of the main challenges is the often non-uniqueness of the geophysical models and that several different models can explain a dataset to an agreeable fit. Moreover, noise and limitations in resolution, which are inherent to field data, are additional obstacles for obtaining a true physical property model of the subsurface. Facing all these challenges, geophysicists have dedicated their efforts for decades to recover models that represent, as close as possible, the true subsurface. Joint inversion and integration of multiple geophysical data are two main approaches that I studied to better resolve subsurface structures. I further used these approaches, together with new software and hardware implementations for data acquisition and inversion, for near-surface applications.  In this thesis, radio-magnetotelluric (RMT), boat-towed RMT, boat-towed controlled source MT (CSMT), electrical resistivity tomography (ERT), and first-arrival traveltime tomography are jointly used for quick clay investigations and fracture zone delineation under shallow water-bodies. The joint approach, as compared with any individual method, shows a better ability to both resolve the geological targets and to assist in understanding the subsurface geology that hosts these targets. For examples: by performing the joint inversion of lake-floor ERT and boat-towed RMT data, a fracture zone is better delineated with greater details compared with single inversion; by employing boat-towed CSMT measurements and jointly inverting with boat-towed RMT data, the subsurface structures, especially at greater depth, are better resolved than by inverting each dataset alone. During my PhD studies, two types of new implementations were employed. (1) Boat-towed data acquisition system was implemented to expand the RMT and CSMT method from land to shallow-water applications. This is significant since many large-scale underground infrastructures are likely to cross these water zones (for example multi-lane train or bypass tunnels, such as the Stockholm bypass). (2) The modification of a well-structured code EMILIA allows joint inversion of boat-towed RMT and lake-floor ERT datasets, and the modification of another well-structured code MARE2DEM can accurately model high frequency CSMT data and handle joint inversion of boat-towed RMT and boat-towed CSMT datasets. Thus, the code modification as another type of new implementation guarantees the success of near-surface applications using the boat-towed RMT and CSMT data acquisition systems. Studies conducted during my PhD work, included under the SEG-GWB (the Society of Exploration Geophysicists - Geoscientists Without Borders) program and the TRUST (TRansparent Underground STructure) umbrella project, are useful for near-surface applications including, for examples, engineering purposes such as planning of underground infrastructures, site characterization in connection with energy or waste storage, and geohazard investigations.

Multi-component induction resistivity and sonic measurements acquired in high-angle wells can be strongly influenced by shoulder-bed effects, anisotropy resulting from sand-shale laminations, and presence of mud-filtrate invasion. Understanding the corresponding biasing effects aids in the interpretation of resistivity and sonic measurements and subsequently leads to more accurate and reliable formation evaluation. This dissertation describes numerical simulation studies examining the effects on multi-component induction and sonic measurements in a variety of complex formation models. Subsequently, a joint inversion scheme is presented that combines resistivity and sonic measurements to estimate in situ petrophysical and elastic properties in the presence of mud-filtrate invasion. To facilitate the simulation study of multi-component induction logs, I develop a new finite-difference algorithm for the numerical simulation of frequency-domain electromagnetic borehole measurements. The algorithm~uses a coupled scalar-vector potential formulation for arbitrary three-dimensional inhomogeneous and electrically anisotropic media. Simulations show that shoulder-bed anisotropy: enhances shoulder-bed effects across sand layers; and impacts invasion sensitivities to significantly alter the assessment of invasion in terms of invaded- and virgin-zone resistivities, radial length, and front shape. For the simulation study of sonic logs, I develop a three-dimensional, finite-difference time-domain algorithm that models elastic wave propagation in a fluid-filled borehole. Simulations show that presence of anisotropy not only alters the degree of dispersion observed in flexural and Stoneley waves, but also alters their responses to invasion. In addition, presence of a dipping shoulder bed can significantly distort flexural dispersion, making it difficult to identify the low frequency asymptote corresponding to formation shear wave velocity. Lastly, I consider a radial one-dimensional model in the development of a joint resistivity and sonic inversion algorithm. This scheme simultaneously inverts array-induction apparent conductivities and sonic flexural and Stoneley dispersions for the rock's elastic moduli and water saturation in the presence of mud-filtrate invasion. Inversions are performed on numerically simulated data for a variety of models reflecting soft and hard rock formations with presence of water- and oil-based mud-filtrate invasion. Results show the estimated invasion profiles display excellent agreement with the true models, and the elastic moduli are estimated to within a few percent of the true values. / text

The layered structure and bulk composition of continental crust contains important clues about its history of mountain-building, about its magmatic evolution, and about dynamical processes that continue to happen now. Geophysical and geological features such as gravity anomalies, surface topography, lithospheric strength and the deformation that drives the earthquake cycle are all directly related to deep crustal chemistry and the movement of materials through the crust that alter that chemistry. The North American continental crust records billions of years of history of tectonic and dynamical changes. The western U.S. is currently experiencing a diverse array of dynamical processes including modification by the Yellowstone hotspot, shortening and extension related to Pacific coast subduction and transform boundary shear, and plate interior seismicity driven by flow of the lower crust and upper mantle. The midcontinent and eastern U.S. is mostly stable but records a history of ancient continental collision and rifting. EarthScope’s USArray seismic deployment has collected massive amounts of data across the entire United States that illuminates the deep continental crust, lithosphere and deeper mantle. This study uses EarthScope data to investigate the thickness and composition of the continental crust, including properties of its upper and lower layers. One-layer and two-layer models of crustal properties exhibit interesting relationships to the history of North American continental formation and recent tectonic activities that promise to significantly improve our understanding of the deep processes that shape the Earth’s surface. Model results show that seismic velocity ratios are unusually low in the lower crust under the western U.S. Cordillera. Further modeling of how chemistry affects the seismic velocity ratio at temperatures and pressures found in the lower crust suggests that low seismic velocity ratios occur when water is mixed into the mineral matrix, and the combination of high temperature and water may point to small amounts of melt in the lower crust of Cordillera.

High-resolution seismic images of lithospheric structures allow us to infer the tectonics that modified the lithosphere. We apply such methods to understand Cenozoic modification of the lithosphere by tectonic and magmatic processes in the tectonically active western United States. Using USArray Transportable and Flexible Array data, we present high-resolution images for three regions in this thesis. (1) In the Mendocino triple junction, we use a joint inversion of Rayleigh-wave dispersion data and receiver functions to obtain a new crust and upper Vs model to ~150km depth. The model shows four distinct, young lithosphere-asthenosphere boundary systems. A low-Vs anomaly beneath the Great Valley-Sierra Nevada reconciles existing slab window models with the mantle-wedge geochemical signatures in Coast Range volcanics, and explains the ~3 Myr delay of the onset of volcanism after slab removal. Uppermost mantle low velocities provide evidence for forearc mantle serpentinization extending along the Cascadia margin. (2) In the Colorado Plateau, a Rayleigh wave tomography model sheds light on the volcanism along the margins and plateau uplift. Strong upper mantle heterogeneity across the plateau edge results from the combined effect of a ~200-400 K temperature difference and ~1% partial melt. A ring of low velocities under the plateau periphery suggests that the rehydrated Proterozoic lithosphere is progressively removed by convective processes. Particularly, a high-Vs anomaly imaged beneath the western plateau adds evidence for a downwelling/delamination hypothesis [Levander et al., 2011]. Thermo-chemical edge-driven convection causing localized lithospheric downwelling provides uplift along the margins and magmatic encroachment into the plateau center. (3) In the final study, we developed a 3-D teleseismic scattering wave imaging technique based on the Kirchhoff approximation and 3-D inverse Generalized Radon Transform. Synthetic tests demonstrate higher resolution imaging for continuous, irregular interfaces or localized scatterers, in comparison to conventional methods. Applied to the High Lava Plains dataset, the transmission coefficient structure shows a deepening Moho near 117.6°W and three negative events that correlate well with the Rayleigh wave low-Vs zones. Images made with the Mendocino data clearly show rapidly decreasing lithosphere-asthenosphere boundary depths from the subduction to transform regime.

Les volcans sont des édifices complexes et hétérogènes. Imager leur structure demande des méthodes adaptées au contexte ainsi qu'à la nature, à la qualité et à la quantité des données disponibles.Ce travail porte sur l'imagerie géophysique de l'île volcanique de Basse-Terre en Guadeloupe, par inversion de données gravimétriques et magnétiques, par tomographie d'ondes de surface extraites de corrélations de bruit sismique et par tomographie de temps d'arrivée des séismes de l'arc des Petites Antilles. Nous obtenons ainsi les premiers modèles tridimensionnels de l'île de Basse-Terre en termes de densité, aimantation et vitesses sismiques. La gravimétrie et le magnétisme conduisent à des modèles de densité et d'aimantation avec une très bonne résolution latérale dans les premiers kilomètres, mais avec une résolution verticale très faible. Les ondes de surface issues des corrélations de bruit présentent une bonne résolution verticale dans les premiers kilomètres, mais résolvent mal les variations latérales de vitesses. La tomographie de temps d'arrivée permet d'imager les vitesses sismiques jusqu'à des profondeurs élevées, avec une bonne résolution latérale, mais une mauvaise résolution verticale. Nous proposons une méthode pour inverser conjointement les données sismologiques et gravimétriques pour produire un modèle de vitesses et de densité qui bénéficie des résolutions complémentaires des différents jeux de données.Nos résultats soulignent une tendance NNO-SSE, avec des vitesses et des densités qui diminuent vers le sud en moyenne, conformément à la migration du volcanisme du nord vers le sud au cours de l'histoire géologique de l'île. Nous observons de faibles densités, vitesses sismiques et aimantations au niveau du dôme du volcan de la Soufrière ainsi que dans la région de Bouillante sur la côte ouest, reflétant la forte altération hydrothermale de ces zones. Deux anciens centres éruptifs majeurs, caractérisés par de fortes densités et vitesses sismiques, sont identifiés : l'un au niveau de la vallée de Beaugendre, l'autre au nord au niveau de la vallée de Petite Plaine. / Volcanoes are complex and heterogeneous edifices. Imaging their structures requires methods that are adapted to the context and to the nature, quality and quantity of available data. This work focuses on the geophysical imaging of the volcanic island of Basse-Terre in Guadeloupe, by performing inversions of gravimetric and magnetic data, ambient noise based surface wave tomography, and travel time tomography from earthquakes of the Lesser Antilles arc. We therefore obtain the first three-dimensional models of Basse-Terre island in terms of density, magnetisation and seismic velocities. Gravimetry and magnetism lead to density and magnetisation models with a very good lateral resoltuion within the first kilometres but with very low vertical resolution. Surface wave tomography from noise correlations shows a good vertical resolution within the first kilometres, but poorly resolves the lateral velocity variations. Travel time tomography allows imaging seismic velocities up to great depths with a good lateral resolution but a poor vertical resolution. We propose a method to invert jointly the seismological and gravimetric data in order to produce a velocity and density model that takes advantage of the complementary resolutions associated with the different datasets.Our results outline a NNW-SSE trend, with velocities and densities roughtly decreasing southwards, in accordance with the southward migration of volcanism across the geological history of the island. We observe low densities, seismic velocities and magnetisations in the area of the dome of the Soufrière volcano as well as in the Bouillante area along the western coast, reflecting the high hydrothermal alteration of these areas. Two major old eruptive centres are identified in the areas of Beaugendre Valley and Petite Plaine Valley.

In this thesis, we have investigated the lithospheric structure beneath the continental part of northern Algeria. We have used data provided by the Algerian Digital Seismic Network (ADSN) to create images (2D maps and cross-sections) of the Moho depth variation and the velocity structure of the crust and upper mantle under the study region. To realize this main objective, this thesis has been divided into two main studies. In the first study, we have used teleseismic P-wave receiver functions jointly inverted with Rayleigh wave dispersion curves obtained from local earthquakes recorded by ADSN broadband stations. The seismic stations are located in different geological settings, including the Tell Atlas, the High Plateaus, and the Saharan Atlas. In the second study, we have applied a different approach by including a different type of data, namely ambient noise. We used the Rayleigh waves generated by ambient noise and recorded by ADSN’s short-period stations, as well as Rayleigh waves obtained from local earthquakes recorded by ADSN’s broadband stations to create a coverage map that allows a 3D imaging of the crustal structure of northern Algeria with an average resolution of about 100 km using the surface wave tomography method. Crustal thickness and the Vp/Vs ratio are first derived by the H–κ stacking method of receiver functions. Then, the joint inversion of receiver functions and Rayleigh wave group velocity dispersion curves have showed the variation of Moho depth in different geological settings. Moho depth clearly increases from north to south and from west to east. The shallowest Moho depths (~20–30 km) have been estimated along the Algerian continental margin and in the Tell Atlas, while the deepest Moho depths are found in the Saharan Atlas and the Aurès mountains (36–44 km), passing through the High Plateaus region where Moho depths vary from 30–36 km. The crustal structure is interpreted by combining the results of both studies. The crust is divided into two main layers throughout the study region. The upper crust has a thickness of around 8 –14 km and an average shear-wave velocity of around 3.0 km/s. A zone of high velocity is also observed in the lower part of the upper crust at a depth of around 10 km under the Mitidja basin in the Tell Atlas. The lower crust has a thickness of about 12–30 km and an average shear-wave velocity of between 3.4–3.8 km/s. In general, the lower crust is thicker than the upper crust, especially in the Saharan Atlas. A thinning of the lower crust is observed approaching the interplate boundary to the north, especially in the western part of the region. Upper mantle shear-wave velocity varies from 4.1 to 4.5 km/s at maximum, and are generally stable below 60 km depth. Two low-velocity zones are clearly observed, particularly in the eastern Tell Atlas and High Plateaus. The first is around 10 km thick in the lower part of the lower crust, and the other lies in the upper mantle at depths of between 40 and 60 km. The obtained results are in accordance with those found previously in the region, particularly those using land gravimetric and seismic data. The combination of all these seismological methods has allowed the integration of a new shear-wave velocity model and 2D crustal structure cross-sections into previous results found in the northern part of Algeria, which is located on a major plate boundary. This provides a better understanding of the geodynamics and tectonics of the western Mediterranean region.