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The detection of finite-time coherent particle sets in Lagrangian trajectory data using data clustering techniques is an active research field at the moment. Yet, the clustering methods mostly employed so far have been based on graph partitioning, which assigns each trajectory to a cluster, i.e. there is no concept of noisy, incoherent trajectories. This is problematic for applications to the ocean, where many small coherent eddies are present in a large fluid domain. In addition, to our knowledge none of the existing methods to detect finite-time coherent sets has an intrinsic notion of coherence hierarchy, i.e. the detection of finite-time coherent sets at different spatial scales. Such coherence hierarchies are present in the ocean, where basin scale coherence coexists with smaller coherent structures such as jets and mesoscale eddies. Here, for the first time in this context, we use the density-based clustering algorithm OPTICS (Ankerst et al., 1999) to detect finite-time coherent particle sets in Lagrangian trajectory data. Different from partition based clustering methods, OPTICS does not require to fix the number of clusters beforehand. Derived clustering results contain a concept of noise, such that not every trajectory needs to be part of a cluster. OPTICS also has a major advantage compared to the previously used DBSCAN method, as it can detect clusters of varying density. Further, clusters can also be detected based on density changes instead of absolute density. Finally, OPTICS based clusters have an intrinsically hierarchical structure, which allows to detect coherent trajectory sets at different spatial scales at once. We apply OPTICS directly to Lagrangian trajectory data in the Bickley jet model flow and successfully detect the expected vortices and the jet. The resulting clustering separates the vortices and the jet from background noise, with an imprint of the hierarchical clustering structure of coherent, small scale vortices in a coherent, large-scale, background flow. We then apply our method to a set of virtual trajectories released in the eastern South Atlantic Ocean in an eddying ocean model and successfully detect Agulhas rings. At larger scale, our method also separates the eastward and westward moving parts of the subtropical gyre. We illustrate the difference between our approach and partition based k-Means clustering using a 2-dimensional embedding of the trajectories derived from classical multidimensional scaling. We also show how OPTICS can be applied to the spectral embedding of a trajectory based network to overcome the problems of k-Means spectral clustering in detecting Agulhas rings.

Visual techniques in general and 3D visualisation in particular have seen considerable adoption within the last 30 years in the geosciences and geology. Techniques such as volume visualisation, for analysing subsurface processes, and photo-coloured LiDAR point-based rendering, to digitally explore rock exposures at the earth’s surface, were applied within geology as one of the first adopting branches of science. A large amount of digital, geological surface- and volume data is nowadays available to desktop-based workflows for geological applications such as hydrocarbon reservoir exploration, groundwater modelling, CO2 sequestration and, in the future, geothermal energy planning. On the other hand, the analysis and data collection during fieldwork has yet to embrace this ”digital revolution”: sedimentary logs, geological maps and stratigraphic sketches are still captured in each geologist’s individual fieldbook, and physical rocks samples are still transported to the lab for subsequent analysis. Is this still necessary, or are there extended digital means of data collection and exploration in the field ? Are modern digital interpretation techniques accurate and intuitive enough to relevantly support fieldwork in geology and other geoscience disciplines ? This dissertation aims to address these questions and, by doing so, close the technological gap between geological fieldwork and office workflows in geology. The emergence of mobile devices and their vast array of physical sensors, combined with touch-based user interfaces, high-resolution screens and digital cameras provide a possible digital platform that can be used by field geologists. Their ubiquitous availability increases the chances to adopt digital workflows in the field without additional, expensive equipment. The use of 3D data on mobile devices in the field is furthered by the availability of 3D digital outcrop models and the increasing ease of their acquisition. This dissertation assesses the prospects of adopting 3D visual techniques and mobile devices within field geology. The research of this dissertation uses previously acquired and processed digital outcrop models in the form of textured surfaces from optical remote sensing and photogrammetry. The scientific papers in this thesis present visual techniques and algorithms to map outcrop photographs in the field directly onto the surface models. Automatic mapping allows the projection of photo interpretations of stratigraphy and sedimentary facies on the 3D textured surface while providing the domain expert with simple-touse, intuitive tools for the photo interpretation itself. The developed visual approach, combining insight from all across the computer sciences dealing with visual information, merits into the mobile device Geological Registration and Interpretation Toolset (GRIT) app, which is assessed on an outcrop analogue study of the Saltwick Formation exposed at Whitby, North Yorkshire, UK. Although being applicable to a diversity of study scenarios within petroleum geology and the geosciences, the particular target application of the visual techniques is to easily provide field-based outcrop interpretations for subsequent construction of training images for multiple point statistics reservoir modelling, as envisaged within the VOM2MPS project. Despite the success and applicability of the visual approach, numerous drawbacks and probable future extensions are discussed in the thesis based on the conducted studies. Apart from elaborating on more obvious limitations originating from the use of mobile devices and their limited computing capabilities and sensor accuracies, a major contribution of this thesis is the careful analysis of conceptual drawbacks of established procedures in modelling, representing, constructing and disseminating the available surface geometry. A more mathematically-accurate geometric description of the underlying algebraic surfaces yields improvements and future applications unaddressed within the literature of geology and the computational geosciences to this date. Also, future extensions to the visual techniques proposed in this thesis allow for expanded analysis, 3D exploration and improved geological subsurface modelling in general. publishedVersion

Registering natural photos to existing 3D surface models, particularly on low-power mobile devices, gathers increasing attention to a variety of application domains. The paper discusses up-to-date computation insights of the technique, condensing available literature and knowledge obtained from experiments across multiple research groups. Challenges like smartphone camera calibration or the sensor-based estimation of location and orientation are current research subjects, for which new data and experimental results are presented. Moreover, computing-related, practical challenges (e.g. device variability) are detailed to increase the technological understanding and reasoning on the limits of mobile devices. An overview of running projects utilising image-to-geometry registration methods shows the potential for mobile devices to, amongst others, improve flood hazard mitigation and hydrocarbon exploration with crowdsourced data.

In the context of the ongoing discussion about a carrier-induced ferromagnetic phase transition in diluted-magnetic II-VI semiconductors (DMS), theoretical studies on coherent dynamics of localized spins coupled with a two-dimensional hole gas (2DHG) in DMS quantum wells (QWs) were done by K.V. KAVOKIN. His key for studying the exchange interaction of the localized spin ensemble (e.g. Mn2+) with the 2DHG is the Larmor frequency of the localized Mn-ion spins and thus their Mn-g-factor. It was shown that the 2DHG affects a time evolution of the (Mn-) spin system in an in-plane magnetic field resulting in the reduction of its Larmor frequency (Mn-g-factor) under the influence of an oscillating effective field of holes. This is called magnetic soft mode (behaviour). The experimental access for demonstrating this Mn-g-factor reduction with increasing hole concentration is the method of Multi-Spin-Flip (SF) Raman scattering combined with the variation of the carrier concentration by photo-excitation with an additional light source (two-colour experiment). The main motivation for this thesis was the experimental confirmation of the theoretically predicted magnetic soft mode and the analysis of its dependence on the hole-concentration and external B-field, as well as its disappearance with increasing sample temperature. For that purpose, CdMnTe/CdMgTe QWs (Mn: 0.6%, 1.0%) positioned close to the sample surface (13−19nm) were investigated in an in-plane applied external magnetic field (up to 4.5T in Voigt-geometry) via a two-colour experiment i.e. using two light sources. This allows the spin excitation of Mn-ions by simultaneously tuning the hole-concentration towards the ferromagnetic phase transition by photo-generated carriers. Thus, one tuneable laser is responsible for resonant below-barrier excitation as a probe for Multi-SF Raman scattering. The other laser excites photo-generated carriers from above barrier (2.41eV) for tuning the hole concentration in the QW. Positioning the QW close to the sample surface causes a surface-induced p-doping of the QW (intrinsic hole concentration in the QW) and enables the active tuning of the hole concentration by photo-generated carriers due to different tunnelling behaviour of electrons and holes from the QW to the surface. The Mn-g-factor was decreased by quasi-continuously increasing the above-barrier illumination (and thus the hole concentration), while the below-barrier excitation (Multi-PR probe) was kept at a constant low power. This results in a Mn-g-factor reduction starting from its atomic value g=2.01 to lowest evaluated Mn-g-factor in this thesis g=1.77. This is a magnetic softening of 12%. Apart from the general magnetic soft mode behaviour at low temperatures, one of the main experimental results in this thesis is the confirmation of the theoretical prediction that the magnetic soft mode behaviour in the external B-field does not only depend on the carrier concentration but also on the B-field strength itself. An additional aspect is the temperature dependence of the magnetic soft mode. The Mn-g-factor decrease is suppressed with increasing temperature almost reaching the atomic Mn-g-factor at 4.2K (g=1.99). This behaviour is due to the T-induced weakening of the transverse 2DHG spin susceptibility. The results of the investigations concerning the cap layer thickness impact on the QW carrier characteristics were investigated in the cap thickness range of 13nm to 19nm. The cap thickness configures on the one hand the intrinsic hole concentration of the QW ("2DHG offset") due to the surface-induced p-doping and sets the "starting point" for the Mn-g-factor reduction. On the other hand the cap thickness determines the probability of electron tunnelling to the surface and thus the efficiency of the hole tuning by light. The latter is the criterion for the range of Mn-g-factor reduction by light. This two dependences were pointed out by the photo-generated hole influence on the QW PL-spectra which results in tuning the exciton-trion ratio. In summary both mechanisms are of relevance for the hole tuning and thus for the magnetic soft-mode behaviour. The mechanism of tunnelling time prevails at small cap layer thicknesses while the surface-induced p-doping plays the major role for larger cap thicknesses (> 25nm). In conclusion, the presented method in this thesis is a sensitive tool to study the dynamics of the spin excitations and the paramagnetic susceptibility in the vicinity of the hole-induced ferromagnetic phase transition., Im Zusammenhang mit den aktuellen Diskussionen über einen ladungsträgerinduzierten ferromagnetischen Phasenübergang in verdünnt-magnetischen II-VI-Halbleitern wurden von K.V. KAVOKIN theoretische Untersuchungen zu kohärenter Dynamik von lokalisierten Spins durchgeführt, welche mit dem zweidimensionalen Lochgas im DMS Quantentrog (QT) koppeln. Die Larmorfrequenz der lokalisierten Mn-Ionen Spins und der damit verbundene Mn-g-Faktor sind dabei der experimentelle Zugang, um die Wechselwirkung des lokalisierten Spinensembles mit dem zweidimensionalen Lochgas zu untersuchen. Das 2DHG ruft eine zeitliche Entwicklung des (Mn-) Spinsystems in einem in der Quantentrogebene angelegten äußeren Magnetfeld hervor. Dies hat die Verringerung der Larmorfrequenz und damit des Mn-g-Faktors, beeinflusst durch ein oszillierendes effektives Austauschfeld der Löcher zur Folge. Dies wird magnetisches Softmode-Verhalten genannt. Multi-Spin-Flip(SF)-Raman-Spektroskopie in Verbindung mit einer zusätzlichen Lichtquelle (genannt Zwei-Farben-Experiment) ist das probate Mittel, um diese Reduzierung des Mn-g-Faktors durch die photo-generierte Erhöhung der Lochkonzentration des 2DHG zu demonstrieren. Die experimentelle Bestätigung des theoretisch vorhergesagten magnetischen Softmode-Verhaltens, sowie dessen Abhängigkeit von der Lochkonzentration und dem externen B-Feld, also auch dessen Verschwinden mit steigender Probentemperatur zu analysieren, war die Motivation dieser Arbeit. Aus diesem Grund wurden nahe (13-19nm) an der Probenoberflache liegende CdMnTe/CdMgTe Quantentroge (Mn: 0,6%; 1,0%) in einem parallel zur Quantentrogebene angelegten externen Magnetfeld (mit bis zu 4,5T) mittels Zwei-Farben-Experiment (d.h. mittels zweier Laser-Lichtquellen) untersucht. Dieses ermöglicht die Anregung der Mn-Spins bei gleichzeitiger Erhöhung der Lochkonzentration in Richtung des ferromagnetischen Phasenübergangs durch photo-generierte Ladungsträger. Dabei dient ein durchstimmbarer Laser zur resonanten Anregung im Quantentrog als Lichtquelle für die Multi-SF-Raman-Streuung. Der andere Laser hingegen erzeugt photogenerierte Ladungsträger oberhalb der Quantentrogbarriere (2,41eV), um die Lochkonzentration im Quantentrog einzustellen. Die Reduzierung des Mn-g-Faktors erfolgte durch quasikontinuierliche Erhöhung der Beleuchtung oberhalb der Barriere und folglich auch der Lochkonzentration, während die resonante Anregungsleistung im Quantentrog (d.h. die Multi-Spin-Flip-Sonde) niedrig und konstant gehalten wurde. Hiermit wurde die Verringerung des Mn-g-Faktors nachgewiesen, ausgehend von dessen atomaren Wert g=2,01 hin zu dem, in dieser Arbeit kleinsten ermittelten Wert von g =1,77. Dies entspricht einem magnetischen "softening" von 12%. Neben dem allgemeinen magnetischen Softmode-Verhalten bei niedriger Temperatur, war eines der wichtigsten experimentellen Ergebnisse dieser Arbeit die Bestätigung der theoretisch vorhergesagten Abhängigkeit des magnetischen Softmode-Verhaltens von der Magnetfeldstärke selbst und nicht nur von der Lochkonzentration im externen Magnetfeld. Die Mn-g-Faktor-Reduzierung wirkt sich bei kleinen B-Feldern stärker aus. Ein weiterer experimenteller Aspekt ist die Temperaturabhängigkeit des magnetischen Softmode-Verhaltens. Mit steigender Temperatur wird die Mn-g-Faktor-Reduzierung unterdrückt und der g-Faktor erreicht bei 4,2K mit g=1,99 fast seinen atomaren Wert. Grund dafür ist die temperaturinduzierte Abschwächung der transversalen 2DHG-Spin-Suszeptibilität. Die Auswirkung der Cap-Schichtdicke auf das Verhalten der Ladungsträgercharakteristik im Quantentrog wurde für Cap-Dicken im Bereich von 13nm bis 19nm untersucht. Die Cap-Dicke legt einerseits, durch die oberflächeninduzierte p-Dotierung, die intrinsische Lochkonzentration des Quantentrogs fest ("2DHG offset") und damit den "Startpunkt" für die Mn-g-Faktor-Reduzierung. Andererseits bestimmt die Cap-Dicke die Tunnelwahrscheinlichkeit der Elektronen zur Oberfläche und damit wiederum die Effizienz der Lochkonzentrationsbeeinflussung durch das eingestrahlte Licht. Letzteres ist das Kriterium dafür, wie groß der Einflussbereich ist, in dem eine Mn-g-Faktor-Reduzierung durch Licht stattfinden kann. Durch den Einfluss der photo-generierten Löcher auf das Quantentrog-PL-Spektrum und der damit verbundenen Beeinflussung des Exziton-Trion-Verhältnisses, konnten die beiden oben genannten Abhängigkeiten herausgearbeitet werden. Zusammenfassend sind beide Mechanismen für die Loch-Abstimmung im QT und damit für das magnetische soft-mode Verhalten von Bedeutung. Während der Mechanismus der Tunnelwahrscheinlichkeit bei schmalen Cap-Dicken überwiegt, spielt die oberflächeninduzierte p-Dotierung des QTs bei größeren Cap-Stärken (>25nm) die Hauptrolle. Fazit: Die, in dieser Arbeit präsentierte Methode ist ein sensibles Werkzeug, um die Dynamik der Spin-Anregungen und der paramagnetischen Suszeptibilität im Hinblick auf den Loch-induzierten ferromagnetischen Übergang zu untersuchen.