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Geomagnetic paleosecular variations (PSVs) are an expression of geodynamo processes inside the Earth’s liquid outer core. These paleomagnetic time series provide insights into the properties of the Earth’s magnetic field, from normal behavior with a dominating dipolar geometry, over field crises, such as pronounced intensity lows and geomagnetic excursions with a distorted field geometry, to the complete reversal of the dominating dipole contribution. Particularly, long-term high-resolution and high-quality PSV time series are needed for properly reconstructing the higher frequency components in the spectrum of geomagnetic field variations and for a better understanding of the effects of smoothing during the recording of such paleomagnetic records by sedimentary archives.
In this doctorate study, full vector paleomagnetic records were derived from 16 sediment cores recovered from the southeastern Black Sea. Age models are based on radiocarbon dating and correlations of warming/cooling cycles monitored by high-resolution X-ray fluorescence (XRF) elementary ratios as well as ice-rafted debris (IRD) in Black Sea sediments to the sequence of ‘Dansgaard-Oeschger’ (DO) events defined from Greenland ice core oxygen isotope stratigraphy.
In order to identify the carriers of magnetization in Black Sea sediments, core MSM33-55-1 recovered from the southeast Black Sea was subjected to detailed rock magnetic and electron microscopy investigations. The younger part of core MSM33-55-1 was continuously deposited since 41 ka. Before 17.5 ka, the magnetic minerals were dominated by a mixture of greigite (Fe3S4) and titanomagnetite (Fe3-xTixO4) in samples with SIRM/κLF >10 kAm-1, or exclusively by titanomagnetite in samples with SIRM/κLF ≤10 kAm-1. It was found that greigite is generally present as crustal aggregates in locally reducing micro-environments. From 17.5 ka to 8.3 ka, the dominant magnetic mineral in this transition phase was changing from greigite (17.5 – ~10.0 ka) to probably silicate-hosted titanomagnetite (~10.0 – 8.3 ka). After 8.3 ka, the anoxic Black Sea was a favorable environment for the formation of non-magnetic pyrite (FeS2) framboids.
Aiming to avoid compromising of paleomagnetic data by erroneous directions carried by greigite, paleomagnetic data from samples with SIRM/κLF >10 kAm-1, shown to contain greigite by various methods, were removed from obtained records. Consequently, full vector paleomagnetic records, comprising directional data and relative paleointensity (rPI), were derived only from samples with SIRM/κLF ≤10 kAm-1 from 16 Black Sea sediment cores. The obtained data sets were used to create a stack covering the time window between 68.9 and 14.5 ka with temporal resolution between 40 and 100 years, depending on sedimentation rates.
At 64.5 ka, according to obtained results from Black Sea sediments, the second deepest minimum in relative paleointensity during the past 69 ka occurred. The field minimum during MIS 4 is associated with large declination swings beginning about 3 ka before the minimum. While a swing to 50°E is associated with steep inclinations (50-60°) according to the coring site at 42°N, the subsequent declination swing to 30°W is associated with shallow inclinations of down to 40°. Nevertheless, these large deviations from the direction of a geocentric axial dipole field (I=61°, D=0°) still can not yet be termed as 'excursional', since latitudes of corresponding VGPs only reach down to 51.5°N (120°E) and 61.5°N (75°W), respectively. However, these VGP positions at opposite sides of the globe are linked with VGP drift rates of up to 0.2° per year in between. These extreme secular variations might be the mid-latitude expression of the Norwegian–Greenland Sea excursion found at several sites much further North in Arctic marine sediments between 69°N and 81°N.
At about 34.5 ka, the Mono Lake excursion is evidenced in the stacked Black Sea PSV record by both a rPI minimum and directional shifts. Associated VGPs from stacked Black Sea data migrated from Alaska, via central Asia and the Tibetan Plateau, to Greenland, performing a clockwise loop. This agrees with data recorded in the Wilson Creek Formation, USA., and Arctic sediment core PS2644-5 from the Iceland Sea, suggesting a dominant dipole field. On the other hand, the Auckland lava flows, New Zealand, the Summer Lake, USA., and Arctic sediment core from ODP Site-919 yield distinct VGPs located in the central Pacific Ocean due to a presumably non-dipole (multi-pole) field configuration.
A directional anomaly at 18.5 ka, associated with pronounced swings in inclination and declination, as well as a low in rPI, is probably contemporaneous with the Hilina Pali excursion, originally reported from Hawaiian lava flows. However, virtual geomagnetic poles (VGPs) calculated from Black Sea sediments are not located at latitudes lower than 60° N, which denotes normal, though pronounced secular variations. During the postulated Hilina Pali excursion, the VGPs calculated from Black Sea data migrated clockwise only along the coasts of the Arctic Ocean from NE Canada (20.0 ka), via Alaska (18.6 ka) and NE Siberia (18.0 ka) to Svalbard (17.0 ka), then looping clockwise through the Eastern Arctic Ocean.
In addition to the Mono Lake and the Norwegian–Greenland Sea excursions, the Laschamp excursion was evidenced in the Black Sea PSV record with the lowest paleointensities at about 41.6 ka and a short-term (~500 years) full reversal centered at 41 ka. These excursions are further evidenced by an abnormal PSV index, though only the Laschamp and the Mono Lake excursions exhibit excursional VGP positions. The stacked Black Sea paleomagnetic record was also converted into one component parallel to the direction expected from a geocentric axial dipole (GAD) and two components perpendicular to it, representing only non-GAD components of the geomagnetic field. The Laschamp and the Norwegian–Greenland Sea excursions are characterized by extremely low GAD components, while the Mono Lake excursion is marked by large non-GAD contributions. Notably, negative values of the GAD component, indicating a fully reversed geomagnetic field, are observed only during the Laschamp excursion.
In summary, this doctoral thesis reconstructed high-resolution and high-fidelity PSV records from SE Black Sea sediments. The obtained record comprises three geomagnetic excursions, the Norwegian–Greenland Sea excursion, the Laschamp excursion, and the Mono Lake excursion. They are characterized by abnormal secular variations of different amplitudes centered at about 64.5 ka, 41.0 ka and 34.5 ka, respectively. In addition, the obtained PSV record from the Black Sea do not provide evidence for the postulated 'Hilina Pali excursion' at about 18.5 ka. Anyway, the obtained Black Sea paleomagnetic record, covering field fluctuations from normal secular variations, over excursions, to a short but full reversal, points to a geomagnetic field characterized by a large dynamic range in intensity and a highly variable superposition of dipole and non-dipole contributions from the geodynamo during the past 68.9 to 14.5 ka.
Of Trees and Birds
(2019)
Gisbert Fanselow’s work has been invaluable and inspiring to many researchers working on syntax, morphology, and information structure, both from a theoretical and from an experimental perspective. This volume comprises a collection of articles dedicated to Gisbert on the occasion of his 60th birthday, covering a range of topics from these areas and beyond. The contributions have in common that in a broad sense they have to do with language structures (and thus trees), and that in a more specific sense they have to do with birds. They thus cover two of Gisbert’s major interests in- and outside of the linguistic world (and perhaps even at the interface).
The thesis comprises three experimental studies, which were carried out to unravel the short- as well as the long-term mechanical properties of shale rocks. Short-term mechanical properties such as compressive strength and Young’s modulus were taken from recorded stress-strain curves of constant strain rate tests. Long-term mechanical properties are represented by the time– dependent creep behavior of shales. This was obtained from constant stress experiments, where the test duration ranged from a couple minutes up to two weeks. A profound knowledge of the mechanical behavior of shales is crucial to reliably estimate the potential of a shale reservoir for an economical and sustainable extraction of hydrocarbons (HC). In addition, healing of clay-rich forming cap rocks involving creep and compaction is important for underground storage of carbon dioxide and nuclear waste.
Chapter 1 introduces general aspects of the research topic at hand and highlights the motivation for conducting this study. At present, a shift from energy recovered from conventional resources e.g., coal towards energy provided by renewable resources such as wind or water is a big challenge. Gas recovered from unconventional reservoirs (shale plays) is considered a potential bridge technology.
In Chapter 2, short-term mechanical properties of two European mature shale rocks are presented, which were determined from constant strain rate experiments performed at ambient and in situ deformation conditions (confining pressure, pc ≤ 100 MPa, temperature, T ≤ 125 °C, representing pc, T - conditions at < 4 km depth) using a Paterson– type gas deformation apparatus. The investigated shales were mainly from drill core material of Posidonia (Germany) shale and weathered material of Bowland (United Kingdom) shale. The results are compared with mechanical properties of North American shales. Triaxial compression tests performed perpendicular to bedding revealed semibrittle deformation behavior of Posidonia shale with pronounced inelastic deformation. This is in contrast to Bowland shale samples that deformed brittle and displayed predominantly elastic deformation. The static Young’s modulus, E, and triaxial compressive strength, σTCS, determined from recorded stress-strain curves strongly depended on the applied confining pressure and sample composition, whereas the influence of temperature and strain rate on E and σTCS was minor. Shales with larger amounts of weak minerals (clay, mica, total organic carbon) yielded decreasing E and σTCS. This may be related to a shift from deformation supported by a load-bearing framework of hard phases (e.g., quartz) towards deformation of interconnected weak minerals, particularly for higher fractions of about 25 – 30 vol% weak phases. Comparing mechanical properties determined at reservoir conditions with mechanical data applying effective medium theories revealed that E and σTCS of Posidonia and Bowland shale are close to the lower (Reuss) bound. Brittleness B is often quoted as a measure indicating the response of a shale formation to stimulation and economic production. The brittleness, B, of Posidonia and Bowland shale, estimated from E, is in good agreement with the experimental results. This correlation may be useful to predict B from sonic logs, from which the (dynamic) Young’s modulus can be retrieved.
Chapter 3 presents a study of the long-term creep properties of an immature Posidonia shale. Constant stress experiments (σ = const.) were performed at elevated confining pressures (pc = 50 – 200 MPa) and temperatures (T = 50 – 200 °C) to simulate reservoir pc, T - conditions. The Posidonia shale samples were acquired from a quarry in South Germany. At stresses below ≈ 84 % compressive strength of Posidonia shale, at high temperature and low confining pressure, samples showed pronounced transient (primary) creep with high deformation rates in the semibrittle regime. Sample deformation was mainly accommodated by creep of weak sample constituents and pore space reduction. An empirical power law relation between strain and time, which also accounts for the influence of pc, T and σ on creep strain was formulated to describe the primary creep phase. Extrapolation of the results to a creep period of several years, which is the typical time interval for a large production decline, suggest that fracture closure is unlikely at low stresses. At high stresses as expected for example at the contact between the fracture surfaces and proppants added during stimulation measures, subcritical crack growth may lead to secondary and tertiary creep. An empirical power law is suggested to describe secondary creep of shale rocks as a function of stress, pressure and temperature. The predicted closure rates agree with typical production decline curves recorded during the extraction of hydrocarbons. At the investigated conditions, the creep behavior of Posidonia shale was found to correlate with brittleness, calculated from sample composition.
In Chapter 4 the creep properties of mature Posidonia and Bowland shales are presented. The observed long-term creep behavior is compared to the short-term behavior determined in Chapter 2. Creep experiments were performed at simulated reservoir conditions of pc = 50 – 115 MPa and T = 75 – 150 °C. Similar to the mechanical response of immature Posidonia shale samples investigated in Chapter 3, creep strain rates of mature Bowland and Posidonia shales were enhanced with increasing stress and temperature and decreasing confining pressures. Depending on applied deformation conditions, samples displayed either only a primary (decelerating) or in addition also a secondary (quasi-steady state) and subsequently a tertiary (accelerating) creep phase before failure. At the same deformation conditions, creep strain of Posidonia shale, which is rich in weak constituents, is tremendously higher than of quartz-rich Bowland shale. Typically, primary creep strain is again mostly accommodated by deformation of weak minerals and local pore space reduction. At the onset of tertiary creep most of the deformation was accommodated by micro crack growth. A power law was used to characterize the primary creep phase of Posidonia and Bowland shale. Primary creep strain of shale rocks is inversely correlated to triaxial compressive strength and brittleness, as described in Chapter 2.
Chapter 5 provides a synthesis of the experimental findings and summarizes the major results of the studies presented in Chapters 2 – 4 and potential applications in the Exploration & Production industry.
Chapter 6 gives a brief outlook on potential future experimental research that would help to further improve our understanding of processes leading to fracture closure involving proppant embedment in unconventional shale gas reservoirs. Such insights may allow to improve stimulation techniques aimed at maintaining economical extraction of hydrocarbons over several years.
Determining the optimal grid resolution for topographic analysis on an airborne lidar dataset
(2019)
Digital elevation models (DEMs) are a gridded representation of the surface of the Earth and typically contain uncertainties due to data collection and processing. Slope and aspect estimates on a DEM contain errors and uncertainties inherited from the representation of a continuous surface as a grid (referred to as truncation error; TE) and from any DEM uncertainty. We analyze in detail the impacts of TE and propagated elevation uncertainty (PEU) on slope and aspect.
Using synthetic data as a control, we define functions to quantify both TE and PEU for arbitrary grids. We then develop a quality metric which captures the combined impact of both TE and PEU on the calculation of topographic metrics. Our quality metric allows us to examine the spatial patterns of error and uncertainty in topographic metrics and to compare calculations on DEMs of different sizes and accuracies.
Using lidar data with point density of ∼10 pts m−2 covering Santa Cruz Island in southern California, we are able to generate DEMs and uncertainty estimates at several grid resolutions. Slope (aspect) errors on the 1 m dataset are on average 0.3∘ (0.9∘) from TE and 5.5∘ (14.5∘) from PEU. We calculate an optimal DEM resolution for our SCI lidar dataset of 4 m that minimizes the error bounds on topographic metric calculations due to the combined influence of TE and PEU for both slope and aspect calculations over the entire SCI. Average slope (aspect) errors from the 4 m DEM are 0.25∘ (0.75∘) from TE and 5∘ (12.5∘) from PEU. While the smallest grid resolution possible from the high-density SCI lidar is not necessarily optimal for calculating topographic metrics, high point-density data are essential for measuring DEM uncertainty across a range of resolutions.
Determining the optimal grid resolution for topographic analysis on an airborne lidar dataset
(2019)
Digital elevation models (DEMs) are a gridded representation of the surface of the Earth and typically contain uncertainties due to data collection and processing. Slope and aspect estimates on a DEM contain errors and uncertainties inherited from the representation of a continuous surface as a grid (referred to as truncation error; TE) and from any DEM uncertainty. We analyze in detail the impacts of TE and propagated elevation uncertainty (PEU) on slope and aspect.
Using synthetic data as a control, we define functions to quantify both TE and PEU for arbitrary grids. We then develop a quality metric which captures the combined impact of both TE and PEU on the calculation of topographic metrics. Our quality metric allows us to examine the spatial patterns of error and uncertainty in topographic metrics and to compare calculations on DEMs of different sizes and accuracies.
Using lidar data with point density of ∼10 pts m−2 covering Santa Cruz Island in southern California, we are able to generate DEMs and uncertainty estimates at several grid resolutions. Slope (aspect) errors on the 1 m dataset are on average 0.3∘ (0.9∘) from TE and 5.5∘ (14.5∘) from PEU. We calculate an optimal DEM resolution for our SCI lidar dataset of 4 m that minimizes the error bounds on topographic metric calculations due to the combined influence of TE and PEU for both slope and aspect calculations over the entire SCI. Average slope (aspect) errors from the 4 m DEM are 0.25∘ (0.75∘) from TE and 5∘ (12.5∘) from PEU. While the smallest grid resolution possible from the high-density SCI lidar is not necessarily optimal for calculating topographic metrics, high point-density data are essential for measuring DEM uncertainty across a range of resolutions.
The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequences "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means.
The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.
The advances in modern geodetic techniques such as the global navigation satellite system (GNSS) and synthetic aperture radar (SAR) provide surface deformation measurements with an unprecedented accuracy and temporal and spatial resolutions even at most remote volcanoes on Earth. Modelling of the high-quality geodetic data is crucial for understanding the underlying physics of volcano deformation processes. Among various approaches, mathematical models are the most effective for establishing a quantitative link between the surface displacements and the shape and strength of deformation sources. Advancing the geodetic data analyses and hence, the knowledge on the Earth’s interior processes, demands sophisticated and efficient deformation modelling approaches. Yet the majority of these models rely on simplistic assumptions for deformation source geometries and ignore complexities such as the Earth’s surface topography and interactions between multiple sources.
This thesis addresses this problem in the context of analytical and numerical volcano deformation modelling. In the first part, new analytical solutions for triangular dislocations (TDs) in uniform infinite and semi-infinite elastic media have been developed. Through a comprehensive investigation, the locations and causes of artefact singularities and numerical instabilities associated with TDs have been determined and these long-standing drawbacks have been addressed thoroughly. This approach has then been extended to rectangular dislocations (RDs) with full rotational degrees of freedom. Using this solution in a configuration of three orthogonal RDs a compound dislocation model (CDM) has been developed. The CDM can represent generalized volumetric and planar deformation sources efficiently. Thus, the CDM is relevant for rapid inversions in early warning systems and can also be used for detailed deformation analyses. In order to account for complex source geometries and realistic topography in the deformation models, in this thesis the boundary element method (BEM) has been applied to the new solutions for TDs. In this scheme, complex surfaces are simulated as a continuous mesh of TDs that may possess any displacement or stress boundary conditions in the BEM calculations. In the second part of this thesis, the developed modelling techniques have been applied to five different real-world deformation scenarios. As the first and second case studies the deformation sources associated with the 2015 Calbuco eruption and 2013–2016 Copahue inflation period have been constrained by using the CDM. The highly anisotropic source geometries in these two cases highlight the importance of using generalized deformation models such as the CDM, for geodetic data inversions. The other three case studies in this thesis involve high-resolution dislocation models and BEM calculations. As the third case, the 2013 pre-explosive inflation of Volcán de Colima has been simulated by using two ellipsoidal cavities, which locate zones of pressurization in the volcano’s lava dome. The fourth case study, which serves as an example for volcanotectonics interactions, the 3-D kinematics of an active ring-fault at Tendürek volcano has been investigated through modelling displacement time series over the 2003–2010 time period. As the fifth example, the deformation sources associated with North Korea’s underground nuclear test in September 2017 have been constrained. These examples demonstrate the advancement and increasing level of complexity and the general applicability of the developed dislocation modelling techniques.
This thesis establishes a unified framework for rapid and high-resolution dislocation modelling, which in addition to volcano deformations can also be applied to tectonic and humanmade deformations.