No description available.

No description available.

No description available.

The main contribution of the present thesis is in two aspects. The first one, which is the heart of the thesis, is to explore the fundamental relation between rough paths and their signatures. Our main goal is to give a geometric characterization of the kernel of the signature map in different situations. In Chapter Two, we start by establishing a general fact that a continuous Jordan curve on a Riemannian manifold can be arbitrarily well approximated by piecewise minimizing geodesic interpolations which are again Jordan. This result enables us to prove a generalized version of Green’s theorem for planar Jordan curves with finite p-variation 1 &le; p < 2, and to prove that two such Jordan curves have the same signature if and only if they are equal up to reparametrization. In Chapter Three, we investigate the problem for general weakly geometric rough paths. In particular, we show that a weakly geometric rough path has trivial signature if and only if it is tree-like in the sense we will define later on. In Chapter Four, we study the problem in the probabilistic setting. In particular, we show that for a class of stochastic processes, with probability one the sample paths are determined by their signatures up to reparametrization. A fundamental example is Gaussian processes including fractional Brownian motion with Hurst parameter H > 1/4, the Ornstein-Uhlenbeck process and the Brownian bridge. The second one is an application of rough path theory to the study of nonlinear diffusions on manifolds under the framework of nonlinear expectations. In Chapter Five, we begin by studying the geometric rough path nature of G-Brownian motion. This enables us to introduce rough differential equations driven by G-Brownian motion from a pathwise point of view. Next we establish the fundamental relation between rough (pathwise theory) and stochastic (L²-theory) differential equations driven by G-Brownian motion. This is a crucial point of understanding nonlinear diffusions and their generating heat flows on manifolds from an intrinsic point of view. Finally, from the pathwise point of view we construct G-Brownian motion on a compact Riemannian manifold and establish its generating heat flow for a class of G-functions under orthogonal invariance. As an independent interest, we also develop the Euler-Maruyama scheme for stochastic differential equations driven by G-Brownian motion.

In this project, the time-dependent one-dimensional heat equation with internal heating is solved using eigenfunction expansion, according to the thermoelectric boundary conditions. This derivation of the equation describing time-dependent heat flow in a thermoelectric sample or device yields a framework that scientists can use (by entering their own parameters into the equations) to predict the behavior of a system or to verify numerical calculations. Allowing scientists to predict the behavior of a system can help in decision making over whether a particular experiment is worthy of the time to construct and execute it. For experimentalists, it is valuable as a tool for comparison to validate the results of an experiment. The calculations done in this derivation can be applied to pulsed cooling systems, the analysis of Z-meter measurements, and other transient techniques that have yet to be invented. The vast majority of the calculations in this derivation were done by hand, but the parts that required numerical solutions, plotting, or powerful computation, were done using Mathematica 8. The process of filling in all the steps needed to arrive at a solution to the time-dependent heat equation for thermoelectrics yields many insights to the behavior of the various components of the system and provides a deeper understanding of such systems in general.

3D seismic reflection data were acquired by the R/V Langseth and used to extract heat flow information using bottom-simulating reflector (BSR) depths across the southern Costa Rica convergent margin. These data are part of the CRISP Project, which will seismically image the Middle America subduction zone in 3D. The survey was conducted in an area approximately 55x11 km, northwest of the Osa Peninsula, Costa Rica. For the analysis presented here, seismic data were processed using a post-stack time migration. The BSR—a reverse polarity seismic reflection indicating the base of the gas hydrate phase boundary—is imaged clearly within the slope-cover sediments of the margin wedge. If pressure is taken into account, in deep water environments the BSR acts as a temperature gauge revealing subsurface temperatures across the margin. Two heat flow models were used in this analysis. In the Hornbach model BSR depth is predicted using a true 3D diffusive heat flow model combined with Integrated Ocean Drilling Program (IODP) thermal conductivity data and results are compared with actual BSR depth observations to constrain where heat flow anomalies exist. In the second model heat flow values are estimated using the heat flow equation. Uniform heat flow in the region should result in a deeper BSR downslope toward the trench due to higher pressure; however results indicate the BSR is deepest at over 325 meters below the seafloor (mbsf) further landward and shoals near the trench to less than 100 mbsf, suggesting elevated heat flow towards the toe of the accretionary prism. Heat flow values also reflect this relation. In addition to this survey-wide trend, local heat flow anomalies appear in the form of both circular patterns and linear trends extending across the survey, which can be related to mounds, thrust faults, folds, double BSRs, and seafloor erosion imaged in the seismic data. I suggest that these areas of higher local heat flow represent sites where advection of heat from deep, upward-migrating, thermogenically-sourced fluids and/or gases may be taking place. These heat flow trends have implications for not only earthquake nucleation, but also methane hydrate reserve stability. / text

No description available.

The surface heat flow (qs) is paramount for modeling the thermal structure of the lithosphere. Changes in the qs over a distinct lithospheric unit are normally directly reflecting changes in the crustal composition and therewith the radiogenic heat budget (e.g., Rudnick et al., 1998; Förster and Förster, 2000; Mareschal and Jaupart, 2004; Perry et al., 2006; Hasterok and Chapman, 2011, and references therein) or, less usual, changes in the mantle heat flow (e.g., Pollack and Chapman, 1977). Knowledge of this physical property is therefore of great interest for both academic research and the energy industry. The present study focuses on the qs of central and southern Israel as part of the Sinai Microplate (SM). Having formed during Oligocene to Miocene rifting and break-up of the African and Arabian plates, the SM is characterized by a young and complex tectonic history. Resulting from the time thermal diffusion needs to pass through the lithosphere, on the order of several tens-of-millions of years (e.g., Fowler, 1990); qs-values of the area reflect conditions of pre-Oligocene times. The thermal structure of the lithosphere beneath the SM in general, and south-central Israel in particular, has remained poorly understood. To address this problem, the two parameters needed for the qs determination were investigated. Temperature measurements were made at ten pre-existing oil and water exploration wells, and the thermal conductivity of 240 drill core and outcrop samples was measured in the lab. The thermal conductivity is the sensitive parameter in this determination. Lab measurements were performed on both, dry and water-saturated samples, which is labor- and time-consuming. Another possibility is the measurement of thermal conductivity in dry state and the conversion to a saturated value by using mean model approaches. The availability of a voluminous and diverse dataset of thermal conductivity values in this study allowed (1) in connection with the temperature gradient to calculate new reliable qs values and to use them to model the thermal pattern of the crust in south-central Israel, prior to young tectonic events, and (2) in connection with comparable datasets, controlling the quality of different mean model approaches for indirect determination of bulk thermal conductivity (BTC) of rocks. The reliability of numerically derived BTC values appears to vary between different mean models, and is also strongly dependent upon sample lithology. Yet, correction algorithms may significantly reduce the mismatch between measured and calculated conductivity values based on the different mean models. Furthermore, the dataset allowed the derivation of lithotype-specific conversion equations to calculate the water-saturated BTC directly from data of dry-measured BTC and porosity (e.g., well log derived porosity) with no use of any mean model and thus provide a suitable tool for fast analysis of large datasets. The results of the study indicate that the qs in the study area is significantly higher than previously assumed. The new presented qs values range between 50 and 62 mW m⁻². A weak trend of decreasing heat flow can be identified from the east to the west (55-50 mW m⁻²), and an increase from the Dead Sea Basin to the south (55-62 mW m⁻²). The observed range can be explained by variation in the composition (heat production) of the upper crust, accompanied by more systematic spatial changes in its thickness. The new qs data then can be used, in conjunction with petrophysical data and information on the structure and composition of the lithosphere, to adjust a model of the pre-Oligocene thermal state of the crust in south-central Israel. The 2-D steady-state temperature model was calculated along an E-W traverse based on the DESIRE seismic profile (Mechie et al., 2009). The model comprises the entire lithosphere down to the lithosphere–asthenosphere boundary (LAB) involving the most recent knowledge of the lithosphere in pre-Oligocene time, i.e., prior to the onset of rifting and plume-related lithospheric thermal perturbations. The adjustment of modeled and measured qs allows conclusions about the pre-Oligocene LAB-depth. After the best fitting the most likely depth is 150 km which is consistent with estimations made in comparable regions of the Arabian Shield. It therefore comprises the first ever modelled pre-Oligocene LAB depth, and provides important clues on the thermal state of lithosphere before rifting. This, in turn, is vital for a better understanding of the (thermo)-dynamic processes associated with lithosphere extension and continental break-up. / Der Oberflächenwärmefluss (qs) ist maßgeblich für die Modellierung der thermischen Struktur der Lithosphäre. Änderungen im qs, innerhalb eines speziellen lithosphärischen Abschnitts, reflektieren direkt Änderungen in der krustalen Zusammensetzung und damit der radiogenen Wärmeproduktion (e.g., Rudnick et al., 1998; Förster und Förster, 2000; Mareschal und Jaupart, 2004; Perry et al., 2006; Hasterok und Chapman, 2011) oder aber, weniger häufig, Änderungen im Mantelwärmefluss (e.g., Pollack und Chapman, 1977). Die Kenntnis dieses physikalischen Parameters ist daher von großem Interesse, sowohl für die Forschung als auch für die Energiewirtschaft. Die vorliegende Studie befasst sich mit dem qs von Süd- und Zentralisrael als Teil der Sinai Mikroplatte (SM), welche während des Riftings und Auseinanderbrechens der Afrikanischen und Arabischen Platte im Oligozän entstand und durch diese, sehr junge und komplexe tektonische Geschichte, geprägt ist. Die thermische Diffusion benötigt einige Zehner-Millionen Jahre (e.g., Fowler, 1990) um die Lithosphäre zu durchlaufen, qs-Werte der Region reflektieren daher prä-oligozäne Bedingungen. Die thermische Struktur der Lithosphäre in Süd- und Zentralisrael, ist bis heute nur sehr wenig verstanden. Um dieses Problem anzugehen wurden die Parameter die für die qs-Bestimmung benötigt werden, eingehend untersucht. An zehn ehemaligen Wasser- und Erdölexplorationsbohrungen wurden neue Temperaturmessungen durchgeführt, und die Wärmeleitfähigkeit von 240 Bohrkern- und Aufschlussproben wurde im Labor gemessen. Die Wärmeleitfähigkeit ist in der qs-Bestimmung der sensitive Parameter. Die Labormessungen wurden sowohl an trockenen sowie an wasser-gesättigten Proben durchgeführt, was personal-und zeitaufwendig ist. Eine andere Möglichkeit ist die Messung der Wärmeleitfähigkeit im trockenen Zustand und das Konvertieren zu einem saturierten Wert unter der Verwendung von Mischungsgesetzen. Das Vorhandensein eines umfangreichen und sehr diversen Wärmeleitfähigkeit-Datensatzes ermöglicht (1) in Verbindung mit dem Temperaturgradienten die Berechnung von neuen zuverlässigen qs-Werten sowie deren Verwendung zur Modellierung der thermischen Struktur der prä-oligozänen Kruste in Israel und (2) in Verbindung mit vergleichbaren Datensätzen, die vorhandenen Mischungsgesetzte zur indirekten Bestimmung der saturierten Gesamtwärmeleitfähigkeit (BTC) qualitativ zu überprüfen. Die Zuverlässigkeit numerisch bestimmter BTC-Werte variiert für die verschiedenen Mischungsgesetze und ist darüber hinaus stark von der Lithologie der Proben abhängig. Mittels spezifischer Korrekturgleichungen können Abweichungen zwischen gemessenen und berechneten Werten jedoch erheblich reduziert werden. Die Datenanzahl und die statistische Analyse ermöglichte darüber hinaus die Ableitung von lithotypspezifischen Konvertierungsgleichungen, um die saturierte BTC anhand von trocken gemessenen BTC- und Porositätswerten (z.B. aus Logs) zu berechnen. Dieser Ansatz führt, für alle Lithotypen, zu einer guten Reproduzierbarkeit gemessener Werte und ist daher eine nützliche Alternative, wann immer große Probenmengen behandelt werden. Die Ergebnisse dieser Studie zeigen, dass der qs im Untersuchungsgebiet signifikant höher ist, als bisher angenommen. Die qs-Werte, die in dieser Studie für Israel bestimmt wurden, schwanken zwischen 50 und 62 mW m⁻². Ein schwacher Trend abnehmender Werte von Ost nach West (55-50 mW m⁻²), und ein leichter Trend ansteigender Werte vom Toten Meer nach Süden (55-62 mW m⁻²) können identifiziert werden. Diese beobachteten Schwankungen lassen sich mit Variationen in der krustalen Zusammensetzung (Wärmeproduktion) erklären, einhergehend mit regionalen Änderungen der Krustenmächtigkeit. Die neuen qs-Daten können dann, im Zusammenhang mit petrophysikalischen Daten und Informationen über die Struktur und Zusammensetzung der Lithosphäre, verwendet werden um ein Model des prä-oligozänen thermischen Zustandes der Kruste Zentral- und Südisraels abzugleichen. Das stationäre 2-D Temperatur-Modell wurde entlang einer E-W Traverse, basierend auf dem seismischen DESIRE-Profil (Mechie et al., 2009), berechnet. Es reicht bis zur Lithosphären–Asthenosphären Grenze (LAB) und bezieht sich auf das aktuellste Wissen über die prä-oligozäne Lithosphäre, also vor dem Einsetzen von Rifting und plumebedingten thermischen Störungen. Durch den Abgleich zwischen gemessenen und modellierten qs-Werten ist es möglich auf die prä-oligozäne LAB-Tiefe zurückzuschließen. Als wahrscheinlichste Tiefe ergeben sich 150 km, was konsistent ist mit LAB-Tiefen Abschätzungen aus vergleichbaren stabilen Regionen des Arabischen Schildes. Dies liefert wichtige Anhaltspunkte über den thermischen Zustand der Lithosphäre vor dem Einsetzen von Rifting in der Region und ist wiederum entscheidend für ein besseres Verständnis der dynamischen Prozesse in Assoziation mit Extension der Lithosphäre und dem kontinentalem Auseinanderbrechen.

No description available.

After water vapour, CO₂ is the most abundant gas associated with magmatic hydrothermal systems. The detection of anomalous soil temperature gradients, and/or a significant flux of magmatic volatiles, is commonly the only surface signature of an underlying high temperature reservoir. For both heat (as water vapour) and gas to ascend to the surface, structural permeability must exist, as the unmodified bulk permeability of reservoir rock is too low to generate the focussed fluid flow typical of magmatic hydrothermal systems. This thesis reports the investigation into the surface heat and mass flow of the Ohaaki hydrothermal field using detailed surface measurements of CO₂ flux and heat flow. Detailed surface measurements form the basis of geostatistical models that quantify and depict the spatial variability of surface heat and mass flow, across the surface of both major thermal areas, as high resolution pixel plots. These maps, in conjunction with earlier heat and mass flow studies, enable: (i) estimates of the pre-production and current CO₂ emissions and heat flow for the Ohaaki Field; (ii) interpretation of the shallow permeability structures governing fluid flow, and; (iii) the spatial relationships between pressure-induced ground subsidence and permeability. Heat flow and CO₂ flux surveys indicate that at Ohaaki the soil zone is the dominant (≥ 70% and up to 99%) pathway of heat and mass release to the atmosphere from the underlying hydrothermal reservoir. Modelling indicates that although the total surface heat and mass flow at Ohaaki is small, it is highly focused (i.e., high volume per unit area) relative to other fields within the Taupo Volcanic Zone (TVZ). Normalised CO₂ emissions are comparable to other volcanic and hydrothermal fields both regionally and globally. Despite 20 years of production, there is little difference between pre-production and current CO₂ emission rates. However, the similarity of CO₂ emission rates masks a 40% increase in CO₂ emissions from new areas of intense steaming ground that have developed in response to production of the field for electrical energy production. This increase in thermal ground emissions is offset by emission losses associated with the drying up of all steam heated pools and alkali-Cl outflows from the Ohaaki West (OHW) thermal area, in response to production-induced pressure decline. The location of surface thermal areas is governed by the occurrence of buried or partially emergent lava domes, whereas the magnitude of CO₂ flux, mass flow, and heat flow occurring within each thermal area is determined by the proximity of each dome (thermal areas) to major upflow zones. Buried or partially emergent silicic lava domes act as cross-stratal pathways for fluid flow, connecting the underlying reservoir to the surface, and bypassing several hundred metres of the poorly permeable Huka Falls Formation (HFF) caprock. For each dome complex the permeable structures governing fluid flow are varied. At Ohaaki West, thermal activity is controlled by a deep-rooted concentric fracture zone, developed during eruption of the Ohaaki Rhyolite dome. Within the steam-heated Ohaaki East (OHE) thermal area, flow is controlled by a high permeability fault damage zone (Broadlands Fault) developed within the apex of the Broadlands Dacite dome. Structures controlling alkali-Cl fluid flow at OHW also iii appear to control the occurrence and shape of major subsidence bowls (e.g., the Main Ohaaki Subsidence Bowl), the propagation of pressure decline to surface, and the development and localization of pore fluid drainage. Across the remainder of the Ohaaki field low amplitude ground subsidence is controlled by the extent of aquifer and aquitard units that underlie the HFF, and proximity to the margins of the hot water reservoir. The correlation between the extent of low amplitude ground subsidence and the margins of the field reflects the coupled relationship between the hot water reservoir and reservoir pressure. Only where thick vapour-phase zones buffer the vertical propagation of deep-seated pressure decline to the surface (i.e., OHE thermal area), is ground subsidence not correlated with subvertical structural permeability developed within the HFF. This thesis makes contributions to regional and global research on geothermal and hydrothermal systems by: (i) quantifying the origin, mass, and upward transport of magmatic carbon from geothermal reservoirs; (ii) assessing the changes to the natural surface heat and mass flow of the Ohaaki Field following 20 years of production; (iii) establishing the utility of surface CO₂ flux and heat flow surveys to identify major upflow zones, estimate minimum mass flow, and determine the enthalpy of reservoirs; (iv) providing insight into the hydrothermal, structural and lithological controls over hydrothermal fluid flow; (v) demonstrating the influence of extinct silicic lava domes as important structural elements in the localisation of hydrothermal fluid flow; (vi) identifying the hydrostructural controls governing the spatial variability in the magnitude of pressure-induced ground subsidence, from which predictive models of subsidence risk may be defined, and; (vii) developing new technologies and characterising methods used for detailed assessment of surface heat and mass flow.