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Inversion and Joint Inversion of Electromagnetic and Potential Field Data
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
2014 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Inversion und kombinierte Inversion von elektromagnetischen und Potentialfelddaten (German)
Abstract [en]

In this thesis, four inversion problems of different scale and difficulty are solved. Two of them are electromagnetic inverse problems. Two more are joint inversion problems of potential field data and other types of data. First, a linear approximation, which is a generalization of the low-induction-number approximation standard in slingram dual-loop interpretation is developed and used for rapid two and three dimensional inversion. The approximation takes induction within a background half-space into account and can thus be applied in conductive scenarios, where otherwise a rigorous electromagnetic modeling would be required. Second, a three-dimensional inversion of airborne tensor very-low-frequency data with a rigorous forward modeling at its core is developed. For dealing with the large scale of the forward problem, a nested fast-Fourier-transform-based integral equation method is introduced, wherein electromagnetic interactions are arranged according to their range and larger ranges are treated with less accuracy and effort. The inversion improves the traditional interpretation through data derived maps by providing a conductivity model, thus constraining the upper few hundred meters of the crust down to the shallowest conductor and allowing the study of its top in three dimensions. The third inversion problem is the the joint inversion of refraction and geoelectric data. By requiring the velocity and resistivity models to share a common, laterally variable layered geometry, easily interpretable models, which are reasonable in many geological near surface situations (e.g., groundwater exploration in Quaternary sediments), are produced directly from the joint inversion. Finally, a joint inversion of large scale potential field data from a gabbro intrusion is presented. Gravity and magnetic data are required to abide to a petrophysical constraint, which is derived from extensive field sampling. The impact of the constraint is maximized under the provision that both data sets are explained equally well as they would be through individual inversions. This leads to a simple and clearly defined intrusion geometry, consistent for both the density and magnetic susceptibility distribution. In all presented inversion problems, field data sets are successfully inverted, the results are appraised through synthetic tests and, if available, through comparison with independent data.

Abstract [de]

Diese Arbeit hat die Lösung von vier geophysikalischen Umkehraufgaben, sogenannten Inversionsproblemen, zum Gegenstand. Zwei dieser Aufgaben befassen sich mit der Inversion elektromagnetischer Daten, zwei weitere sind Probleme der kombinierten Inversion von Datensätzen aus unterschiedlichen geophysikalischen Messverfahren. Im ersten Problem wird die für die Auswertung elektromagnetischer Zweispulensystemdaten typische lineare Näherung der kleinen Induktionszahlen als Bornsche Näherung verallgemeinert, ihre Anwendbarkeit durch exakte Berücksichtigung der Induktionsvorgänge in einem beliebigen homogenen Halbraum von schlechtleitenden auf gutleitende Untergründe ausgedehnt und schließlich zur zwei- und dreidimensionalen Inversion eingesetzt. Dadurch kann auch im leitfähigen Untergrund eine aufwändige exakte Modellierung vermieden werden. Im zweiten Problem wird eine dreidimensionale Inversion von flugzeuggestützten Längstwellenmessungen entwickelt und als ihre Grundlage eine exakte elektromagnetische Rechnung erdacht. Damit wird traditionelle kartengestützte Dateninterpretation durch ein dreidimensionales Leitfähigkeitsmodell ergänzt, welches die oberen hundert bis dreihundert Meter der Erdkruste bis hin zur Tiefe des obersten Leiters abbildet, so dass dessen Oberflächenform erkundet werden kann. Die enorme Problemgröße wird durch eine Fouriertransformationsmethode bewältigt, welche die elektromagnetischen Wechselwirkungen nach ihrer Reichweite einteilt, die Fernwirkungen mit entsprechend verringerter Genauigkeit behandelt und dadurch eine erhebliche Anzahl an Rechnungen einspart. Im dritten Problem werden refraktionsseismische und geoelektrische Messungen kombiniert, indem sowohl das Geschwindigkeits- als auch das Widerstandsmodell mit einer gemeinsamen, lateral veränderlichen und durch beide Datensätze bestimmten Schichtstruktur versehen werden. Ein solches, durch Schichten definiertes Inversionsergebnis, stellt in vielen oberflächennahen Anwendungen, beispielsweise im Grundwasserbereich, ein sinnvolles Abbild der Erde dar. Im vierten Problem werden Schweremessungen und Magnetfeldmessungen, die über einer Gabbrointrusion aufgenommen wurden, mittels einer empirischen petrophysikalischen Beziehung vereinigt, welche aus Labormessungen an einer großen Anzahl von Gesteinsproben abgeleitet wurde. Hierbei wird der Einfluss dieser Modellkopplung solange maximiert, wie beide Datensätze mit derjenigen Genauigkeit angepasst werden können, welche vorher in Einzelinversionen erreicht wurde. Das Ergebnis ist ein einfaches, geometrisch konsistentes Modell der Verteilungen von Dichte und magnetischer Suszeptibilität. In allen vier Aufgaben wurden erfolgreich reale Felddaten invertiert. Die Güte der Ergebnisse wurde mittels synthetischer Experimente untersucht und, so vorhanden, mit unabhängigen Informationen verglichen.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. , 108 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1116
Keyword [en]
Inversion, Electromagnetic methods, Joint inversion, Potential Field methods
Keyword [de]
Inversion, Elektromagnetische Verfahren, Joint-Inversion, Potentialverfahren
National Category
Geophysics
Research subject
Geophysics with specialization in Solid Earth Physics
Identifiers
URN: urn:nbn:se:uu:diva-215673ISBN: 978-91-554-8856-7 (print)OAI: oai:DiVA.org:uu-215673DiVA: diva2:688113
Public defence
2014-02-28, Hambergsalen, Geocentrum, Villavägen 16, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2014-02-06 Created: 2014-01-15 Last updated: 2014-02-10
List of papers
1. Inversion of slingram electromagnetic induction data using a Born approximation
Open this publication in new window or tab >>Inversion of slingram electromagnetic induction data using a Born approximation
2013 (English)In: Geophysics, ISSN 0016-8033, E-ISSN 1942-2156, Vol. 78, no 4, E201-E212 p.Article in journal (Refereed) Published
Abstract [en]

We present an efficient approximate inversion scheme for near-surface loop-loop EM induction data (slingram) that can be applied to obtain 2D or 3D models on a normal desktop computer. Our approach is derived from a volume integral equation formulation with an arbitrarily conductive homogeneous half-space as a background model. The measurements are not required to fulfill the low induction number condition (low frequency and conductivity). The high efficiency of the method is achieved by invoking the Born approximation around a half-space background. The Born approximation renders the forward operator linear. The choice of a homogeneous half-space yields closed form expressions for the required electromagnetic normal fields. It also yields a translationally invariant forward operator, i.e., a highly redundant Jacobian. In connection with the application of a matrix-free conjugate gradient method, this allows for very low memory requirements during the inversion, even in three dimensions. As a consequence of the Born approximation, strong conductive deviations from the background model are underestimated. Highly resistive anomalies are in principle overestimated, but at the same time difficult to resolve with induction methods. In the case of extreme contrasts, our forward model may fail in simultaneously explaining all the data collected. We applied the method to EM34 data from a profile that has been extensively studied with other electromagnetic methods and compare the results. Then, we invert three conductivity maps from the same area in a 3D inversion.

National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-207107 (URN)10.1190/GEO2012-0484.1 (DOI)000322716500020 ()
Available from: 2013-09-10 Created: 2013-09-09 Last updated: 2017-12-06Bibliographically approved
2. Inversion of airborne tensor VLF data using integral equations
Open this publication in new window or tab >>Inversion of airborne tensor VLF data using integral equations
2014 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 198, no 2, 775-794 p.Article in journal (Refereed) Published
Abstract [en]

The Geological Survey of Sweden has been collecting airborne tensor very low frequency data (VLF) over several decades, covering large parts of the country. The data has been an invaluable source of information for identifying conductive structures that can among other things be related to water-filled fault zones, wet sediments that fill valleys or ore mineralizations. Because the method only uses two differently polarized plane waves of very similar frequency, vertical resolution is low and interpretation is in most cases limited to maps that are directly derived from the data. Occasionally, 2-D inversion is carried out along selected profiles. In this paper, we present for the first time a 3-D inversion for tensor VLF data in order to further increase the usefulness of the data set. The inversion is performed using a non-linear conjugate gradient scheme (Polak-RibiSre) with an inexact line-search. The gradient is obtained by an algebraic adjoint method that requires one additional forward calculation involving the adjoint system matrix. The forward modelling is based on integral equations with an analytic formulation of the half-space Green's tensor. It avoids typically required Hankel transforms and is particularly amenable to singularity removal prior to the numerical integration over the volume elements. The system is solved iteratively, thus avoiding construction and storage of the dense system matrix. By using fast 3-D Fourier transforms on nested grids, subsequently farther away interactions are represented with less detail and therefore with less computational effort, enabling us to bridge the gap between the relatively short wavelengths of the fields (tens of metres) and the large model dimensions (several square kilometres). We find that the approximation of the fields can be off by several per cent, yet the transfer functions in the air are practically unaffected. We verify our code using synthetic calculations from well-established 2-D methods, and trade modelling accuracy off against computational effort in order to keep the inversion feasible in both respects. Our compromise is to limit the permissible resistivity to not fall below 100 Omega m to maintain computational domains as large as 10 x 10 km(2) and computation times on the order of a few hours on standard PCs. We investigate the effect of possible local violations of these limits. Even though the conductivity magnitude can then not be recovered correctly, we do not observe any structural artefacts related to this in our tests. We invert a data set from northern Sweden, where we find an excellent agreement of known geological features, such as contacts or fault zones, with elongated conductive structures, while high resistivity is encountered in probably less disturbed geology, often related to topographic highs, which have survived predominantly glacial erosion processes. As expected from synthetic studies, the resolution is laterally high, but vertically limited down to the top of conductive structures.

Keyword
Electromagnetic theory, Electrical properties, Numerical approximations and analysis, Numerical solutions, Inverse theory
National Category
Geophysics
Research subject
Geophysics with specialization in Solid Earth Physics
Identifiers
urn:nbn:se:uu:diva-215658 (URN)10.1093/gji/ggu161 (DOI)000339717700009 ()
Available from: 2014-01-15 Created: 2014-01-15 Last updated: 2017-12-06
3. Joint inversion of seismic refraction and resistivity data using layered models: Applications to groundwater investigation
Open this publication in new window or tab >>Joint inversion of seismic refraction and resistivity data using layered models: Applications to groundwater investigation
2015 (English)In: Geophysics, ISSN 0016-8033, E-ISSN 1942-2156, Vol. 80, no 1, EN43-EN55 p.Article in journal (Refereed) Published
Abstract [en]

We developed a method for joint inversion of seismic refraction and resistivity data, using sharp-boundary models with few layers (typically three). We demonstrated the usefulness of the approach via examples from near-surface case studies involving shallow groundwater exploration and geotechnical investigations, although it should also be applicable to other types of layered environments, e.g., sedimentary basins. In our model parameterization, the layer boundaries were common for the resistivity and velocity distributions. Within the layers, only lateral variations in the material parameters (resistivity and velocity) were allowed, and we assumed no correlation between these. The inversion was performed using a nonlinear least-squares algorithm, using lateral smoothing to the layer boundaries and to the materialparameters. Depending on the subsurface conditions, the smoothing can be applied either to the depth of the layer boundaries or to the layer thicknesses. The forward responses and Jacobian for refraction seismics were calculated through ray tracing. The resistivity computations were performed with finite differences and a cell-to-layer transform for the Fréchet derivatives. Our method performed well in synthetic tests, and in the case studies, the layer boundaries were in good agreement with in situ tests and seismic reflection data, although minimum-structure inversion generally has a better data fit due to more freedom to introduce model heterogeneity. We further found that our joint inversion approach can provide more accurate thickness estimates for seismic hidden layers.

Keyword
inversion, near surface, resistivity, engineering, refraction
National Category
Geophysics
Research subject
Geophysics with specialization in Solid Earth Physics
Identifiers
urn:nbn:se:uu:diva-215665 (URN)10.1190/GEO2013-0476.1 (DOI)000352105900022 ()
Available from: 2014-01-15 Created: 2014-01-15 Last updated: 2017-12-06Bibliographically approved
4. Joint inversion of gravity, magnetic and petrophysical data - A case study from a gabbro intrusion in Boden, Sweden
Open this publication in new window or tab >>Joint inversion of gravity, magnetic and petrophysical data - A case study from a gabbro intrusion in Boden, Sweden
Show others...
2015 (English)In: Geophysics, ISSN 0016-8033, E-ISSN 1942-2156, Vol. 80, no 5, B131-B152 p.Article in journal (Refereed) Published
Keyword
inversion, gravity, magnetics, petrophysics
National Category
Geophysics
Research subject
Geophysics with specialization in Solid Earth Physics
Identifiers
urn:nbn:se:uu:diva-215670 (URN)
Funder
Swedish Research Council
Available from: 2014-01-15 Created: 2014-01-15 Last updated: 2017-12-06

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