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1

Chen, Xiaoming. "Two-dimensional constrained anisotropic inversion of magnetotelluric data." Phd thesis, Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6316/.

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Tectonic and geological processes on Earth often result in structural anisotropy of the subsurface, which can be imaged by various geophysical methods. In order to achieve appropriate and realistic Earth models for interpretation, inversion algorithms have to allow for an anisotropic subsurface. Within the framework of this thesis, I analyzed a magnetotelluric (MT) data set taken from the Cape Fold Belt in South Africa. This data set exhibited strong indications for crustal anisotropy, e.g. MT phases out of the expected quadrant, which are beyond of fitting and interpreting with standard isotropic inversion algorithms. To overcome this obstacle, I have developed a two-dimensional inversion method for reconstructing anisotropic electrical conductivity distributions. The MT inverse problem represents in general a non-linear and ill-posed minimization problem with many degrees of freedom: In isotropic case, we have to assign an electrical conductivity value to each cell of a large grid to assimilate the Earth's subsurface, e.g. a grid with 100 x 50 cells results in 5000 unknown model parameters in an isotropic case; in contrast, we have the sixfold in an anisotropic scenario where the single value of electrical conductivity becomes a symmetric, real-valued tensor while the number of the data remains unchanged. In order to successfully invert for anisotropic conductivities and to overcome the non-uniqueness of the solution of the inverse problem it is necessary to use appropriate constraints on the class of allowed models. This becomes even more important as MT data is not equally sensitive to all anisotropic parameters. In this thesis, I have developed an algorithm through which the solution of the anisotropic inversion problem is calculated by minimization of a global penalty functional consisting of three entries: the data misfit, the model roughness constraint and the anisotropy constraint. For comparison, in an isotropic approach only the first two entries are minimized. The newly defined anisotropy term is measured by the sum of the square difference of the principal conductivity values of the model. The basic idea of this constraint is straightforward. If an isotropic model is already adequate to explain the data, there is no need to introduce electrical anisotropy at all. In order to ensure successful inversion, appropriate trade-off parameters, also known as regularization parameters, have to be chosen for the different model constraints. Synthetic tests show that using fixed trade-off parameters usually causes the inversion to end up by either a smooth model with large RMS error or a rough model with small RMS error. Using of a relaxation approach on the regularization parameters after each successful inversion iteration will result in smoother inversion model and a better convergence. This approach seems to be a sophisticated way for the selection of trade-off parameters. In general, the proposed inversion method is adequate for resolving the principal conductivities defined in horizontal plane. Once none of the principal directions of the anisotropic structure is coincided with the predefined strike direction, only the corresponding effective conductivities, which is the projection of the principal conductivities onto the model coordinate axes direction, can be resolved and the information about the rotation angles is lost. In the end the MT data from the Cape Fold Belt in South Africa has been analyzed. The MT data exhibits an area (> 10 km) where MT phases over 90 degrees occur. This part of data cannot be modeled by standard isotropic modeling procedures and hence can not be properly interpreted. The proposed inversion method, however, could not reproduce the anomalous large phases as desired because of losing the information about rotation angles. MT phases outside the first quadrant are usually obtained by different anisotropic anomalies with oblique anisotropy strike. In order to achieve this challenge, the algorithm needs further developments. However, forward modeling studies with the MT data have shown that surface highly conductive heterogeneity in combination with a mid-crustal electrically anisotropic zone are required to fit the data. According to known geological and tectonic information the mid-crustal zone is interpreted as a deep aquifer related to the fractured Table Mountain Group rocks in the Cape Fold Belt.
Tektonische und geologische Prozesse verursachen häufig eine strukturelle Anisotropie des Untergrundes, welche von verschiedenen geophysikalischen Methoden beobachtet werden kann. Zur Erstellung und Interpretation geeigneter, realistischer Modelle der Erde sind Inversionsalgorithmen notwendig, die einen anisotropen Untergrund einbeziehen können. Für die vorliegende Arbeit habe ich einen magnetotellurischen (MT) Datensatz vom Cape Fold Gürtel in Südafrika untersucht. Diese Daten weisen auf eine ausgeprägte Anisotropie der Kruste hin, da z.B. die MT Phasen außerhalb des erwarteten Quadranten liegen und nicht durch standardisierte isotrope Inversionsalgorithmen angepasst und ausgewertet werden können. Um dieses Problem zu beheben, habe ich eine zweidimensionale Inversionsmethode entwickelt, welche eine anisotrope elektrische Leitfähigkeitsverteilungen in den Modellen zulässt. Die MT Inversion ist im allgemeinen ein nichtlineares, schlecht gestelltes Minimierungsproblem mit einer hohen Anzahl an Freiheitsgraden. Im isotropen Fall wird jeder Gitterzelle eines Modells ein elektrischer Leitfähigkeitswert zugewiesen um den Erduntergrund nachzubilden. Ein Modell mit beispielsweise 100 x 50 Zellen besitzt 5000 unbekannte Modellparameter. Im Gegensatz dazu haben wir im anisotropen Fall die sechsfache Anzahl, da hier aus dem einfachen Zahlenwert der elektrischen Leitfähigkeit ein symmetrischer, reellwertiger Tensor wird, wobei die Anzahl der Daten gleich bleibt. Für die erfolgreiche Inversion von anisotropen Leitfähigkeiten und um die Nicht-Eindeutigkeit der Lösung des inversen Problems zu überwinden, ist eine geeignete Einschränkung der möglichen Modelle absolut notwendig. Dies wird umso wichtiger, da die Sensitivität von MT Daten nicht für alle Anisotropieparameter gleich ist. In der vorliegenden Arbeit habe ich einen Algorithmus entwickelt, welcher die Lösung des anisotropen Inversionsproblems unter Minimierung einer globalen Straffunktion berechnet. Diese besteht aus drei Teilen: der Datenanpassung, den Zusatzbedingungen an die Glätte des Modells und die Anisotropie. Im Gegensatz dazu werden beim isotropen Fall nur die ersten zwei Parameter minimiert. Der neu definierte Anisotropieterm wird mit Hilfe der Summe der quadratischen Abweichung der Hauptleitfähigkeitswerte des Modells gemessen. Die grundlegende Idee dieser Zusatzbedingung ist einfach. Falls ein isotropes Modell die Daten ausreichend gut anpassen kann, wird keine elektrische Anisotropie zusätzlich in das Modell eingefügt. Um eine erfolgreiche Inversion zu garantieren müssen geeignete Regularisierungsparameter für die verschiedenen Nebenbedingungen an das Modell gewählt werden. Tests mit synthetischen Modellen zeigen, dass bei festgesetzten Regularisierungsparametern die Inversion meistens entweder in einem glatten Modell mit hohem RMS Fehler oder einem groben Modell mit kleinem RMS Fehler endet. Die Anwendung einer Relaxationsbedingung auf die Regularisierung nach jedem Iterationsschritt resultiert in glatteren Inversionsmodellen und einer höheren Konvergenz und scheint ein ausgereifter Weg zur Wahl der Parameter zu sein. Die vorgestellte Inversionsmethode ist im allgemeinen in der Lage die Hauptleitfähigkeiten in der horizontalen Ebene zu finden. Wenn keine der Hauptrichtungen der Anisotropiestruktur mit der vorgegebenen Streichrichtung übereinstimmt, können nur die dazugehörigen effektiven Leitfähigkeiten, welche die Projektion der Hauptleitfähigkeiten auf die Koordinatenachsen des Modells darstellen, aufgelöst werden. Allerdings gehen die Informationen über die Rotationswinkel verloren. Am Ende meiner Arbeit werden die MT Daten des Cape Fold Gürtels in Südafrika analysiert. Die MT Daten zeigen in einem Abschnitt des Messprofils (> 10 km) Phasen über 90 Grad. Dieser Teil der Daten kann nicht mit herkömmlichen isotropen Modellierungsverfahren angepasst und daher mit diesen auch nicht vollständig ausgewertet werden. Die vorgestellte Inversionsmethode konnte die außergewöhnlich hohen Phasenwerte nicht wie gewünscht im Inversionsergebnis erreichen, was mit dem erwähnten Informationsverlust der Rotationswinkel begründet werden kann. MT Phasen außerhalb des ersten Quadranten können für gewöhnlich bei Anomalien mit geneigter Streichrichtung der Anisotropie gemessen werden. Um diese auch in den Inversionsergebnissen zu erreichen ist eine Weiterentwicklung des Algorithmus notwendig. Vorwärtsmodellierungen des MT Datensatzes haben allerdings gezeigt, dass eine hohe Leitfähigkeitsheterogenität an der Oberfläche in Kombination mit einer Zone elektrischer Anisotropie in der mittleren Kruste notwendig sind um die Daten anzupassen. Aufgrund geologischer und tektonischer Informationen kann diese Zone in der mittleren Kruste als tiefer Aquifer interpretiert werden, der im Zusammenhang mit den zerrütteten Gesteinen der Table Mountain Group des Cape Fold Gürtels steht.
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2

Le, Van Anh Cuong. "Cooperative Inversion of Magnetotelluric and Seismic Data." Thesis, Curtin University, 2017. http://hdl.handle.net/20.500.11937/59652.

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Cooperative inversion is the beneficial transference of information from one geophysical technique to another for improving the recovery of subsurface rock properties. The research’s focus is the development and comparison of new strategies for cooperatively inverting seismic and magnetotelluric data. This is intended to improve the recovery of subsurface electrical conductivity. The developed techniques are applied to two industry scale case sites containing large co-located seismic and MT surveys.
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3

Alvarez, Aramberri Julen. "hp-Adaptive Simulation and Inversion of Magnetotelluric Measurements." Thesis, Pau, 2015. http://www.theses.fr/2015PAUU3056/document.

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La magnéto-tellurique (MT) (Cagniard 1953, Tikhonov 1950) est une technique d'exploration de la Terre basée sur des mesures de champs électromagnétiques (EM). Une source naturelle (non artificielle) harmonique en temps et située dans l'ionosphère (Weaver 1994) produit un champ EM régi par les équations de Maxwell. Les champs électromagnétiques sont enregistrés par plusieurs récepteurs placés sur la surface de la Terre. Ces mesures sont utilisées pour produire une image du sous-sol à partir d'un procédé d'inversion utilisant des méthodes numériques. Nous utilisons la méthode hp-FEM résultant d'une extension du travail de Demkowicz 2005. Nous avons développé un logiciel qui résout, pour la première fois, le problème MT avec des éléments finis auto-adaptatifs. La méthode hp-FEM permet des raffinements locaux, à la fois en taille h et en ordre p sur les éléments, ce qui est un avantage notoire puisque la combinaison de ces deux types de critères permet de mieux capter la présence de singularités, fournissant ainsi des erreurs de discrétisation faible. C'est donc une méthode très précise dont la convergence est exponentielle (Gui and Babuska 1986, Babuska and Guo 1996). En raison des défis d'implémentation encore non résolus (Demkowicz et al. 2002) et de la complexité technique des calculs hp-FEM en 3D, nous nous limitons, dans ce travail, à des calculs en 1D et 2D.Le domaine de calcul est tronqué par un matériau absorbant (Perfectly Matched Layer PML, Berenger 1994), qui est conçu pour s'adapter automatiquement aux propriétés physiques des matériaux. En particulier, il s'ajuste efficacement à l'interface air-sol, où le contraste entre la conductivité des matériaux atteint jusqu'à seize ordres de grandeur. Dans cette thèse, nous présentons également des résultats préliminaires pour la mise en place d'une technique dimensionnelle adaptative plus connue sous le nom de DAM (Dimensionally Adaptive Method (DAM)). Lorsque la distribution de la résistivité du sous-sol dépend de multiples variables spatiales, une analyse correcte de la dimensionnalité (Ledo 2005, Martí et al. 2009, Weaver and Agarwal 2000) rend parfois possible de considérer les différentes régions avec des dimensions spatiales différentes. Par exemple, il est parfois possible d’interpréter la distribution comme une formation unidimensionnelle plus quelques hétérogénéités en 2D (ou 3D). Basée sur cette interprétation, la DAM tire profit d’une telle situation. Ainsi, l'idée principale de cette méthode est d'effectuer l'adaptativité sur la dimension spatiale en commençant par un problème de faible dimension et en utilisant les résultats obtenus pour minimiser le coût des problèmes de dimension supérieure. Nous commençons l'inversion avec un modèle 1D. Les résultats de ce problème d'inversion 1D sont utilisés comme information a priori sur les modèles de dimension supérieure. Un avantage fondamental de cette approche est que nous pouvons utiliser les solutions des problèmes de dimension inférieure précédemment calculées comme composantes du terme de régularisation associé à un problème de dimension supérieure afin d'augmenter la robustesse de l'inversion. Cette thèse propose également une analyse numérique rigoureuse de divers aspects des problèmes MT. En particulier, nous avons: (a) étudié l'effet de la source, (b) effectué une analyse fréquentielle de sensibilité, (c) illustré l'augmentation du taux de convergence lorsque l'adaptativité hp est employée, (d) séparé les effets 1D et 2D dans la solution numérique et (e) exploré l'intérêt de considérer différentes variables pour effectuer l'inversion
The magnetotelluric (MT) method is a passive exploration technique that aims at estimating the resistivity distribution of the Earth's subsurface, and therefore at providing an image of it. This process is divided into two different steps. The first one consists in recording the data. In a second step, recorded measurements are analyzed by employing numerical methods. This dissertation focuses in this second task. We provide a rigorous mathematical setting in the context of the Finite Element Method (FEM) that helps to understand the MT problem and its inversion process. In order to recover a map of the subsurface based on 2D MT measurements, we employ for the first time in Mts a multi-goal oriented self adaptive hp-Finite Element Method (FEM). We accurately solve both the full formulation as well as a secondary field formulation where the primary field is given by the solution of a 1D layered media. To truncate the computational domain, we design a Perfectly Matched Layer (PML) that automatically adapts to high-contrast material properties that appear within the subsurface and on the air-ground interface. For the inversion process, we develop a first step of a Dimensionally Adaptive Method (DAM) by considering the dimension of the problem as a variable in the inversion. Additionally, this dissertation supplies a rigorous numerical analysis for the forward and inverse problems. Regarding the forward modelization, we perform a frequency sensitivity analysis, we study the effect of the source, the convergence of the hp-adaptivity, or the effect of the PML in the computation of the electromagnetic fields and impedance. As far as the inversion is concerned, we study the impact of the selected variable for the inversion process, the different information that each mode provides,and the gains of the DAM approach
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4

Zhang, Ai Jun. "Modelling and inversion of two-dimensional magnetotelluric data." Thesis, University of Edinburgh, 1988. http://hdl.handle.net/1842/14717.

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5

Lu, Xinyou. "Inversion of controlled-source audio-frequency magnetotelluric data /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/6799.

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6

Wilhelms, Wenke. "Development of a three-dimensional all-at-once inversion approach for the magnetotelluric method." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2016. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-207548.

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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.
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7

Ulugergerli, Emin Ugur. "Development and application of 2D magnetotelluric inversion in complex domain." Thesis, University of Leicester, 1998. http://hdl.handle.net/2381/30430.

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The magnetotelluric method is widely used in the investigation of the geo-electric structure of the earth. The field data are traditionally inverted to reveal the subsurface structure solved using regularised iterative inversion techniques. These interpretation schemes effect matrix computations in real domain due to operational simplicity. The speed of convergence of these techniques is controlled by the calculation type and the size of the program or more specifically, size of the matrices used. A common problem encountered when dealing with real matrices in 2D regularised inversion is their huge size. To partly overcome this problem, a new inversion strategy using complex singular value decomposition techniques has been successfully developed. The use of analytical partial derivatives and a variety of problem regularization measures ensure that the scheme is stable and rapidly convergent. In this method, instead of using the Cagniard apparent resistivity and phase, the frequency normalised impedance is adopted as the interpretative data functions for improved model resolution. Sample applications to several synthetic and to field data from Parnaiba Basin in Brazil proved successful and are presented in this thesis. It is also found that the complex form of the data-space and parameter-space eigenvectors contain information on parameter resolution. Suggestions are made for further studies especially of methods of improving parameter resolution in 2D inversion.
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8

Shan, Chunling. "Natural and Controlled Source Magnetotelluric Data Processing and Modeling." Doctoral thesis, Uppsala universitet, Geofysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-229917.

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In this thesis, four studies using different geophysical electromagnetic methods are presented. In the first study dealing with airborne measurements, the noise response due to the rotation of the aircraft and the aircraft itself as a metallic conductive body on the Earth's electromagnetic response in very low frequency and low frequency band was investigated. The magnetic fields are independent of the aircraft in the VLF band and part of the LF band. But at higher frequencies (above 100 kHz), the signals are more influenced by the aircraft. The aircraft also generates its own noise frequencies which are mixed with the radio transmitter signals. The second and third studies are applications of radio-, controlled source-magnetotellurics and electrical resistivity tomography methods at a quick-clay landslide site in southwest Sweden. The data are processed and modeled in 2D and 3D, and the models are compared with high-resolution seismic and geotechnical data. The obtained results were further validated and refined by performing synthetic tests in the second study. The third study shows that the 3D models provide larger and more continuous volume of the quick clay structure than traditional 2D models. Both studies have shown that integrated application of geophysical methods for landslides is ideal. Quick clays often overlie the coarse-grained layers showing an increase of resistivity values in the models. In the fourth study, a new audio magnetotelluric data acquisition technique is developed and is named moving magnetotellurics (MMT). In this new technique, the magnetic sensors are placed on the ground and only 15 to 20 minutes data are acquired for each station, which usually is enough to cover the frequency range 30-300 Hz. The new technique is more efficient and convenient than the traditional magnetotelluric method, and test measurements have shown that it is an applicable method in shallow depth studies.
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9

Yan, Ping. "Inversion of Magnetotelluric Data Constrained by Borehole Logs and Reflection Seismic Sections." Doctoral thesis, Uppsala universitet, Geofysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-303498.

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This thesis presents two new algorithms for doing constrained Magnetotelluric (MT) inversion based on an existing Occam 2D inversion program. The first algorithm includes borehole resistivity logs as prior information to constrain resistivity directly in the vicinity of boreholes. The second algorithm uses reflection seismic data as prior constraints to transfer structural information from seismic images to 2D resistivity models. These two algorithms are efficient (proved through tests of synthetic examples) and widely applicable. In this thesis, they have been successfully applied to the COSC (Collisional Orogeny in the Scandinavian Caledonides) MT data. The COSC project aims to study the mountain belt dynamics in central Sweden by drilling two 2.5 km deep boreholes. MT data were collected to locate the main décollement that separates the overlying Caledonian allochthons and the underlying Precambrian basement, as the main décollement is associated with very conductive Alum shale. The previous interpretation based on part of the COSC seismic profile (CSP) was that the main décollement was located along a reflection with depth of 4.5 km underneath Åre and ~3 km underneath Mörsil, in central Jämtland. The MT resistivity model reveals a very conductive layer in the central and western parts of the profile, the top of which coincides with the first seismic reflection. This means that the first conductive alum shale layer occurs at less than 1 km depth, supporting a new interpretation of the main décollement at shallower depth. In a re-interpretation of the CSP data based on the MT model, the main décollement occurs a few hundred metres below the top of the conductor and is coincident with a laterally continuous seismic reflection. Further, the overlying seismic reflections resemble imbricated alum shale of the Lower Allochthon. MT inversion using seismic constraints from CSP gives further support to the new interpretation. Moreover, MT investigations were conducted in the Alnö alkaline and carbonatite ring-intrusion complex in Sweden. 2D and 3D resistivity models inverted from MT data together with resistivity and porosity laboratory measurements delineate a fossil magma chamber as a resistive anomaly surrounded by electrically conductive up-doming and ring-shaped faults and fractures.
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Chen, Xiaoming [Verfasser], and Ute [Akademischer Betreuer] Weckmann. "Two-dimensional constrained anisotropic inversion of magnetotelluric data / Xiaoming Chen. Betreuer: Ute Weckmann." Potsdam : Universitätsbibliothek der Universität Potsdam, 2012. http://d-nb.info/1029243824/34.

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11

Zbinden, Dominik. "Inversion of 2D Magnetotelluric and Radiomagnetotelluric data with Non-Linear Conjugate Gradient techniques." Thesis, Uppsala universitet, Geofysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-256900.

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I implemented and tested the method of Non-Linear Conjugate Gradients (NLCG) to invert magnetotelluric (MT) and radiomagnetotelluric (RMT) data in two dimensions. The forward problem and the objective function gradients were computed using finite-difference methods. The NLCG algorithm was applied to three field data sets to test the performance of the code. It was then compared to the inversion techniques of Occam and damped Occam considering the quality of the output resistivity models and the computation times. The implemented code was further investigated by testing two line search techniques to reduce the objective function along a given search direction. The first line search procedure was constrained to the first Wolfe condition, leading to a rather inexact line search. The second, more thorough line search, was additionally constrained to the second Wolfe condition. Three preconditioners were applied to the NLCG algorithm and their performance was analysed. The first preconditioner was set to the diagonal of the approximate Hessian matrix and updated every 20-th iteration. Preconditioners two and three were updated with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm using the identity matrix and the diagonal of the approximate Hessian matrix as start preconditioners, respectively. The tests showed that the method of NLCG is more efficient pertaining to computation times compared to the Gauss-Newton (GN) based techniques (Occam and damped Occam). For the two smaller data sets that were inverted, the NLCG inversion was two to four times faster than Occam and damped Occam. For the larger data set, the NLCG inversion converged more than one order of magnitude faster than the GN based inversion techniques. This is because GN methods require to evaluate the entire sensitivity matrix to update the model, whereas NLCG only needs to compute a matrix-vector product of the Jacobian. Moreover, expensive operations such as matrix products and direct inversions of linearised systems are avoided by NLCG. A limitation of the NLCG algorithm is that it is prone to converge to local minima due to the fixed Lagrange multiplier that is used in the penalty function. Occam inversion, which determines the optimal Lagrange multiplier as part of the inversion, did not show such problems. The line search tests of the NLCG algorithm showed that an inexact line search yields higher convergence per CPU time than a more exact line search. In accordance to previous studies, preconditioning accelerated the convergence of the NLCG algorithm considerably. The preconditioners updated with the BFGS algorithm achieved highest convergence. Choosing the identity matrix as a start preconditioner led to fast but unstable convergence. The reasons for that could not be determined completely. Taking the diagonal of the approximate Hessian as a start preconditioner instead of the identity matrix led to slower convergence for most of the inversion tests, but convergence could be stabilised. All the tests performed within this project led to a robust implementation of the NLCG algorithm. A default set-up pertaining to line search and preconditioning could be established. However, the NLCG set-up can be adjusted by the user to improve convergence for a specific data set. This makes the algorithm implemented in this thesis more flexible than previously introduced NLCG codes. Preconditioning can certainly still be improved with further tests. Moreover, a future project will be to extend the 2D code to 3D, where NLCG should perform especially well, because the number of model parameters is usually higher in 3D.
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12

Mackie, Randall Lee. "Three-dimensional magnetotelluric modeling and inversion with applications to the California Basin and Range Province." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/13753.

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13

Bjänndal, Erik. "Geophysical investigation of the Arvidsjaur volcanics and the Archean-Proterozoic boundary." Thesis, Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-72632.

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In this work the magnetic and magnetotelluric (MT) geophysical methods have been used to produce two 3D models for the Laver area in southern Norrbotten. A new discovery of a porphyry copper deposit located at the Lill-Laverberget was reported by Boliden in 2012. The goal with the models is to form a better understanding of the setting for the porphyry deposit and to see if any of the geophysical methods are suited to be used in exploration for it. For starters an edge detector (Beiki, 2010) was used on magnetic data to identify structures and petrological contacts in the area. The magnetic data was modelled using the SimPEG (Cocket, et al., 2015) inversion software to create a 3D model over the area. The Magnetic method quite clearly managed to resolve the volcanic units in the Laver area. MT data was collected during fieldwork in September of 2018 and modelled using the MOD3DEM (Egbert & Kelbert, 2012) inversion software. The MT model did not show any clear anomalies that could be related to the deposit.
I detta arbete så har de magnetiska och magnetotelluriska (MT) geofysiska metoderna används för att skapa två 3D modeller över Laverområdet i södra Norrbotten. I området finns en porfyrkopparfyndighet som Boliden rapporterade in 2012. Målet med båda modellerna är att fördjupa förståelsen för bildningsmiljön för fyndigheten och för att se hur lämpade de geofysiska metoderna är för prospektering. Det första steget var att använda befintliga magnetiska data och processa den med ED funktionen (Beiki, 2010) för att identifiera strukturer och bergartskontakter i området. Den magnetiska data användes för att producera en 3D modell med inversionsprogrammet SimPEG (Cocket, et al., 2015). Denna modell kunde skilja mellan vulkaniska och övriga bergarter i området. Magnetotelluriska data samlades in i september 2018 och modellerades med MOD3DEM (Egbert & Kelbert, 2012), denna modell hade dock problem att finna anomalier i området.
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14

Cherevatova, M. (Maria). "Electrical conductivity structure of the lithosphere in western Fennoscandia from three-dimensional magnetotelluric data." Doctoral thesis, Oulun yliopisto, 2014. http://urn.fi/urn:isbn:9789526207100.

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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
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15

Mohammadi, Soroor. "Processing and Modeling of Gravity, Magnetic and Electromagnetic Data in the Falkenberg Area, Sweden." Thesis, Uppsala universitet, Geofysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-232714.

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Falkenberg area is located in southwest Sweden formed in the Sveconorwegian orogen and contains an extremely complex geological structure. Multiple geophysical datasets have been acquired and together with available petrophysical information, models corresponding to the subsurface geological structures were generated. The collected data comprise ground magnetic, AMT (Audio Magnetotelluric) and RMT (Radio Magnetotelluric) data. The available airborne magnetic and ground gravity data acquired by the Geological Survey of Sweden (SGU) as well as the reflection seismic section from a study made by Uppsala University further aids in obtaining substantially improved interpretation of the geometry of the structures along the AMT profile. The principal objective of this profile was to delineate and map the possible deformation zone crossed by the profile. The AMT study was expected to complement existing geophysical data and improve existing interpretations. The Ullared deformation zone contains decompressed eclogite facies rocks. The presented results were obtained by comparison of different geophysical methods along the profile. The susceptibility model and resistivity model show that eclogites have higher resistivity and susceptibility than the surrounding structures. However use of the Occam type of inversion on the AMT data, makes the resistivity model smoother than the susceptibility model and as a results it is difficult to estimate the dip of the structures. The AMT profile and the seismic section show the same dip direction (NE) for the eclogite bearing structures although due to the smoothing in the AMT model the dips seen in the seismic section cannot be recovered in the resistivity model.
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16

Plasman, Matthieu. "Rupture lithosphérique continentale dans le rift Africain : apport de l'inversion conjointe." Thesis, Brest, 2017. http://www.theses.fr/2017BRES0029/document.

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L'inversion conjointe géophysique est la méthode la plus efficace pour imager l'intérieur de la Terre. En intégrant plusieurs techniques géophysiques elle permet de réduire les incertitudes inhérentes à chacune et ainsi améliorer la compréhension de la Terre. Dans cette étude, nous utilisons les techniques des fonctions récepteur (RF) en sismologie, de la magnétotellurique (MT) et de la gravimétrie qui permettent de caractériser respectivement la vitesse des ondes S, la résistivité électrique et la densité du sous-sol.Le but de ce travail de recherche se divise en deux parties: une première, méthodologique, sur le développement d'une nouvelle approche d'inversion conjointe en 3D et une deuxième avec l'application de ces techniques (en approche jointe ou séparée) sur la Divergence Nord Tanzanienne pour mieux comprendre le phénomène de rupture continentale. Pour la partie méthodologie deux approches ont été développées : une entre les données de MT et de gravimétrie avec un calcul original de l'effet gravimétrique de la topographie qui permet de réduire le nombre de mailles tout en gardant une résolution satisfaisante ; et une deuxième méthode entre les données de MT et de RF par une nouvelle approche d'extrapolation des modèles 1D de vitesse en pseudo modèle 3D de vitesse. L'application de ces techniques sur la Tanzanie a permis de mettre en évidence un certain nombre de structures lithosphériques dont deux zones majeures à faible vitesse dans la croûte inférieure et dans le manteau supérieur. Cette dernière semble refléter des interactions entre des structures héritées d'âge protérozoïque et le panache mantellique Africain
Geophysical joint inversion attempts to reproduce as best as possible the interior of the Earth. By integrating several geophysical techniques the joint inversion reduces the uncertainties of each methods and improves our understanding of the Earth structure. In this study we use the receiver functions (RF), the magnetotelluric (MT) and the gravity methods which enable to charaterize the Swave velocity, the electrical resistivity and the density, respectively. The objective of this research work is divided in two parts; first with the development of a new 3D joint inversion approach and then with the application of these methods (on a joint or separate approach) on the North Tanzanian Divergence to better understand the continental breakup.For the methodologic part two approaches have been developed; one between the MT and gravity data with an original computation of the topographic effect which decreases the number of cells while keeping a satisfaying resolution. And a second method between the MT and RF data where pseudo 3D velocity model are created and combined with the MT models to better takes into account the physical properties of the receiver function. The application of these methods on the Tanzania highlighted several lithospheric structures and particularly two low-velocity areas in the lower crust and the upper mantle. This latter suggests interactions with Proterozoic inherited structures and the African plume material
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17

Wittke, Jan [Verfasser], Bülent [Gutachter] Tezkan, Klaus [Gutachter] Spitzer, and Becken [Gutachter] Michael. "Meshless methods for Maxwell’s equations with applications to magnetotelluric modelling and inversion / Jan Wittke ; Gutachter: Bülent Tezkan, Klaus Spitzer, Becken Michael." Köln : Universitäts- und Stadtbibliothek Köln, 2017. http://d-nb.info/1148623698/34.

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18

Meqbel, Naser Mohammad Meqbel [Verfasser]. "The electrical conductivity structure of the Dead Sea Basin derived from 2D and 3D inversion of magnetotelluric data / Naser Mohammad Meqbel Meqbel." Berlin : Freie Universität Berlin, 2009. http://d-nb.info/1023785021/34.

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19

Ars, Jean-Michel. "Inversion conjointe géophysique appliquée à l'exploration en géothermie profonde dans le Massif Central." Thesis, Brest, 2018. http://www.theses.fr/2018BRES0025.

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Le développement de l’énergie géothermique a conduit à l’exploitation de ressources établies dans des contextes géologiques et géodynamiques très variés. L’exploration géophysique de ces réservoirs complexes nécessite l’utilisation de plusieurs méthodes d’imagerie complémentaire. Ce travail de thèse porte sur l’exploration d’une ressource géothermique située en contexte de socle fracturé dans le Massif Central français par magnétotellurique, tomographie de bruit ambiant et gravimétrie.La magnétotellurique est une méthode d’imagerie 3D résolvante qui est sensible à la présence d’eau et aux argiles d’altération hydrothermale mais limitée par sa couverture spatiale. La tomographie de bruit sismique présente une bonne résolution verticale mais ne résout pas les variations horizontales de vitesse. Cette méthode est sensible aux variations des propriétés mécaniques des roches et donc aux milieux fracturés. Enfin la gravimétrie apporte une contrainte sur les variations lithologiques et possède une bonne résolution latérale mais une faible résolution verticale.Nous présentons une méthode d’inversion conjointe des données sismiques et gravimétriques sous contrainte d’un modèle de résistivité obtenu par inversion magnétotellurique indépendante. L’inversion conjointe nécessite de définir des couplages entre modèles. Par absence de connaissance a priori de relations pétrophysiques, nous avons couplé les modèles de densité, de résistivité et de vitesse avec une loi qui contraint les paramètres à être corrélés en moyenne. Cette stratégie vise à faire ressortir des relations caractéristiques des objets géologiques de la ressource géothermique.Cette méthodologie d’inversion conjointe a été testée sur des modèles synthétiques. L’application aux données réelles acquises dans le Massif Central a permis de définir une zone en profondeur de forte corrélation interprétée comme la transition ductile fragile. La partie intermédiaire des modèles, plus homogène, permet de distinguer différentes unités géologiques séparées par une zone de faille. Enfin la partie superficielle se distingue par une forte hétérogénéité des paramètres résultants probablement de processus d’altération de surface
The development of geothermal energy has led to the exploitation of resources established in varied geological and geodynamic contexts. Geophysical exploration of these complex reservoirs requires the use of several complementary imaging methods. This PhD thesis focuses on the exploration of a geothermal resource located within the fractured basement in the French Massif Central using magnetotelluric, ambient noise tomography and gravimetry. Magnetotelluric is a 3D imaging method with a good resolution power that is sensitive to the presence of water and hydrothermal weathering clays but is limited by its spatial coverage. Seismic noise tomography has a good vertical resolution but does not resolve well horizontal velocity variations. This method is sensitive to variations of the mechanical properties of rocks and thus to fractured media. Finally gravimetry brings constraint on the lithological variations and has a good lateral resolution but lacks vertical resolution.We present a method of joint inversion of seismic and gravimetric data under the constraint of a resistivity model obtained by independent magnetotelluric inversion. Joint inversion requires defining model couplings. By lack of prior knowledge of petrophysical relationships, we have coupled the density, resistivity and velocity models with a law that constraints the parameters to be correlated on average.This strategy aims to bring out the characteristic relationships of the geological objects of the geothermal resource. This joint inversion methodology has been tested on synthetic models. The application to the real data acquired in the Massif Central has made it possible to define a deep zone of high correlation interpreted as the fragile ductile transition. The intermediate part of the models, more homogeneous, allows to distinguish different geological units separated by a fault zone. Finally the superficial part is distinguished by strong heterogeneity of the parameters resulting probably from surface alteration process
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20

Ismail, Nazli. "Controlled Source Radiomagnetotelluric (CSRMT) Applications in Environmental and Resource Exploration." Doctoral thesis, Uppsala universitet, Geofysik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-102750.

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An integrated use of radio magnetotelluric (RMT) and controlled source tensor magnetotelluric (CSTMT) measurements, the so-called CSRMT method, has been employed in environmental and resource exploration studies. A number of case histories, including a groundwater investigation in glacial deposits, a study of fracture zones for geotechnical purposes and a mining exploration study of a copper deposit, are presented in this thesis in order to illustrate the usefulness and capability of the CSRMT method. The resolutions of the estimated models using various types of data are studied. Magnetotelluric transfer functions are used to analyze the dimensionality, the near surface resistivity distortions and the near field effects in the case of CSTMT data analysis. The near field effects in CSTMT data have also been identified by performing 2½D forward modelling. Data analysis, dimensionality tests and forward modelling show that at the lowest frequencies used the CSTMT transfer functions are generally distorted by source effects, except when the source-receiver distances are sufficient large compared with the penetration depth. Regarding CSTMT transfer functions, apparent resistivities are generally less distorted than phases. TM mode transfer functions are more affected by the sources than TE mode, while tipper vectors generally contain source signatures at all frequencies. Based on the analysis of dimensionality and source effects 2D inverse modelling of CSTMT and RMT data, as well as their combination, have been performed under the plane wave assumption. The RMT method proved to be a powerful tool for imaging the upper 50 m near-surface, but their penetration depth reduces as a conductive layer structures cover the targets at depth. The penetration depth can be increased by including the CSTMT data in the modelling if the measurements are in the far field range. The resolution of the deeper parts of the models may be improved by performing a joint inversion of TE and TM modes, if the strike direction is well-defined. Alternatively, inversion of determinant data can be performed, since the determinant data are less affected by 3D structures and source effects. However the resolution of the determinant models is somewhat degraded compared to the models inverted from combined TE and TM modes.
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21

Galiana, Blanch Savitri. "Two-dimensional modeling and inversion of the controlled-source electromagnetic and magnetotelluric methods using finite elements and full-space PDE-constrained optimization strategies." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/400616.

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The controlled-source electromagnetics (CSEM) and magnetotellurics (MT) methods are common geophysical tools for imaging the Earth's electrical interior. To appreciate measured data, both methods require forward and inverse modeling of the subsurface with the ultimate goal of finding a feasible model for which the simulated data reasonably fits the observations. The goodness of this fit depends on the error in the measured data, on the numerical error and on the degree of approximation inferred by numerical modeling. Therefore, active research focuses on new methods for modeling and inversion to improve accuracy and reliability for increasingly complex scenarios. In a first step, physical factors such as anisotropy, topography and realistic sources must be taking into account. Second, numerical methods need to be assessed in terms of solution accuracy, time efficiency and memory demand. The finite elements (FE) methods offer much flexibility in model geometry and contain quality control mechanisms for the solution, as shape function order and adaptive mesh refinement. Most emerging modeling programs are based on FE, however, inversion programs are generally based on finite differences (FD) or integral equation (IE) methods. On the other hand, inverse modeling is usually based on gradient methods and formulated in the reduced-space, where the electrical conductivity is the only optimization variable. Originally, the inverse problem is stated for the EM fields and the conductivity parameter (in the full-space), and constrained by governing partial differential equations (PDEs). The reduced-space strategy eliminates the field variables by applying equality constraints and solves then, the unconstrained problem. A common drawback of this is the repeated costly computation of the forward solution. Solving the PDE-constrained optimization problem directly, in the full-space, has the advantage that it is only necessary to exactly solve the PDEs at the end of the optimization, but it comes at the cost of a larger number of variables. This thesis develops a robust and versatile adaptive unstructured mesh FE program to model the total field for two-dimensional (2-D) anisotropic CSEM and MT data, allowing for arbitrarily oriented, three-dimensional (3-D) sources, for which a two-and-a-half-dimensional (2.5-D) approximation is employed. The formulations of the problems in a FE framework are derived for isotropic and anisotropic subsurface conductivity structures. The accuracy of the solution is controlled and improved by a goal-oriented adaptive mesh refinement algorithm. Exhaustive numerical experiments validate the adaptive FE program for both CSEM and MT methods and on land and marine environments. The influence of the model dimensions, mesh design and order of shape functions on the solution accuracy is studied and notably, an outperformance of quadratic shape functions is found (compared to linear and cubic). Several examples demonstrate the effect of complex scenarios on EM data. In particular, we study the distortion caused by: the bathymetry, the orientation and geometry of the sources and the anisotropy, considering vertical and dipping cases. All examples showcase the importance of adequate consideration of these very common physical features of real world data. Further, a formulation for the 2.5-D CSEM inversion as a PDE-constrained optimization in full-space is derived within a FE framework following two strategies: discretize-optimize and optimize-discretize. The discretize-optimize formulation is implemented using a general purpose optimization algorithm. Two examples, a canonical reservoir model and a more realistic marine model with topography, demonstrate the performance of this inversion scheme, recovering in both cases the model’s main structures within an acceptable data misfit. Finally, the optimize-discretize formulation is derived in a FE framework, as a first step towards a development of an inversion scheme using adaptive FE meshes.
[cat] El mètode de font electromagnètica controlada (CSEM) i el mètode magnetotel.lúric (MT) són tècniques geofísiques usades habitualment per obtenir una imatge de les propietats elèctriques del subsòl terrestre i s'utilitzen independentment, conjuntament i en combinació amb altres tècniques geofísiques. Per poder interpretar les dades, ambdós mètodes necessiten la modelització directa i inversa de la conductivitat elèctrica del subsòl amb l'objectiu final d'obtenir un model coherent per al qual les dades simulades s'ajustin de forma raonable a les observacions. Naturalment, la qualitat d'aquest ajust no només depèn de l'error en les dades mesurades i de l'error numèric, sinó també del grau en l'aproximació física inferit per la modelització numèrica. D'aquesta manera, les recerques actuals se centren a investigar noves metodologies per a la modelització i inversió, per tal d'obtenir models acurats i fiables de les estructures de la Terra en escenaris cada cop més complexos. Un primer pas és millorar les aproximacions en la modelització tenint en compte factors físics com ara l'anisotropia, la topografia o fonts més realistes. En segon lloc, per tal d'acomodar aquests factors en un programa de modelització i inversió i per poder tractar els conjunts de dades típicament llargs, els mètodes numèrics han de ser avaluats en termes de la precisió de la solució, l'eficiència en temps i la demanda en memòria. Els mètodes de modelització en elements finits (FE) són coneguts per oferir una major flexibilitat en la modelització de la geometria i contenen mecanismes de control de la solució, com ara l'ordre de les funcions forma i la tècnica de refinament adaptatiu de la malla. La majoria de programes de modelització emergents estan basats en els FE, i mostren avantatges significatius, però gairebé tots els programes de modelització inversa, encara avui dia, estan basats en el mètode de les diferències finites (FD) o en el mètode de l'equació integral (IE). A més a més, la modelització inversa desenvolupada per a dades electromagnètiques (EM) es basa generalment en mètodes del gradient i es formula en un espai reduït, on les úniques variables d'optimització són els paràmetres del model, és a dir, la conductivitat elèctrica del subsòl. Originalment, el problema invers es formula per als camps EM i per al paràmetre conductivitat, i està constret per les equacions diferencials en derivades parcials (PDEs) que governen les variables camps EM. L'estratègia d'espai reduït elimina les variables camps aplicant lligams d'igualtat i soluciona, doncs, el problema no constret en l'espai reduït dels paràmetres del model. Un desavantatge general d'aquests mètodes és la costosa repetició del càlcul de la solució del problema directe i de la matriu jacobiana de sensibilitats (per mètodes basats en Newton). D'altra banda, també és possible de solucionar el problema invers en l'espai complet de les variables camps EM i del paràmetre conductivitat. Solucionar-hi el problema d'optimització constret per les PDEs té l'avantatge que només és necessari de solucionar exactament el problema directe al final del procés d'optimització, però això comporta el cost addicional de tenir moltes més variables d'optimització i de la presència de lligams d'igualtat. També, en particular, en el marc dels FE, el problema d'optimització constret per les PDEs té l'avantatge afegit d'incloure tècniques sofisticades pròpies dels FE en el procés d'inversió, com ara el refinament adaptatiu de la malla. Aquesta tesi desenvolupa un programa robust i versàtil amb FE i malles irregulars adaptatives per modelar numèricament el camp total de dades CSEM i MT bidimensionals (2D) i anisòtropes, que permet l'ús de fonts tridimensionals (3D) orientades arbitràriament. Per tal de representar fonts CSEM 3D en un model físic 2D, s'utilitza una aproximació dos i mig dimensional (2.5D). Les formulacions FE es deriven per a ambdós mètodes, per a estructures de conductivitat del subsòl isòtropes i anisòtropes. Encara que el cas anisòtrop no és general, inclou anisotropia vertical i de cabussament. La precisió en la solució es controla i millora amb un algoritme de refinament adaptatiu de la malla utilitzant mètodes d'estimació de l'error a posteriori. Una sèrie exhaustiva d'experiments numèrics valida el programa de FE adaptatius per ambdós mètodes, CSEM i MT, i en escenaris terrestres i marins. S'estudia la influència de les dimensions del model, del disseny de la malla i de l'ordre de les funcions forma en l'exactitud de la solució i es troba un comportament notablement superior de les funcions forma quadràtiques comparades amb les lineals o cúbiques. Diferents exemples mostren l'efecte d'escenaris complexos sobre les dades EM, en particular, un model amb batimetria, un model terrestre i un de marí amb fonts orientades i de dimensió finita, un medi amb anisotropia vertical amb un reservori encastat i un altre amb un reservori encastat en una estructura anticlinal. Aquests exemples demostren la importància de considerar adequadament (en termes de modelització directa) característiques físiques com la topografia, l'orientació i geometria de la font i l'anisotropia del medi, que sovint es troben en mesures reals. Juntament amb això, es deriva una formulació per al problema invers 2.5D CSEM com una optimització constreta per les PDEs en l'espai complet i en un marc de FE, seguint dues estratègies diferents: discretització-optimització i optimització-discretització. L'estratègia de discretització-optimització considera que el problema invers es troba en forma discretitzada i deriva les condicions d'optimitat de la Lagrangiana i el pas de Newton. Contràriament, l'aproximació optimització-discretització deriva primer les condicions d'optimitat i el pas de Newton o una aproximació d'aquest, i després discretitza les equacions resultants. La implementació de la formulació discretització-optimització es mostra en dos exemples, un model canònic de reservori i un model marí més realista amb topografia, utilitzant un programa d'optimització de propòsit general, que és una implementació d'un algoritme de programació quadràtica seqüencial (SQP). Encara que no s'utilitza una regularització explícita, l'ús de diferents malles per al paràmetre del model i per a les variables camps, permet recuperar les principals estructures del model i obtenir un ajust de les dades acceptable. Cal dir, però, que l'eficiència en temps i memòria del programa hauria de millorar-se. Finalment, el problema invers 2.5D CSEM es formula com un problema d'optimització constret per les PDEs en l'espai complet i en un marc de FE utilitzant una estratègia d'optimització-discretització i com un primer pas per al desenvolupament d'un esquema d'inversió que utilitzi malles adaptatives de FE.
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22

Tietze, Kristina [Verfasser]. "Investigating the electrical conductivity structure of the San Andreas fault system in the Parkfield-Cholame region, central California, with 3D magnetotelluric inversion / Kristina Tietze." Berlin : Freie Universität Berlin, 2012. http://d-nb.info/1030383065/34.

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23

Vadoodi, Roshanak. "Geophysical vectoring of mineralized systems in northern Norrbotten." Licentiate thesis, Luleå tekniska universitet, Geovetenskap och miljöteknik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-82408.

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The Fennoscandian Shield as a part of a large Precambrian basement area is located in northern Europe and hosts economically important mineral deposits including base metals and precious metals. Regional geophysical data such as potential field and magnetotelluric data in combination with other geoscientific data contain information of importance for an understanding of the crustal and upper mantle structure. Knowledge about regional-scale structures is important for an optimized search for mineralisation. In order to investigate in more detail the spatial distribution of regional electrically conductive structures and near-surface mineral deposits, complementary magnetotelluric measurements have been done within the Precambrian Shield in the north-eastern part of the Norrbotten ore province. The potential field data provided by the Geological Survey of Sweden have been included in the current study. Processing of magnetotelluric data was performed using a robust multi-remote reference technique. The dimensionality analysis of the phase tensors indicates complex 3D structures in the area. A 3D crustal model of the electrical conductivity structure was derived based on 3D inversion of the data using the ModEM code. The final inversion 3D resistivity model revealed the presence of strong crustal conductors with the conductance of more than 3000 S at depth of tens of kilometres within a generally resistive crust. A significant part of the middle crust conductors is elongated in directions that coincide with major ductile deformation zones that have been mapped from airborne magnetic data and geological fieldwork. Some of these conductors have near-surface expression where they spatially correlate with the locations of known mineralisation. Processing and 3D inversion of the regional magnetic and gravity field data were performed, and the structural information derived from these data by using an open-source object-oriented package code written in Python called SimPEG. In this study, a new approach is proposed to extract and analyse the correlation between the modelled physical properties and for domain classification. For this, a neural net Self-Organizing Map procedure (SOM) was used for data reduction and simplification. The input data to the SOM analysis contain resistivity, magnetic susceptibility, and density model values for some selected depth levels. The domain classification is discussed with respect to geological boundaries and composition. The classification is furthermore applied for prediction of favourable areas for mineralisation. Based on visual inspection of processed regional gravity and magnetic field data and a SOM analysis performed on higher-order derivatives of the magnetic data, an interpretation of a sinistral fault with 52 km offset is proposed. The fault is oriented N10E and can be traced 250 km from Karesuando at the Swedish-Finish border southwards to the Archaean-Proterozoic boundary marked by the Luleå-Jokkmokk Zone.
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Wilhelms, Wenke [Verfasser], Klaus [Akademischer Betreuer] Spitzer, Klaus [Gutachter] Spitzer, Michael [Gutachter] Eiermann, and Dmitry [Gutachter] Avdeev. "Development of a three-dimensional all-at-once inversion approach for the magnetotelluric method / Wenke Wilhelms ; Gutachter: Klaus Spitzer, Michael Eiermann, Dmitry Avdeev ; Betreuer: Klaus Spitzer." Freiberg : Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2016. http://d-nb.info/1220912778/34.

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Hering, Philip [Verfasser], Andreas [Akademischer Betreuer] Junge, Colin [Akademischer Betreuer] Brown, Andreas [Gutachter] Junge, and Colin [Gutachter] Brown. "Advances in magnetotelluric data processing, interpretation and inversion, illustrated by a three-dimensional resistivity model of the Ceboruco volcano / Philip Hering ; Gutachter: Andreas Junge, Colin Brown ; Andreas Junge, Colin Brown." Frankfurt am Main : Universitätsbibliothek Johann Christian Senckenberg, 2019. http://d-nb.info/1226180604/34.

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26

Dosso, Stanley Edward. "Inversion and appraisal for the one-dimensional magnetotellurics problem." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/30692.

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The method of magnetotellurics (MT) uses surface measurements of naturally-occurring electromagnetic fields to investigate the conductivity distribution within the Earth. In many interpretations it is adequate to represent the conductivity structure by a one-dimensional (1-D) model. Inferring information about this model from surface field measurements is a non-linear inverse problem. In this thesis, linearized construction and appraisal algorithms are developed for the 1-D MT inverse problem. To formulate a linearized approach, the forward operator is expanded in a generalized Taylor series and second-order terms are neglected. The resulting linear problem may be solved using techniques of linear inverse theory. Since higher-order terms are neglected, the linear problem is only approximate, and this process is repeated iteratively until an acceptable model is achieved. Linearized methods have the advantage that, with an appropriate transformation, a solution may be found which minimizes a particular functional of the model known as a model norm. By explicitly minimizing the model norm at each iteration, it is hypothesized that the final constructed model represents the global minimum of this functional; however, in practice, it is difficult to verify that a global (rather than local) minimum has been found. The linearization of the MT problem is considered in detail in this thesis by deriving complete expansions in terms of Fréchet differential series for several choices of response functional, and verifying that the responses are indeed Fréchet differentiable. The relative linearity of these responses is quantified by examining the ratio of non-linear to linear terms in order to determine the best choice for a linearized approach. In addition, the similitude equation for MT is considered as an alternative formulation to linearization and found to be inadequate in that it implicitly neglects first-order terms. Appropriate choices of the model norm allow linearized inversion algorithms to be formulated which minimize a measure of the model structure or of the deviation from a (known) base model. These inversions construct the minimum-structure and smallest-deviatoric model, respectively. In addition, minimizing I₂ model norms lead to smooth solutions which represent structure in terms of continuous gradients, whereas minimizing I₁ norms yield layered conductivity models with structural variations occurring discontinuously. These two formulations offer complementary representations of the Earth, and in practice, a complete interpretation should consider both. The algorithms developed here consider the model to be either conductivity or log conductivity, include an arbitrary weighting function in the model norm, and fit the data to a specified level of misfit: this provides considerable flexibility in constructing 1-D models from MT responses. Linearized inversions may also be formulated to construct extremal models which minimize or maximize localized conductivity averages of the model. These extremal models provide bounds for the average conductivity over the region of interest, and thus may be used to appraise model features. An efficient, robust appraisal algorithm has been developed using linear programming to extremize the conductivity averages. For optimal results, the extremal models must be geophysically reasonable, and bounding the total variation in order to limit unrealistic structure is an important constraint. Since the extremal models are constructed via linearized inversion, the possibility always exists that the computed bounds represent local rather than global extrema. In order to corroborate the results, extremal models are also computed using simulated annealing optimization. Simulated annealing makes no approximations and is well known for its inherent ability to avoid unfavourable local minima. Although the method is considerably slower than linearized analysis, it represents a general and interesting new appraisal technique. The construction and appraisal methods developed here are illustrated using synthetic test cases and MT field data collected as part of the LITHOPROBE project. In addition, the model construction techniques are used to analyze MT responses measured at a number of sites on Vancouver Island, Canada, to investigate the monitoring of local changes in conductivity as a precursor for earthquakes. MT responses measured at the same site over a period of four years are analyzed and indicate no significant changes in the conductivity (no earthquakes of magnitude greater than 3.0 occurred in this period). Conductivity profiles at a number of sites are also considered in an attempt to infer the regional structure. Finally, a method of correcting linearized inversions is developed. The corrections consist of successively approximating an analytic expression for the linearization error. The method would seem to represent a novel and practical approach that can significantly reduce the number of linearized iterations. In addition, a correspondence between the correction steps and iterations of the modified Newton's method for operators is established.
Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate
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García, Juanatey María de los Ángeles. "Seismics, 2D and 3D Inversion of Magnetotellurics : Jigsaw pieces in understanding the Skellefte Ore District." Doctoral thesis, Uppsala universitet, Geofysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-178060.

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The Skellefte District (SD) is one of the richest metallogenic mining areas in Sweden. The main deposits consist of volcanic-hosted massive sulphides (VHMS) rich in zinc, copper, lead, gold and silver, that have been explored and mined for more than a century. Considering that technological advancements allow deeper mining, and that today new discoveries rarely occur, renewed efforts are now directed at locating targets at greater depths.   Thus, current exploration strategies need to be adapted, and a better understanding of regional scale structures is necessary. To address these questions the project VINNOVA 4D modeling of the Skellefte District was launched. Its main purpose is to unravel the regional structures and tectonic setting of the SD. To accomplish this, new geological and geophysical data have been acquired in two key localities. This thesis presents the contribution from 2D and 3D inversion of magnetotelluric (MT) data and seismic reflection data. The main findings include: conductive hydrothermally altered zones within the otherwise resistive rocks of the Skellefte Group, the depth extension of early and postorogenic intrusions, prominent shear zones in the central part of the district, and enhanced reflectivity and conductivity at the base of the Skellefte Group throughout the SD. Even though the application of these methods is challenged by the complex geological setting of the SD, it is shown that after a careful processing and analysis of the data, they are able to provide a robust image of the deep subsurface. Additionally, the combination of reflection seismics and MT has proved to be a powerful tool for hypothesis testing and to develop the general understanding of the configuration and history of the SD. Furthermore, two 3D inversion models of MT data are presented and compared with the results of standard 2D determinant inversions. The 3D procedure shows significant improvements in data fit and is able to constrain better the observed model features. Although 3D inversion of MT data is not yet a run of the mill scheme and issues like model assessment and galvanic distortion effects need to be further addressed, results from complex environments with areal coverage, are already superior to those from 2D inversions.
Skellefteåfälten är ett av de viktigaste malmdistrikten i Sverige. Malmkropparna består av vulkaniskvärda Massiva Sulfider (VHMS) rika på Zink, Koppar, Bly, Guld och Silver, och har utforskats och brutits i mer än ett sekel. Med tanke på att de senaste tekniska framstegen tillåter djupare brytning, och att nya upptäckter är ovanliga idag, riktas nya ansträngningar mot att lokalisera malm på större djup. Aktuella prospekteringsstrategier måste därför anpassas, och en bättre förståelse av regionala strukturer är nödvändig. För att lösa dessa frågor lanserades projektet VINNOVA 4D modeling of the Skellefte District. Dess främsta syfte är att utreda de regionala strukturerna och det tektoniska läget av Skelleftefältet. För att uppnå detta, har nya geologiska och geofysiska data insamlats vid två viktiga platser i distriktet. Denna avhandling presenterar bidrag från inversionsmodellering i 2D och 3D av magnetotelluriska (MT) data samt resultaten av en reflektionsseismisk profil. De viktigaste resultaten är: bra ledande hydrotermiskt förändrade zoner inom de annars resistiva bergarterna i Skellefte-gruppen, djupet till tidiga och postorogeniska intrusioner, framstående skjuvzoner i den centrala delen av området, och ökad reflektionsförmåga och konduktivitet vid basen av Skellefte-gruppen i hela fältet. Även om tillämpningen av dessa metoder utmanas av fältens komplexa geologiska läge, visas det efter en noggrann bearbetning och analys av data att de ger en robust bild av den lite djupare berggrunden. Dessutom har kombinationen av reflektionsseismik och MT visat sig vara ett kraftfullt verktyg för hypotesprövning och för att utveckla den allmänna förståelsen av Skelleftefältet och dess historia. Därutöver presenteras två 3D inversionsmodeller av MT data och jämförs sedan med resultaten från 2D determinantinversioner. 3D tekniker visar betydande förbättringar av datapassform och begränsar observerade anomalier bättre. Även om 3D inversion av MT data ännu inte är en vanlig teknik och frågor som modellbedömning och galvaniska distorsionseffekter måste behandlas ytterligare, är resultat från komplexa miljöer med lagom yttäckning redan överlägsna.
VINNOVA 4D modeling of the Skellefte District
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Linde, Niklas. "Characterization of Hydrogeological Media Using Electromagnetic Geophysics." Doctoral thesis, Uppsala universitet, Geofysik, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5912.

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Radio magnetotellurics (RMT), crosshole ground penetrating radar (GPR), and crosshole electrical resistance tomography (ERT) were applied in a range of hydrogeological applications where geophysical data could improve hydrogeological characterization. A profile of RMT data collected over highly resistive granite was used to map subhorizontal fracture zones below 300m depth, as well as a steeply dipping fracture zone, which was also observed on a coinciding seismic reflection profile. One-dimensional inverse modelling and 3D forward modelling with displacement currents included were necessary to test the reliability of features found in the 2D models, where the forward models did not include displacement currents and only lower frequencies were considered. An inversion code for RMT data was developed and applied to RMT data with azimuthal electrical anisotropy signature collected over a limestone formation. The results indicated that RMT is a faster and more reliable technique for studying electrical anisotropy than are azimuthal resistivity surveys. A new sequential inversion method to estimate hydraulic conductivity fields using crosshole GPR and tracer test data was applied to 2D synthetic examples. Given careful surveying, the results indicated that regularization of hydrogeological inverse problems using geophysical tomograms might improve models of hydraulic conductivity. A method to regularize geophysical inverse problems using geostatistical models was developed and applied to crosshole ERT and GPR data collected in unsaturated sandstone. The resulting models were geologically more reasonable than models where the regularization was based on traditional smoothness constraints. Electromagnetic geophysical techniques provide an inexpensive data source in estimating qualitative hydrogeological models, but hydrogeological data must be incorporated to make quantitative estimation of hydrogeological systems feasible.
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Conway, Dennis. "Advances in Magnetotelluric Modelling: Time-Lapse Inversion, Bayesian Inversion and Machine Learning." Thesis, 2018. http://hdl.handle.net/2440/120299.

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This thesis presents advancements to the area of magnetotelluric (MT) modelling. There are three main aims to this work. The first aim is to implement an inversion to model time-lapse MT data in a temporal dimension. The algorithm considers the entire dataset at once, with penalisations for model roughness in both the spatial and temporal dimensions. The inversion is tested on synthetic data, as well as a case-study from a coal-seam gas dewatering survey. Second is to explore the problem of nonuniqueness in MT data inversion by implementing a 1D Bayesian inversion using an efficient sampler. The implemented model includes a novel way of regularising MT inversion by allowing the strength of smoothing to vary between different models. The Bayesian inversion is tested on synthetic and case-study datasets with results matching known data. The third aim is to implement a proxy function for the 3D MT forward function based on artificial neural networks. This allows for rapid evaluation of the forward function and the use of evolutionary algorithms to invert for resistivity structures. The evolutionary search algorithm is tested on synthetic data sets and a case-study data set from the Curnamona Province, South Australia. Together, these three novel algorithms and software implementations represent a contribution to the toolkit of MT modelling.
Thesis (Ph.D.) -- University of Adelaide, School of Physical Sciences, 2018
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Markovic, Milenko. "Joint inversion of magnetotelluric and seismic data for crustal characterization." Doctoral thesis, 2014. http://hdl.handle.net/10451/10955.

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Tese de doutoramento, Ciências Geofísicas e da Geoinformação (Geofisíca), Universidade de Lisboa, Faculdade de Ciências, 2014
The research that has been performed in this thesis contributes to integration two different geophysical methods (magnetotellurics and seismic refraction). Pattern recognition has not been used for the cooperative inversion of these two methods before. This study demonstrates potential of soft clustering methods for integration of two data sets. Gathering information from both inversions, a multiparameter model was made. This multi-parameter model contains regions, each of which is characterized by a consistent relationship between the model parameters. Both synthetic and field data results were used to discuss an assumption that mutual exchange of information can lead to better results of inversions in both cases. The method developed in this thesis was successfully applied at experimental data collected in the Iberian Pyrite Belt.
A investigação desenvolvida nesta tese é uma contribuição para a integração de dois métodos geofísicos (magneto-telúrico e sísmica de refracção). A técnica de reconhecimento de padrões não tinha sido ainda utilizada na inversão cooperativa de dados destes dois métodos. Este estudo mostra as potencialidades dos métodos de análise de “clusters” na integração dos dois conjuntos de dados.Um modelo “multi-parâmetros” foi desenvolvido para extrair informação de ambos os métodos geofísicos.Este modelo contém regiões caracterizadas por relações consistentes entre os parâmetros. Resultados obtidos com dados sintéticos e de campo foram usados para mostrar que o uso da informação contida nos dois conjuntos de dados conduz a melhores resultados. O método desenvolvido nesta tese foi aplicado, com resultados satisfatórios, a um conjunto de dados reais obtidos na Faixa Piritosa.
Fundação para a Ciência e Tecnologia (FCT, SFRH/BD/66455/2009)
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Thiel, Stephan. "Modelling and inversion of magnetotelluric data for 2-D and 3-D lithospheric structure, with application to obducted and subducted terranes." 2008. http://hdl.handle.net/2440/48492.

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The thesis presents the application of the magnetotelluric (MT) sounding method to image Earth’s crust in Oman and South Australia. The aim of these MT surveys is to provide constraints on the geological interpretation of emplacement scenarios and the tectonic evolution of the geological domain. The thesis concentrates on the methodological aspects of the MT technique, e.g. the data analysis and modelling of electromagnetic fields. The phase tensor approach by Caldwell et al. (2004) is applied to the data and provides insights into the dimensionality of the MT data in even complex and electrically distorted terranes. Modelling and inversion of the MT data is performed with various 2-D and 3-D codes to show how the interpretation of the data can benefit from multiple modelling approaches. Data collected in a 2-D survey across the Oman ophiolite mountains show complex behaviour and 2-D inversion and 3-D forward modelling resolve ambiguities in the emplacement scenario of the Oman ophiolite. It is believed that initial underthrusting of the Jurassic-Cretaceous oceanic lithosphere was followed by exhumation. Further oceanic thrusting subsequently led to rising of lower-plate eclogites and eventually gravitational collapse of the ophiolite onto the margin (Gray et al., 2000). The 3-D inversion code by (Siripunvaraporn et al., 2005a) was expanded to incorporate static shift corrections and inversion model misfits have therefore improved significantly compared to inversion models without static shift correction. 2-D and 3-D surveys across the South Australian Gawler Craton reveal deep crustal conductors which are connected to near surface mineralisation systems of the IOCG Olympic Dam deposit in the north-eastern part of the craton and the Au-dominated central Gawler Craton provinces.
Thesis (Ph.D.) -- University of Adelaide, School of Earth and Environmental Sciences, 2008
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Siripunvaraporn, Weerachai. "An efficient data-subspace two-dimensional magnetotelluric inversion and its application to high resolution profile across the San Andreas Faults at Parkfield, California." Thesis, 1999. http://hdl.handle.net/1957/29703.

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Simpson, Janelle Maree. "Understanding interpretation limitations due to MT inversion variability: examples from the Mount Isa Province, Queensland, Australia." Thesis, 2019. http://hdl.handle.net/2440/122614.

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Exploration undercover presents a significant challenge and relies heavily on the effective interpretation of geophysical data. Magnetotelluric (MT) surveying is an ideal method for characterising these covered terranes because it provides resolution from the shallow cover into the deep earth. Undercover terranes often lack constraining information, creating a significant impediment for translating geophysical features into geological interpretations. This thesis presents advances for understanding MT inversion uncertainty to produce better geological interpretations in data-poor areas. The project area is along strike from major Pb-Zn-Ag deposits at Mount Isa and George Fischer, and includes the location of a proposed suture between the Mount Isa Province and the North Australian Craton. The structure is interpreted from potential field data by previous workers but is not observable in outcrop. The prospective Proterozoic packages are concealed beneath 200-1200 m of Phanerozoic cover and consequently exploration success in this area has been very poor. The project dataset contains 1600 audiomagnetotelluric (AMT; 10-4 to 100 seconds) and broadband MT (BBMT; 10-2 to 103 seconds) sites; with approximate survey dimensions of 90 km north-south with line spacing of 5 km, and 150 km east-west with inter-site spacing of 2 km. The project area has scarce geological and geophysical information, and there is an inadequate understanding of the macro-scale geological structure. Three studies were undertaken with the aim of creating a new geological interpretation for the area. These studies were based on quantifying inversion variability and integration of information during interpretation. One study presents a workflow to objectively assess the variability of models produced during 3D magnetotelluric inversion. The workflow uses a sequential inversion methodology to examine model variability while minimising the computational demand of 3D inversion. The results highlight the high degree of variability permissible in 3D MT inversion models and reinforce the clear impact inversion parameterisation has on the inversion models. Our method allows objective differentiation between well- and poorly-constrained features. The second study integrates the results of 3D magnetotelluric inversion and variability analysis from the previous study, with deep crustal seismic and potential field data to refine our understanding of the southern Mount Isa Province. A new crustal-scale west-dipping feature is identified that is adjacent to a major change in crustal thickness and associated with a major change in crustal resistivity (that extends at least 400 km to the north). There is additionally a conductor located on or just above the interface and significant changes in the potential field response corresponding to both upper crustal and lower crustal depths. The structure is spatially associated with a low-resistivity feature (interpreted to be due to fluid movement or alteration), extends into the shallow crust and represents a possible exploration target. The third study is focused on resolving the depth to basement and basin morphology of the Neoproterozoic-Mesozoic cover basins in the project area. Resolving the depth to basement from MT data is inherently difficult due to the data’s insensitivity to the top of a resistive package (such as crystalline basement rocks). We used a combination of 1D probabilistic inversion, 2D deterministic inversion and synthetic modelling of downhole resistivity data to produce the final interpretation. The interpretation includes the base of the Eromanga Basin, an intra-Georgina Basin low-resistivity layer and depth to basement, all of which have associated error estimates. Understanding variability in geophysical inversion is integral to the construction of a well-supported geological interpretation. This is especially true for areas where constraining information is limited or absent. We demonstrate that an understanding of data resolution and model uncertainty enables interpretation of new, worthwhile geological information from MT inversion even in data-poor greenfield terranes. Our new interpretation de-risks mineral exploration and provide new insights into crustal structures important for exploration targeting.
Thesis (Ph.D.) -- University of Adelaide, School of Physical Sciences, 2019
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Persichetti, Joseph A. "Interpretation of 3-D controlled source audio magnetotelluric data collected at the Hanford Nuclear Reservation using 2-D inversion algorithms." 2002. http://catalog.hathitrust.org/api/volumes/oclc/50484606.html.

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Thesis (M.S.)--University of Wisconsin--Madison, 2002.
Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 122-125).
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Blatter, Daniel. "Constraining fluid properties in the mantle and crust using Bayesian inversion of electromagnetic data." Thesis, 2020. https://doi.org/10.7916/d8-b6nw-b545.

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Recent advances in computational power, as well as the hard work of a handful of brilliant scientists, have made Bayesian inversion of geophysical observations possible. This development is highly significant, as it permits the quantification of uncertainty, not only on the inverted model parameters, but also on related properties of interest. This dissertation focuses on the application of a particular kind of Bayesian inversion – trans-dimensional Markov chain Monte Carlo – to electromagnetic data, specifically airborne transient electromagnetic, magnetotelluric, and surface-towed controlled source electromagnetic data. In chapters 2-4, these data, both real and synthetic, are inverted for 1D models of subsurface electrical resistivity. In chapter 5, magnetotelluric data are inverted for 2D models of resistivity – the first time, to the best of my knowledge, that trans-dimensional Bayesian inversion of magnetotelluric data for 2D models has been achieved. In each instance, the uncertainty on bulk resistivity provided by the Bayesian inversion is used to estimate uncertainty on related subsurface properties, including pore fluid resistivity and salinity, porosity, melt fraction, melt volatile content, and bulk mantle volatile inventory. Chapter 1 introduces the topic of Bayesian inversion of electromagnetic data. Chapter 2 concerns trans-dimensional Bayesian inversion of airborne transient electromagnetic data. These data were collected above Taylor Glacier in the McMurdo Dry Valleys region of Antarctica in 2011, and were inverted using deterministic inverse methods to image a conductive channel beneath the glacier, interpreted as a package of brine-saturated sediments. The Bayesian inversion of these data confirms the existence of a conductive channel and provides quantitative uncertainties on the resistivity as a function of depth. These uncertainties are used in conjunction with Archie’s Law to estimate uncertainty on the resistivity of the pore fluids in the sediments. Additionally, the Kullback-Leibler divergence – a statistical measure of the dissimilarity of two distributions – is introduced as a measure of how much influence the observations have on the model parameters as a function of depth. The utility of Bayesian inversion in estimating the noise floor necessary to effectively resolve model structure is demonstrated. In chapter 3, a joint Bayesian framework for inverting electromagnetic data is introduced. A modified version of the algorithm utilized in chapter 2 is applied to jointly invert marine magnetotelluric and surface-towed controlled source electromagnetic data. These data were collected offshore New Jersey in 2015 to image a freshwater aquifer in the continental shelf. Deterministic inversions of this data clearly image a resistive body at depths consistent with low salinity from bore hole measurements collocated with the electromagnetic survey. The Bayesian inversion of this data set again confirms the existence of the resistive region while further providing uncertainty on the inverted resistivity with depth. In some instances, bimodality in the posterior distribution is found, demonstrating the importance of Bayesian inverse methods for fully exploring the model space. The uncertainty on bulk resistivity is used in conjunction with Archie’s Law and the porosity from bore hole measurements in a Monte Carlo framework to estimate uncertainty in the salinity of the pore water as a function of depth for three well locations. These estimates match well with measured salinities at these locations, validating the use of the Bayesian posterior in the context of a Monte Carlo framework to estimate uncertainty on related physical properties. In chapter 4, seafloor magnetotelluric data are again inverted for 1D models of subsurface resistivity, this time to image a conductive channel at the base of the lithosphere. The data are a subset of a deployment of 50 Broadband MT instruments on the seafloor above the Cocos plate offshore Nicaragua. Deterministic inversions of this data revealed a conductive structure at 45-70 km depth, beneath the Cocos plate. This earlier analysis concluded that melt was required at the lithosphere-asthenosphere boundary (LAB) to explain the inverted resistivity, but the deterministic inverse tools available at the time did not permit quantitative uncertainties – on the conductive anomaly itself, the requirement for partial melt, the degree of partial melt, or the degree of mantle hydration. Bayesian inversion of data from two magnetotelluric sites confirm that the conductor is indeed robust, and that melt is required by nearly 100% of the models that fit the data. Further, the resistivity uncertainty from the Bayesian inversion is used in conjunction with petrological modeling of partial melting in the mantle and an estimated probability distribution for temperature to place constraints on the degree of partial melt and mantle volatile (water and carbon) inventory over the depth range 45-63 km. This analysis concludes that large melt fractions and either high temperatures or a high degree of mantle hydration are likely needed to explain the resistivities produced by the Bayesian inversion, potentially explaining the mechanism for plate sliding that enables plate tectonics. Finally, chapter 5 introduces 2D trans-dimensional Bayesian inversion of magnetotelluric data, for the first time to my knowledge. A Gaussian Process-parametrized, trans-dimensional Markov chain Monte Carlo algorithm is used with MARE2DEM to invert synthetic data as well as field data from the Gemini data set from the Gulf of Mexico. For Bayesian inversion to be computationally feasible beyond inverting for 1D models, the cost of forward modeling must be reduced, as well as the number of model parameters that the algorithm must sample over. The first challenge is addressed through high performance computing. The forward modeling is performed on a cluster. In addition, we implement parallel tempering, where multiple Markov chains are run in parallel and swap models at each iteration, vastly increasing the rate at which the model space is explored and sampled. The curse of dimensionality is addressed by utilizing a Machine Learning technique known as a Gaussian Process to represent the model with far fewer parameters than required in a typical discrete finite difference or finite element representation of the subsurface. The Bayesian inversion of the Gemini data successfully recovers the model structure obtained by deterministic inversion of the same data, but additionally provides uncertainty on bulk resistivity. This thesis demonstrates the power and utility of Bayesian inversion to move beyond single estimates of subsurface resistivity. Not only does the work in this dissertation show that Bayesian inversion can provide uncertainty on inverted resistivity, it shows that these inverted uncertainties can be used to place quantitative constraints on parameters related to bulk resistivity. This is crucial to rendering the information obtained from inversion of electromagnetic data useful to disciplines far beyond electromagnetic geophysics.
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Schnaidt, Sebastian. "Improving uncertainty estimation in geophysical inversion modelling." Thesis, 2015. http://hdl.handle.net/2440/111402.

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Numerical inversion modelling is an integral part of geophysical data interpretation. Growing computational resources are used to invert ever-growing data sets and higher dimensional data. However, models without meaningful uncertainty estimates are difficult to interpret reliably and limited attention has been paid to the advancement of model quality estimation techniques to keep up with the more sophisticated inversion schemes. The employment of meaningful uncertainty estimation methods is often hindered by the complicated implementation of those methods, and inadequate model quality estimators are frequently used. This project was aimed at the advancement of model uncertainty estimation, to enable a more common use. Two different approaches were developed, approaching the problem from different directions: Firstly, a bootstrap resampling approach for the qualitative estimation of model uncertainties is presented. The algorithm is characterised by an easy implementation and the fact that it can provide model quality estimation capabilities to existing inversion algorithms without requiring access to the inversion algorithm's source code. A given data set is repeatedly resampled to create multiple realisations of the data set. Each realisation is individually inverted and the variations between the generated models are analysed and visualised to generate interpretable uncertainty maps. The capabilities of the approach are demonstrated using the example of synthetic and real 2-D magnetotellurics data. Secondly, the multi-objective joint optimisation algorithm MOJO is presented, which aims to remedy the common shortcomings of classical joint inversion approaches. Joint inversion modelling is a powerful tool to improve model results and reduce the effects of data noise and solution nonuniqueness. Nevertheless, the classic joint inversion approaches have a variety of shortcomings, such as a dependency on the choice of data weights, optimising only a single solution resulting in inadequate uncertainty estimates, and the risk of model artefacts being introduced by the accidental joint inversion of incompatible data. MOJO is based on the concept of Pareto-optimality and treats each data set as a separate objective, avoiding data-weighting. The algorithm generates solution ensembles, which are statistically analysed to provide model uncertainty estimates. The shapes and evolutions of the solutions ensemble's distribution in objective space is dependent on the level of compatibility between the data set. The solution distributions are compared against a theoretical solution distribution corresponding to perfectly compatible data to estimate the compatibility state of any given objective-pair, allowing to distinguish between compatible and incompatible data, as well as identify data sets that are neither mutually exclusive nor sensitive to common features. MOJO's effectiveness was demonstrated in extensive feasibility studies on synthetic data as well as real data. The algorithm is adaptive and can be expanded to incorporate a variety of different data types. Additionally, ways were explored to make the communication of the modelling results and the model quality estimates as clear and concise as possible, to allow the user to make an informed decision and avoid misinterpretations.
Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Physical Sciences, 2015.
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Soeffky, P. "Delineating the deep crustal fluid link between the Paralana Enhanced Geothermal System and the Beverley Uranium Mine using magnetotellurics." Thesis, 2012. http://hdl.handle.net/2440/95486.

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The global demand for clean energy alternatives is constantly increasing, creating significant interest for more sustainable energy resources such as uranium and geothermal. Australia is host to over 25% of the world's known uranium resources as well as having significant geothermal potential. The Mount Painter Domain, in the Northern Flinders Ranges in South Australia, is in a region of anomalously high heat flow generated by radiogenic decay of uranium and thorium rich granites. Two distinct uranium deposits have formed from dissolved uranium carried from the ranges by fluids, being deposited where reduction in sediment pH precipitates uranium. In May 2012 a magnetotelluric profile was collected, extending from the Northern Flinders Ranges to the Lake Frome embayment to help constrain existing resistivity models. Precipitation of uranium at the Beverley Mine site is anomalous as no surface water flow is present, suggesting the presence of subsurface processes. This pathway is linked to a 50m conductive body at the brittle-ductile boundary of the mid-crust, directly under the Paralana geothermal prospect. 3D modelling of the Paralana geothermal prospect suggests deep conductive features connecting with features at the surface.
Thesis (B.Sc.(Hons)) -- University of Adelaide, School of Earth and Environmental Sciences, 2012
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