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1
Cocks, David. "Mathematical modelling of dune formation." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442818.
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This study is concerned with the mathematical modelling of the formation and subsequent evolution of sand dunes, both beneath rivers (fluvial) and in deserts (Aeolian). Dunes are observed in the environment in many different shapes and sizes; we begin by discussing qualitatively how and why the different forms exist. The most important aspect of a successful model is the relationship between the bed shape and the shear stress that the flow exerts on the bed. We first discuss a simple model for this stress applied to fluvial dunes, which is able to predict dune-like structures, but does not predict the instability of a flat bed which we would hope to find. We therefore go on to look at improved models for the shear stress based on theories of turbulent flow and asymptotic methods, using assumptions of either a constant eddy viscosity or a mixing length model for turbulence. Using these forms for the shear stress, along with sediment transport laws, we obtain partial integrodifferential equations for the evolution of the bed, and we study these numerically using spectral methods. One important feature of dunes which is not taken into account by the above models is that of the slip face - a region of constant slope on the downwind side of the dune. When a slip face is present, there is a discontinuity in the slope of the bed, and hence it is clear that flow separation will occur. Previous studies have modelled separated flow by heuristically describing the boundary of the separated region with a cubic or quintic polynomial which joins smoothly to the bed at each end. We recreate this polynomial form for the wake profile and demonstrate a method for including it into an evolution system for dunes. The resulting solutions show an isolated steady-state dune which propagates downstream. From the asymptotic framework developed earlier with a mixing length model for turbulence, we are able, using techniques of complex analysis, to model the shape of the wake region from a purely theoretical basis, rather than the heuristic one used previously. We obtain a Riemann-Hilbert problem for the wake profile, which can be solved using well-known techniques. We then use this method to calculate numerically the wake profile corresponding to a number of dune profiles. Further, we are able to find an exact solution to the wake profile problem in the case of a sinusoidally shaped dune with a slip face. Having found a method to calculate the shear stress exerted on the dune from the bed profile in the case of separated flow, we then use this improved estimate of the shear stress in an evolution system as before. In order to do this efficiently, we consider an alternative method for calculating the wake profile based on the spectral method used for solving the evolution system. We find that this system permits solutions describing an isolated dune with a slip face which propagates downstream without changing shape. All of the models described above are implemented in two spatial dimensions; the wind is assumed to blow in one direction only, and the dunes are assumed to be uniform in a direction perpendicular to the wind flow. While this is adequate to explain the behaviour of transverse dunes, other dune shapes such as linear dunes, barchans, and star dunes are by nature three-dimensional, so in order to study the behaviour of such dunes, the extension of the models to three dimensions is essential. While most of the governing equations generalize easily, it is less obvious how to extend the model for separated flow, due to its reliance on complex variables. We implement some three-dimensional evolution models, and discuss the possibility of modelling three-dimensional flow separation.
2
Hewitt, Ian. "Mathematical modelling of geophysical melt drainage." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509957.
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Fluid flows involving transport of a liquid phase in close proximity with its solid phase involve continuous transfer of mass and heat, which can influence the nature of the drainage that occurs. We consider mathematical models for two such situations; magma flow in the mantle and water flow beneath glaciers. In part I, we derive a model for porous flow within a partially molten column of mantle undergoing decompression melting. By ignoring composition effects, and by scaling the equations appropriately, approximate analytical solutions can be found for one-dimensional upwelling, which allow the region and extent of melting to be determined. We study the dynamics of open channels of melt flow in the same situation, and find that such channels would have low pressure compared to the surrounding porous flow, and therefore draw in melt from a region of the size of a compaction length. We suggest that such channels could form through the unstable effects of melting caused by heat transfer by the upwelling melt. We emphasise the similarity with channels of meltwater that are known to exist beneath ice. In part II we pose a generalised model for subglacial water flow, which is described as an effective porous medium, the pore space being determined from an evolution equation. This is used to investigate the flow into a channel, which is found to be drawn from a surrounding region whose size, we suggest, determines the spacing between major drainage channels beneath ice sheets. These are compared to the observed spacing of eskers. A critical condition on the discharge necessary to sustain a channel is found, which may provide a criteria to decide where and when channelised drainage occurs. Lastly, a simple drainage model is used to explain seasonal variations in the velocity of a valley glacier.
3
Cassidy, Nigel John. "The application of mathematical modelling in the interpretation of near-surface archaeological ground-penetrating radar." Thesis, Keele University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.344057.
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Ng, F. S. L. "Mathematical modelling of subglacial drainage and erosion." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244772.
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The classical theory of channelized subglacial drainage,due orginally to Röthlisberger (1972) and Nye (1976), considers water flow in an ice channel overlying a rigid, impermeable bed. At steady flow, creep closure of the channel walls is counteracted by melt-back due to heat dissipation, and this leads to an equilibrium relation between channel water pressure and discharge. More generally, such a balance exhibits an instability that can be used to describe the mechanics of catastrophic flood events known as `jökulhlaups'. In this thesis, we substantiate these developments by exploring a detailed model where the channel is underlain by subglacial till and the flow supports a sediment load. Attention is given to the physics of bed processes and its effect on channel morphology. In particular, we propose a theory in which the channel need not be semi-circular, but has independently evolving depth and width determined by a local balance between melting and closure, and in which sediment erosion and deposition is taken into account. The corresponding equilibrium relation indicates a reverse dependence to that in the classical model, justifying the possibility of the subglacial canals envisaged by Walder and Fowler (1994). Theoretical predictions for sediment discharge are also derived. Regarding time-dependent flood drainage, we demonstrate how rapid channel widening caused by bank erosion can explain the abrupt recession observed in the flood hydrographs. This allows us to produce an improved simulation of the 1972 jökulhlaup from Grímsvötn, Iceland, and self-consistently, a plausible estimate for the total sediment yield. We also propose a mechanism for the observed flood initiation lake-level at Grímsvötn. These investigations expose the intimate interactions between drainage and sediment transport, which have profound implications on the hydrology, sedimentology and dynamics of ice masses, but which have received little attention.
5
Schoof, C. "Mathematical models of glacier sliding and drumlin formation." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249325.
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One of the central difficulties in many models of glacier and ice sheet flow lies in the prescription of boundary conditions at the bed. Often, processes which occur there dominate the evolution of the ice mass as they control the speed at which the ice is able to slide over the bed. In part I of this thesis, we study two complications to classical models of glacier and ice sheet sliding. First, we focus on the effect of cavity formation on the sliding of a glacier over an undeformable, impermeable bed. Our results do not support the widely used sliding law $u_b = C\tau_b^pN^{-q}$, but indicate that $\tau_b/N$ actually decreases with $u_b/N$ at high values of the latter, as suggested previously for simple periodic beds by Fowler (1986). The second problem studied is that of an ice stream whose motion is controlled by bed obstacles with wavelengths comparable to the thickness of ice. By contrast with classical sliding theory for ice of constant viscosity,the bulk flow velocity does not depend linearly on the driving stress. Indeed, the bulk flow velocity may even be a multi-valued function of driving stress and ice thickness. In the second part of the thesis, attention is turned to the formation of drumlins. The viscous till model of Hindmarsh (1998) and Fowler (2000) is analysed in some detail. It is shown that the model does not predict the formation of three-dimensional drumlins, but only that of two-dimensional features, which may be interpreted as Rogen moraines. A non-linear model allows the simulation of the predicted bedforms at finite amplitude. Results obtained indicate that the growth of bedforms invariably leads to cavitation. A model for travelling waves in the presence of cavitation is also developed, which shows that such travelling waves can indeed exist. Their shape is, however, unlike that of real bedforms, with a steep downstream face and no internal stratification. These results indicate that Hindmarsh and Fowler's model is probably not successful at describing the processes which lead to the formation of streamlined subglacial bedforms.
6
Fay, Gemma Louise. "Mathematical modelling of turbidity currents." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:62bb9382-1c50-47f3-8f59-66924cc31760.
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Turbidity currents are one of the primary means of transport of sediment in the ocean. They are fast-moving, destructive fluid flows which are able to entrain sediment from the seabed and accelerate downslope in a process known as `ignition'. In this thesis, we investigate one particular model for turbidity currents; the `Parker model' of Parker, Pantin and Fukushima (1986), which models the current as a continuous sediment stream and consists of four equations for the depth, velocity, sediment concentration and turbulent kinetic energy of the flow. We propose two reduced forms of the model; a one-equation velocity model and a two-equation shallow-water model. Both these models give an insight into the dynamics of a turbidity current propagating downstream and we find the slope profile to be particularly influential. Regions of supercritical and subcritical flow are identified and the model is solved through a combination of asymptotic approximations and numerical solutions. We next consider the dynamics of the four-equation model, which provides a particular focus on Parker's turbulent kinetic energy equation. This equation is found to fail catastrophically and predict complex-valued solutions when the sediment-induced stratification of the current becomes large. We propose a new `transition' model for turbulent kinetic energy which features a switch from an erosional, turbulent regime to a depositional, stably stratified regime. Finally, the transition model is solved for a series of case studies and a numerical parameter study is conducted in an attempt to answer the question `when does a turbidity current become extinct?'.
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Yang, Xin-She. "Mathematical modelling of compaction and diagenesis in sedimentary basins." Thesis, University of Oxford, 1997. http://ora.ox.ac.uk/objects/uuid:0bdc6c43-4534-4f08-97e2-8a33d6b13e61.
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Sedimentary basins form when water-borne sediments in shallow seas are deposited over periods of millions of years. Sediments compact under their own weight, causing the expulsion of pore water. If this expulsion is sufficiently slow, overpressuring can result, a phenomenon which is of concern in oil drilling operations. The competition between pore water expulsion and burial is complicated by a variety of factors, which include diagenesis (clay dewatering), and different modes (elastic or viscous) of rheological deformation via compaction and pressure solution, which may also include hysteresis in the constitutive behaviours. This thesis is concerned with models which can describe the evolution of porosity and pore pressure in sedimentary basins. We begin by analysing the simplest case of poroelastic compaction which in a 1-D case results in a nonlinear diffusion equation, controlled principally by a dimensionless parameter lambda, which is the ratio of the hydraulic conductivity to the sedimentation rate. We provide analytic and numerical results for both large and small lambda in Chapter 3 and Chapter 4. We then put a more realistic rheological relation with hysteresis into the model and investigate its effects during loading and unloading in Chapter 5. A discontinuous porosity profile may occur if the unloaded system is reloaded. We pursue the model further by considering diagenesis as a dehydration model in Chapter 6, then we extend it to a more realistic dissolution-precipitation reaction-transport model in Chapter 7 by including most of the known physics and chemistry derived from experimental studies. We eventually derive a viscous compaction model for pressure solution in sedimentary basins in Chapter 8, and show how the model suggests radically different behaviours in the distinct limits of slow and fast compaction. When lambda << 1, compaction is limited to a basal boundary layer. When lambda >> 1, compaction occurs throughout the basin, and the basic equilibrium solution near the surface is a near parabolic profile of porosity. But it is only valid to a finite depth where the permeability has decreased sufficiently, and a transition occurs, marking a switch from a normally pressured environment to one with high pore pressures.
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Silva, Maria Gabriela Melo. "Preservação da amplitude na migração da equação da onda." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307300.
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Orientadores: Joerg Schleicher, Amelia NovaisDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Em meios homogêneos, o operador diferencial da equação da onda cheia pode ser substituído pelo produto de dois operadores diferenciais. Cada um destes operadores gera uma equação da onda de sentido único. As soluções destas equações descrevem a propagação de uma onda para baixo e uma para cima, respectivamente. Estas soluções possuem os mesmos tempos de trânsito e amplitudes que a onda cheia, uma vez que satisfazem as mesmas equações iconal e de transporte. No entanto, em meios heterogêneos, estas ondas de sentido único satisfazem somente a mesma equação iconal que a onda cheia. Zhang et al. (2003) mostraram como obter equações da onda de sentido único de amplitude verdadeira de modo que estas possuam tanto os mesmos tempos de trânsito como as mesmas amplitudes da onda cheia. Com base nestas equações, desenvolveram uma migração da equação da onda de amplitude verdadeira para seções de fonte comum. Nosso objetivo neste trabalho é modificar a migração de Gazdag (1980), de tal maneira que esta passe a utilizar as equações da onda de sentido único de amplitude verdadeira ao invés das equações de sentido único padrão, para realizar uma migração da equação da onda em amplitude verdadeira para seções de afastamento nulo
Abstract: In homogeneous media, the two-way wave operator can be substituted by the product of two one-way wave operators each of which generates a one-way wave equation. One of these equations has a downgoing wave and the other has an upgoing wave as a solution. Those oneway waves have the same travei time and amplitudes as the full wave since they satisfy the same eikonal and transport equation. However, in heterogeneous media, the standard one-way waves satisfy only the same eikonal equation as the full wave. Thus, in this case, the amplitudes of the migrated section obtained through a migration method based on the standard wave equations are incorrect. Zhang et al. (2003) described how to modify the standard one-way waves in order to produce the true amplitude one-way waves, which not only have the same travei times but also the same amplitudes as the full wave. They use these true amplitudes one-way wave equations to preserve the amplitudes in common-shot wave-equation migration. Our goal is to modify Gazdag migration (Gazdag, 1980) in such a way that it uses the true amplitude one-way wave equations instead of the standard ones, in order to realize a true amplitude wave equation migration for zero-offset data
Mestrado
Geofisica
Mestre em Matemática Aplicada
9
Nicholson, Lindsey. "Modelling melt beneath supraglacial debris : implications for the climatic response of debris-covered glaciers." Thesis, University of St Andrews, 2005. http://hdl.handle.net/10023/10264.
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Understanding how debris-covered glaciers respond to climate is necessary in order to evaluate future water resources and glacier flood hazard potential, and to make sense of the glacier chronology in mountain regions, In order achieve this, it is necessary to improve the current understanding of how surface debris affects glacier ablation rate, and to develop methods by which the ablation of debris-covered glaciers can be predicted under various climatic scenarios. This thesis develops a numerical surface energy balance model that uses simple meteorological data to calculate melt beneath a debris layer of given thickness and thermal characteristics. Field data from three contrasting sites demonstrate that the assumptions made within the model concerning the thermal properties of supraglacial debris are valid during most ablation conditions and that model performance is considerably better than previous models. Model results indicate that the effect of debris on melt rate is highly dependent on meteorological conditions. Under colder climates, thin debris can accelerate ice melt by extending the ablation period at both diurnal and seasonal scales. However, in milder mid- summer conditions, even a very thin debris cover inhibits melt rate compared to that of exposed ice. The new melt model is applied to produce the first quantified ablation gradients for debris- covered glaciers, and to model the evolution of ice surfaces under a debris layer of variable thickness. Modelled ablation gradients are qualitatively similar to hypothetical ones outlined previously, and quantitatively similar to those measured in the field. The ablation gradients are used to explore the factors affecting the response of debris-covered glaciers to climate change. Beneath a debris layer of variable thickness, the melt model produced ablation topography, as observed in the field, which underwent topographic inversion over time in response to debris redistribution. Debris thickness variability was found to cause calculated ablation rate to increase compared to that calculated using a mean debris thickness by one to two orders of magnitude, suggesting that melt calculations made on the basis of spatially averaged debris thickness may be inaccurate.
10
Wijns, Christopher P. "Exploring conceptual geodynamic models : numerical method and application to tectonics and fluid flow." University of Western Australia. School of Earth and Geographical Sciences, 2005. http://theses.library.uwa.edu.au/adt-WU2005.0068.
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Geodynamic modelling, via computer simulations, offers an easily controllable method for investigating the behaviour of an Earth system and providing feedback to conceptual models of geological evolution. However, most available computer codes have been developed for engineering or hydrological applications, where strains are small and post-failure deformation is not studied. Such codes cannot simultaneously model large deformation and porous fluid flow. To remedy this situation in the face of tectonic modelling, a numerical approach was developed to incorporate porous fluid flow into an existing high-deformation code called Ellipsis. The resulting software, with these twin capabilities, simulates the evolution of highly deformed tectonic regimes where fluid flow is important, such as in mineral provinces. A realistic description of deformation depends on the accurate characterisation of material properties and the laws governing material behaviour. Aside from the development of appropriate physics, it can be a difficult task to find a set of model parameters, including material properties and initial geometries, that can reproduce some conceptual target. In this context, an interactive system for the rapid exploration of model parameter space, and for the evaluation of all model results, replaces the traditional but time-consuming approach of finding a result via trial and error. The visualisation of all solutions in such a search of parameter space, through simple graphical tools, adds a new degree of understanding to the effects of variations in the parameters, the importance of each parameter in controlling a solution, and the degree of coverage of the parameter space. Two final applications of the software code and interactive parameter search illustrate the power of numerical modelling within the feedback loop to field observations. In the first example, vertical rheological contrasts between the upper and lower crust, most easily related to thermal profiles and mineralogy, exert a greater control over the mode of crustal extension than any other parameters. A weak lower crust promotes large fault spacing with high displacements, often overriding initial close fault spacing, to lead eventually to metamorphic core complex formation. In the second case, specifically tied to the history of compressional orogenies in northern Nevada, exploration of model parameters shows that the natural reactivation of early normal faults in the Proterozoic basement, regardless of basement topography or rheological contrasts, would explain the subsequent elevation and gravitationally-induced thrusting of sedimentary layers over the Carlin gold trend, providing pathways and ponding sites for mineral-bearing fluids.
11
Hu, Xiaogang. "A hydrological analysis of icing formation /." Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=42054.
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Icings are common hydrological phenomena in arctic and subarctic regions. Their bodies are made up of the accumulation of ice layers formed by the freezing of overflow water during the winter season. Icing formation is a process involving a complex system of thermodynamics and hydrodynamics. In this thesis, the formation mechanics of river icings and ground icings are studied in terms of both thermal and hydrological processes.The energy exchange systems during icing layer formation involve two ice water interfaces and some intra-layer water flow. Using energy balance analysis, this research finds that the outgoing energy components can be ranked according to their importance, with sensible heat being the most important component, radiation heat loss being of secondary importance, and latent heat loss being the least important factor. Further, this research illustrates that the heat conduction between the underlying ice and a newly formed icing layer is time dependent. For example, during the first half cycle of icing layer formation, heat is conducted into the underlying ice, but during the second half of the cycle the heat is conducted in an opposite direction.
During icing layer formation, the energy input is supplied mainly by water and incoming solar radiation. Intra-layer running water provides a significant amount of energy when air temperatures are milder, but its significance decreases when air temperatures become colder. Solar radiation during the day may also play an important role in the energy supply regime.
River icing formation involves several hydrological processes. The location of a river icing is basically controlled by the channel slope. The damming effect of icing mass plays a significant role in the extension of the icing body, especially in the upstream direction. River icings grow slowly, and generally experience three stages of development, namely the 'freeze-up' stage, 'obstruction' stage and 'overflow' stage, the third stage dominating icing growth. The formation of each icing layer is virtually a small-scale reproduction of these three stages. The model simulation shows that the thickness of icing accumulation increases with an increase in the initial water depth in the channel, but simulation also shows that there is a limiting threshold. The thickness of icing accumulation decreases when the initial channel water depth exceeds this threshold.
The growth of an icing is an event-dominated discontinuous process. Even during one icing layer formation, simultaneous growth occurs only within a very limited distance. At a specific location, icing growth is related temporally only over a short period of time. As a discontinuous process, icing spreading and thickening during an overflow event depends entirely on the climatic and topographical conditions.
Even though icing layering is influenced by many variables, under small discharge rates, as in the case of ground icing growth, statistical analyses show that the mean spreading length of an overflow event can be described efficiently by five variables: discharge, the temperature of the water, the product of air temperature and wind speed, air temperature and the icing surface slope previous to overflow. The maximum spreading length, however, may only be controlled by four variables: discharge, water temperature, air temperature and the product of air temperature and wind speed. Under field conditions, when wind speed is not measured, this wind related variable may be dropped with only a small decrease in confidence level.
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Honório, Bruno César Zanardo 1983. "Aplicação da transformada wavelet na atenuação de ruídos e determinação de ciclos sedimentares em perfis geofísicos." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263063.
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Orientadores: Alexandre Campane Vidal, Emilson Pereira LeiteDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências
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Resumo: Perfis geofísicos de poços são importantes fontes de informação para o estudo de rochas em subsuperfície, sendo comumente utilizados na caracterização de reservatórios de petróleo. É sabido que os sinais obtidos como respostas do meio geológico contêm ruídos que podem afetar a interpretação do objeto estudado e que a transformada wavelet (WT) é melhor adaptada que a transformada de Fourier (FT) para a análise de sinais não-estacionários, como aqueles obtidos da perfilagem geofísica. Por outro lado, existem diversos parâmetros que devem ser considerados quando se trabalha com a WT, tais como a escolha da função wavelet base (wavelet mãe), o nível de decomposição, assim como a função e as regras que "controlam" como e quais coeficientes serão utilizados para reconstrução do sinal. Este estudo analisa o processo de atenuação de ruídos em perfis geofísicos de poços através da transformada wavelet ortogonal. Numa primeira abordagem, foi estudado o processo de atenuação em sinais sintéticos e então, foi estudado o processo em perfis geofísicos reais. Uma vez que os dados de perfis de poços são geralmente utilizados para a classificação de litologias, foi proposto um método associado com o algoritmo de classificação K-Vizinhos Mais Próximos (KNN) para investigar como as diferentes combinações dos parâmetros afetam os sinais de saída e o seu desempenho na classificação litológica, tornando assim um processo conduzido pelos dados. Foi investigada as funções de thresholding tradicionalmente empregadas (hard e soft threshold) bem como uma recente abordagem (customized threshold), sendo esta a que proporcionou melhores resultados. O potencial da transformada wavelet como ferramenta para auxiliar na interpretação geológica é evidenciado pela identificação de importantes características geológicas, como regiões de cimentação carbonática e a determinação de ciclos sedimentares, do Campo de Namorado, Bacia de Campos, Brasil
Abstract: Geophysical well logs are an important tool for the characterization of subsurface rocks, being commonly used in the study of reservoir geology. It is well known that signals obtained as responses from geological media contain noise that can affect their interpretation, and that wavelet transform (WT) is more suitable than the Fourier transform (FT) to denoise non-stationary signals, as the ones obtained from well logs. On the other hand, there are several parameters that must be considered when working with the WT, such as the wavelet basis function choice (mother wavelet), the decomposition level and also the function and rules that "control" which and how the coefficients will be used for signal reconstruction. This study analyzes the process of denoising geophysical well log data by orthogonal wavelet transform. In a first approach, it was studied the denoising process in synthetic signals and then, the process in real geophysical well logs. Since the well log data are usually used in lithology classification, we propose a method associated with the K-Nearest Neighbor (KNN) classification algorithm to investigate how different combinations of parameters affect the output signals and its performance in the lithological classification, thus making a data driven process. It was evaluated the thresholding function traditionally used (hard e soft threshold) as well a recent approach (customized threshold), this being the one that provided better results. The potential of the wavelet transform as a tool to aid geological interpretation is evidenced by the identification of important geological features, such as regions of carbonate cementation and determination of sedimentary cycles of the Namorado Field, Campos Basin, Brazil
Mestrado
Reservatórios e Gestão
Mestre em Ciências e Engenharia de Petróleo
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Zhong, Yiming. "Modelling sediment transportation and overland flow." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:a45eefae-5a0f-4917-9abb-261ae792f2ee.
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The erosion and transport of fertile topsoil is a serious problem in the U.S., Australia, China and throughout Europe. It results in extensive environmental damage, reduces soil fertility and productivity, and causes significant environmental loss. It is as big a threat to the future sustainability of global populations as climate change, but receives far less attention. With both chemicals (fertilizers, pesticides, herbicides) and biological pathogens (bacteria, viruses) preferentially sorbing to silt and clay sized soil particles, estimating contaminant fluxes in eroded soil also requires predicting the transported soils particle size distribution. The Hairsine-Rose (HR) erosion model is considered in this thesis as it is one of the very few that is specifically designed to incorporate the effect of particle size distribution, and differentiates between non-cohesive previously eroded soil compared with cohesive un-eroded soil. This thesis develops a new extended erosion model that couples the HR approach with the one-dimensional St Venant equations, and an Exner bed evolution equation to allow for feedback effects from changes in the local bed slope on surface hydraulics and erosion rates to be included. The resulting system of 2I +3 (where I = number of particle size classes) nonlinear hyperbolic partial differential equations is then solved numerically using a Liska-Wendroff predictor corrector finite difference scheme. Approximate analytical solutions and series expansions are derived to overcome singularities in the numerical solutions arising from either boundary or initial conditions corresponding to a zero flow depth. Three separate practical applications of the extended HR model are then considered in this thesis, (i) flow through vegetative buffer strips, (ii) modelling discharge hysteresis loops and (iii) the growth of antidunes, transportational cyclic steps and travelling wave solutions. It is shown by comparison against published experimental flume data that predictions from the extended model are able to closely match measurements of deposited sediment distribution both upstream and within the vegetative buffer strip. The experiments were conducted with supercritical inflow to the flume which due to the increased drag from the vegetative strip, resulted in a hydraulic jump just upstream of the vegetation. As suspended sediment deposited at the jump, this resulted in the jump slowly migrating upstream. The numerical solutions were also able to predict the position and hydraulic jump and the flow depth throughout the flume, including within the vegetative strip, very well. In the second application, it is found that the extended HR model is the first one that can produce all known types of measured hysteresis loops in sediment discharge outlet data. Five main loop types occur (a) clockwise, (b) counter-clockwise, (c,d) figure 8 of both flow orientations and (e) single curve. It is clearly shown that complicated temporal rainfall patterns or bed geometry are not required to developed complicated hysteresis loops, but it is the spatial distribution of previously eroded sediment that remains for the start of a new erosion event, which primarily governs the form of the hysteresis loop. The role of the evolution of the sediment distribution in the deposited layer therefore controls loop shape and behavior. Erosion models that are based solely on suspended sediment are therefore unable to reproduce these hysteretic loops without a priori imposing a hysteretic relationship on the parameterisations of the erosion source terms. The rather surprising result that the loop shape is also dominated by the suspended concentration of the smallest particle size is shown and discussed. In the third application, a linear stability analysis shows that instabilities, antidunes, will grow and propagate upstream under supercritical flow conditions. Numerical simulations are carried out that confirm the stability analysis and show the development and movement of antidunes. For various initial parameter configurations a series of travelling antidunes, or transportational cyclic steps, separated by hydraulic jumps are shown to develop and evolve to a steady form and wave speed. Two different forms arise whereby (a) the deposited layer completely shields the underlying original cohesive soil so that the cohesive layer plays no role in the speed or shape of the wave profile or (b) the cohesive soil is exposed along the back of the wave such that both the non-cohesive and cohesive layers affect the wave profile. Under (a) the solutions are obtained up to an additive constant as the actual location of the boundary of the cohesive soil is not required, whereas for (b) this constant must be determined in order to find the location on the antidune from where the cohesive soil becomes accessible. For single size class soils the leading order travelling wave equations are fairly straightforward to obtain for both cases (a) and (b). However for multi-size class soils, this becomes much more demanding as up to 2I + 3 parameters must be found iteratively to define the solution as each size class has its own wave profile in suspension and in the antidune.
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Pila, Matheus Fabiano 1979. "A redatumação de Kirchhoff de empilhamento único em amplitude verdadeira." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307297.
Full textAbstract:
Orientadores: Joerg Dietrich Wilhelm Schleicher, Maria Amelia Novais SchleicherTese (doutorado - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-19T12:49:36Z (GMT). No. of bitstreams: 1 Pila_MatheusFabiano_D.pdf: 9692582 bytes, checksum: 422912b9753d685de0277a6d91cf8f0a (MD5) Previous issue date: 2011
Resumo: Entende-se por datum a superfície onde estão posicionados os pares fonte-receptor usados na aquisição sísmica. Este datum pode ser plano ou irregular e sua profundidade pode variar. O objetivo da redatumação é transformar o dado sísmico adquirido na superfície original em um dado simulado adquirido em outra superfície. Obtém-se assim um novo dado, como se tivesse sido adquirido em uma superfície de geometria e profundidade diferentes. A vantagem deste processo seria eliminar a propagação indesejada da onda sísmica em camadas com forte variação na velocidade. A transformação correta das amplitudes, do dado na superfície original para os dados no novo datum, é de importância fundamental. Um dado com esta propriedade poderia ser usado em diversos processos que necessitam de um dado com amplitude verdadeira, possibilitando melhor caracterização de possíveis reservatórios, por exemplo. Um destes processos seria a migração Kirchhoff em amplitude verdadeira. Na literatura, existem trabalhos que discutem e comprovam que uma transformação de configuração em amplitude verdadeira pode ser obtida encadeando os processos de migração e demigração com funções peso. Nesta tese, nós estendemos este resultado e derivamos um operador de redatumação em amplitude verdadeira, ao considerar que neste encadeamento podemos também mudar a profundidade dos pares fonte-receptor, tanto no dado sísmico de entrada quanto no simulado de saída. Processos Kirchhoff como este dependem de um bom modelo de velocidades para poder calcular as correções de tempo de trânsito de cada traço. Ao longo deste trabalho, foi possível verificar como a cinemática da redatumação independe da velocidade abaixo do novo datum. Esta velocidade afeta apenas a função peso que corrige as amplitudes. No entanto, após alguns testes foi possível verificar que pequenas incertezas inseridas nesta variável produzem pouco erro relativo na amplitude final
Abstract: The surface where the source-receiver pairs used in the seismic aquisition are positioned is called a datum. This datum can be flat or irregular and the depth may vary. The main goal of redatuming is to transform the seismic data acquired on the original surface into simulated data as if acquired on another datum. The advantage of this process is that it can eliminate undesired seismic wave propagation in layers with strong velocity variation or strong topography. The correct amplitude transformation, from the original surface data to the new datum, is of fundamental importance if the data are to be used in subsequent true-amplitude processes that allow better characterization of potential reservoirs, for example. One of these processes is the true-amplitude migration. In the literature, there are studies that argue and prove that a true-amplitude configuration transform can be obtained by chaining the weighted migration and demigration integral operators. In this thesis, we extend this result and derive a true-amplitude redatuming operator. For this purpuse, we consider that in this chaining procedure, we can also change the depth of the source-receiver pairs, either in the input or simulated output configuration. Kirchhoff processes like this one depend on a good velocity model in order to calculate traveltime corrections for each trace. Throughout this work, we demonstrated that the kinematics of redatuming is independent of the velocity below the new datum. This velocity affects only the weight function that corrects the amplitudes. However, our numerical tests indicated that small uncertainties inserted in this variable resulted in little relative error in the final amplitude
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Thurley, Matthew J. (Matthew John) 1971. "Three dimensional data analysis for the separation and sizing of rock piles in mining." Monash University, Dept. of Electrical and Computer Systems, 2002. http://arrow.monash.edu.au/hdl/1959.1/7855.
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Campbell, Lucy J. "Nonlinear critical layer development of forced wave packets in geophysical shear flows." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ64529.pdf.
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Harris, Matthew W. "Numerical realization of the generalized Carrier-Greenspan transform for the shallow water wave equations." Thesis, University of Alaska Fairbanks, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1598961.
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Run-up of long waves in sloping U-shaped bays is studied analytically in the framework of the 1-D nonlinear shallow-water theory. By assuming that the wave flow is uniform along the cross-section, the 2-D nonlinear shallow-water equations are reduced to a linear semi-axis variable-coefficient 1-D wave equation via the generalized Carrier-Greenspan transformation (Rybkin et al., 2014). A spectral solution is developed by solving the linear semiaxis variable-coefficient 1-D equation via separation of variables and then applying the inverse Carrier-Greenspan transform. To compute the run-up of a given long wave a numerical method is developed to find the eigenfunction decomposition required for the spectral solution in the linearized system. The run-up of a long wave in a bathymetry characteristic of a narrow canyon is then examined.
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Graf, Kateryna Verfasser], Michael [Akademischer Betreuer] [Herty, and Martin [Akademischer Betreuer] Bücker. "Optimization methods for mathematical models for geophysical flows / Kateryna Graf ; Michael Herty, Martin Bücker." Aachen : Universitätsbibliothek der RWTH Aachen, 2021. http://d-nb.info/1238791239/34.
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Frey, Sarah E. "Characterization of instabilities in the problem of elastic planetary tides." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/280697.
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In 1911, A. E. H. Love published a linear elastic model for the tidal deformation of planetary bodies. Using numerical techniques that were unavailable to Love, surprising behaviors of the tidal solution have been found: tides of finite, even substantial, height are possible in the presence of an infinitesimal tide raiser, thus indicating some sort of instability. The Love tidal model was for the deformation of a homogeneous sphere. In order to better understand the nature of the instabilities in this model, I consider the effect of adding a radially dependent density profile to the model. For a given singularity, an increase in the initial density gradient causes the singularity to change locations in parameter space. For steep enough density gradient, the singularity is pushed outside the realm of physically meaningful parameter space for certain initial radial density profiles. Self-gravitation appears to be the likely mechanism for the driving of the tidal instability. The nature of the behavior of self-gravitation will be studied by considering an exact elastic formulation of the problem. In this way, a more complete view of the processes involved in the tidal deformation of a body can be explored. I find that each of the curves of singularity loci observed in the tidal problem correspond to instabilities in different modes for the exact elastic self-gravitation problem.
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Hsia, Chun-Hsiung. "Bifurcation and stability in fluid dynamics and geophysical fluid dynamics." [Bloomington, Ind.] : Indiana University, 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3223038.
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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2006."Title from dissertation home page (viewed June 28, 2007)." Source: Dissertation Abstracts International, Volume: 67-06, Section: B, page: 3165. Adviser: Shouhong Wang.
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Ross, Christopher P. "AVO limitations near salt structures." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/31010.
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Rhines, Andrew Nelson. "Past and Future Climate Variability: Extremes, Scaling, and Dynamics." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467324.
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Severe impacts result from extreme events such as heat waves, droughts, cold spells, and floods. Characterizing and predicting variations in climate that give rise to these phenomena is important for mitigating their effects on human and natural systems. This thesis investigates whether climate variability is measurably changing and describes the observational basis for recent shifts in the temperature distribution. New methodology is presented that robustly estimates local distributional changes and permits for mapping them to regional or global scales, overcoming limitations of previous analyses. Contrary to the widespread view that climate variability has increased in recent decades, these analyses show that temperature variability has generally declined — albeit with important regional differences.
Historical observations of temperature are crucial for long-term monitoring of Earth's climate. However, hundreds of millions of daily observations contain precision-related biases that prevent their use in distributional analyses. A new machine-learning algorithm automatically corrects for these biases, enabling their use in long-term climate studies. The algorithm increases the number of usable observations by an order of magnitude and has many applications in quality control and signal classification. As the observations sample Earth's climate sparsely in space and time, sophisticated statistical methods are used to map local signals to estimates of the full spatial field and its uncertainties. Much of the observed contraction of variability is shown to stem from decreased meridional temperature gradients due to amplified arctic warming in the northern hemisphere.
Short-term extremes are also contextualized with the low frequency variability inferred from paleoclimate observations and simulations. Spectral estimates used to measure variability on different time scales are shown to be surprisingly robust to unavoidable time-uncertainty present in all proxy records. Oxygen isotope records from Greenland that are widely used as temperature proxies therefore contain reliable signals of past climate variability on 1–60,000 year time scales, though the extent to which these reliably preserve temperature signals remains uncertain. In a further study we examine the validity of this temperature proxy using a set of global paleoclimate simulations with moisture source tracking, quantifying a seasonality bias that may explain the paleothermometer's damped response during glacial periods.Engineering and Applied Sciences - Applied Math
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Brazier, Richard Anthony 1967. "Seismic wave propagation stitching: Matching local and global techniques." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/282549.
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Multiple methods exist for modeling with synthetic seismograms, each with its own characteristic application; local and detailed; global and asymptotic; body and/or surface waves. Events such as the nuclear tests in the Tarim Basin in China, recorded at regional distances require more than one such characteristic. A successful model would need detail close in and a global result. The ability to join two methods can therefore be very powerful. Within this text the exploration is of finite difference and discrete wavenumber integration methods. The basis of the conversion between methods is the idea in Huygen's principle of representing a wave front as multiple sources, then propagated as an alternate method. Modeling detail locally, finite difference eventually becomes computationally intensive or undetailed. Representation theory replaces finite difference with discrete wavenumber integration propagating to the receiver at a regional distance. The requirement for multiple sources means that efficiency and optimization of methods are paramount.
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Warneford, Emma S. "The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:6604fcac-afe6-4abe-8a6f-6a09de4f933f.
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Observations of Jupiter show a super-rotating (prograde) equatorial jet that has persisted for decades. Shallow water simulations run in the Jovian parameter regime reproduce the mixture of robust vortices and alternating zonal jets observed on Jupiter, but the equatorial jet is invariably sub-rotating (retrograde). Recent work has obtained super-rotating equatorial jets by extending the standard shallow water equations to relax the height field towards its mean value. This Newtonian cooling-like term is intended to model radiative cooling to space, but its addition breaks key conservation properties for mass and momentum. In this thesis the radiatively damped thermal shallow water equations are proposed as an alternative model for Jovian atmospheres. They extend standard shallow water theory by permitting horizontal variations of the thermodynamic properties of the fluid. The additional temperature equation allows a Newtonian cooling term to be included while conserving mass and momentum. Simulations reproduce equatorial jets in the correct directions for both Jupiter and Neptune (which sub-rotates). Quasi-geostrophic theory filters out rapidly moving inertia-gravity waves. A local quasi-geostrophic theory of the radiatively damped thermal shallow water equations is derived, and then extended to cover whole planets. Simulations of this global thermal quasi-geostrophic theory show the same transition, from sub- to super-rotating equatorial jets, seen in simulations of the original thermal shallow water model as the radiative time scale is decreased. Thus the mechanism responsible for setting the direction of the equatorial jet must exist within quasi-geostrophic theory. Such a mechanism is developed by calculating the competing effects of Newtonian cooling and Rayleigh friction upon the zonal mean zonal acceleration induced by equatorially trapped Rossby waves. These waves transport no momentum in the absence of dissipation. Dissipation by Newtonian cooling creates an eastward zonal mean zonal acceleration, consistent with the formation of super-rotating equatorial jets in simulations, while the corresponding acceleration is westward for dissipation by Rayleigh friction.
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Rzeznik, Andrew Joseph. "Applied math in geophysical fluids : partially trapped wave problems and mining plumes." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/120657.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 129-132).
The first portion of this work focuses on leaky modes in the atmospheric sciences. Leaky modes (related to quasi-modes, scattering resonances, and the singularity expansion method) are discrete, oscillatory and decaying modes that arise in conservative systems where waves are partially trapped. By replacing the infinite domain with a finite domain and appropriate boundary conditions it is possible in many cases to construct a complete basis for the solution in terms of these modes. Formulating such effective boundary conditions requires a notion of the direction of propagation of the waves. For this purpose we introduce a generalization of the concept of group speed for exponentially decaying but conservative waves. This is found via an extended modulation argument and a generalization of Whitham's Average Lagrangian theory. The theory also shows that a close relationship exists between the branch cuts of the dispersion relation and the propagation direction, and is used to create spectral decompositions for simple problems in internal gravity waves. The last chapter considers deep-sea nodule mining operations, which potentially involve plans for discharge plumes to be released into the water column by surface operation vessels. We consider the effects of non-uniform, realistic stratifications with vertical shear on forced compressible plumes. The plume model is developed to account for the influence of thermal conduction through the discharge pipe and an initial adjustment phase. We investigate the substantial role of compressibility, for which a dimensionless number is introduced to determine its importance compared to that of the background stratification. Our results show that (i) small-scale stratification features can have a significant impact, (ii) in a static ambient there exists a discharge flow rate that minimizes the plume vertical extent, (iii) the ambient velocity profile plays an important role in determining the final plume scale and dilution factor, and (iv) for a typical plume the dilution factor is expected to be several hundred to a thousand.
by Andrew Joseph Rzeznik.
Ph. D.
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Thirunavukkarasu, Senganal. "Impedance Matching for Discrete, Periodic Media and Application to Two-Scale Wave Propagation Models." Thesis, North Carolina State University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3690210.
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Ittharat, Detchai. "3D radio reflection imaging of asteroid interiors." Thesis, Colorado School of Mines, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1557520.
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Imaging the interior structure of comets and asteroids in 3D holds the key for understand- ing early Solar System and planetary processes, aids mitigation of collisional hazards, and enables future space investigation. 3D wavefield extrapolation of time-domain finite differ- ences, which is referred to as reverse-time migration (RTM), is a tool to provide high-quality images of the complex 3D-internal structure of the target. Instead of a type of acquisition that separately deploys one orbiting and one landing satellite, I discuss dual orbiter systems, where transmitter and receiver satellites orbit around the asteroid target at different speeds. The dual orbiter acquisition can provide multi-offset data that improve the image quality by illuminating the target from different directions and by attenuating coherent noise caused by wavefield multi-pathing. Shot-record imaging requires dense and evenly distributed receiver coordinates to fully image the interior structure at every source-location.
I illustrate a 3D imaging method on a complex asteroid model based on the asteroid 433 Eros using realistic data generated from different acquisition designs for the dual orbiter system. In realistic 3D acquisition, the distribution and number of receivers are limited by the acquisition time, revolving speed and direction of both the transmitter and receiver satellites, and the rotation of the asteroid. The migrated image quality depends on different acquisition parameters (i.e., source frequency bandwidth, acquisition time, the spinning rate of the asteroid) and the intrinsic asteroid medium parameters (i.e., the asteroid attenuation factor and an accurate velocity model).
A critical element in reconstructing the interior of an asteroid is to have different ac- quisition designs, where the transmitter and receivers revolve quasi-continuously in different inclinational and latitudinal directions and offer evenly distributed receiver coordinates in the shot-record domain. Among different acquisition designs, the simplest orbit (where the transmitter satellite is fixed in the longitudinal plane and the receiver plane gradually shifts in the latitudinal direction around the asteroid target) offers the best data coverage and requires the least energy to shift the satellite. To obtain reasonable coverage for successfully imaging the asteroid interior, the selected acquisition takes up to eight months. However, this mission is attainable because the propulsion requirements are small due to the slow (< 10 cm/s) orbital velocities around a kilometer-sized asteroid.
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Shi, Bin. "Multiscale Statistical Analysis of Self-Similar Processes with Applications in Geophysics and Health Informatics." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/6887.
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In this dissertation, we address the statistical analysis under
the multiscale framework for the self-similar process. Motivated
by the problems arising from geophysics and health informatics, we
develop a set of statistical measures as discriminative summaries
of the self-similar process. These measures include Multiscale
Schur Monotone (MSM) measures, Geometric Attributes of
Multifractal Spectrum (GAMFS), Quasi-Hurst exponents, Mallat
Model and Tsallis Maxent Model. These measures are used as
methods to quantify the difference (or similarities) or as input
(feature) vectors in the classification model. As the cornstone of
GAMFS, we study the estimation of multifractal spectrum and adopt
a Weighted Least Squares (WLS) schemes in the wavelet domain to
minimize the heteroskedastic effects , which is inherent because
the sample variances of the wavelet coefficients depend on the scale.
We also propose a Combined K-Nearest-Neighbor classifier (Comb-K-NN)
to address the inhomogeneity of the class attributes,
which is indicated by the large variations between subsets of
input vectors. The Comb-K-NN classifier stabilizes the variations
in the sense of reducing the misclassification rates. Bayesian
justifications of Comb-K-NN classifier are provided.
GAMFS, Quasi-Hurst exponents, Mallat Model and Tsallis Maxent
Model are used in the study of assessing the effects of
atmospheric stability on the turbulence measurements in the
inertial subrange. We also formulate the criteria for success in
evaluating how atmospheric stability alters the MFS of a single
flow variable time series as a statistical classification model.
We use the multifractal discriminate model as the solution of this
problem. Also, high frequency pupil-diameter dynamic measurements,
which are well documented as measures of mental workload, are
summarized using both GAMFS and MSM. These summaries are further
used as the feature vector in the Comb-K-NN classifier. The
serious inhomogeneity among subjects in the same user group makes
classification difficult. These difficulties are overcome by using
Comb-K-NN classifier.
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Blackbourn, Luke A. K. "An analytical, phenomenological and numerical study of geophysical and magnetohydrodynamic turbulence in two dimensions." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/4291.
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In this thesis I study a variety of two-dimensional turbulent systems using a mixed analytical, phenomenological and numerical approach. The systems under consideration are governed by the two-dimensional Navier-Stokes (2DNS), surface quasigeostrophic (SQG), alpha-turbulence and magnetohydrodynamic (MHD) equations. The main analytical focus is on the number of degrees of freedom of a given system, defined as the least value $N$ such that all $n$-dimensional ($n$ ≥ $N$) volume elements along a given trajectory contract during the course of evolution. By equating $N$ with the number of active Fourier-space modes, that is the number of modes in the inertial range, and assuming power-law spectra in the inertial range, the scaling of $N$ with the Reynolds number $Re$ allows bounds to be put on the exponent of the spectrum. This allows the recovery of analytic results that have until now only been derived phenomenologically, such as the $k$[superscript(-5/3)] energy spectrum in the energy inertial range in SQG turbulence. Phenomenologically I study the modal interactions that control the transfer of various conserved quantities. Among other results I show that in MHD dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo inverse flux partially neutralises the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. These theoretical results are backed up by high resolution numerical simulations, out of which have emerged some new results such as the suggestion that for alpha turbulence the generalised enstrophy spectra are not closely approximated by those that have been derived phenomenologically, and new theories may be needed in order to explain them.
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Harris, Jamie. "The kinematics, dynamics and statistics of three-wave interactions in models of geophysical flow." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/58419/.
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We study the dynamics, kinematics and statistics of resonant and quasiresonant three-wave interactions appearing in models of geophysical flow. In these dispersive wave systems, the phenomenon of nonlinear resonance broadening plays a significant role across all three different branches of wave turbulence theory: from the statistical, to the discrete, and even the mesoscopic, formed as an intermediate regime between the two. The principal aim of this thesis is to understand the processes by which resonance broadening can induce a transition between each of these three different regimes. Beginning with the discrete case, we study two variants of the isolated triad: one with a constant additive forcing term; and the other in the presence of detuning. We provide a detailed analysis of both of these systems, covering their integrability and boundedness properties, showing that for almost all initial conditions the motion remains quasi-periodic and periodic respectively. Interestingly, we show that moderate amounts of detuning can actually promote energy exchange, increase the period and in rare instances cease to be periodic at all; each of these statements are contrary to what was previously thought. This motivates a more detailed study into the kinematics of resonance broadening. By analysing how the set of quasi-resonant modes develops under increased broadening, we show that a percolation-like transition exists, independent of the dispersion relationship used. At critical levels of broadening, we see the emergence of a single quasi-resonant cluster that begins to dominate the entire system. We argue that the formation of this cluster provides a way of characterising the turbulent state of the system, distinguishing between the discrete and statistical regimes. Through direct numerical simulation of the Charney-Hasegawa-Mima equation, we then assess whether this view is truly representative of the underlying dynamics. Here we find that the generation of quasi-resonantly excited modes can be detected through the statistical measures of total correlation and mutual information. We conclude by suggesting that these techniques have an incredible potential to infer the signature of both resonant and quasi-resonant clusters in fully realised turbulent systems, and yet are also subtle enough to detect qualitative changes in the underlying dynamics between different interacting modes.
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Stewart, Andrew L. "The role of the complete Coriolis force in cross-equatorial transport of abyssal ocean currents." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:6bf3faff-ec7e-4d11-bdfe-c54ae9d03895.
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In studies of the ocean it has become conventional to retain only the component of the Coriolis force associated with the radial component of the Earth’s rotation vector, the so-called “traditional approximation”. We investigate the role of the “non-traditional” component of the Coriolis force, corresponding to the non-radial component of the rotation vector, in transporting abyssal waters across the equator. We first derive a non-traditional generalisation of the multi-layer shallow water equations, which describe the flow of multiple superposed layers of inviscid, incompressible fluid with constant densities over prescribed topography in a rotating frame. We derive these equations both by averaging the three-dimensional governing equations over each layer, and via Hamilton’s principle. The latter derivation guarantees that conservation laws for mass, momentum, energy and potential vorticity are preserved. Within geophysically realistic parameters, including the complete Coriolis force modifies the domain of hyperbolicity of the multi-layer equations by no more than 5%. By contrast, long linear plane waves exhibit dramatic structural changes due to reconnection of the surface and internal wave modes in the long-wave limit. We use our non-traditional shallow water equations as an idealised model of an abyssal current flowing beneath a less dense upper ocean. We focus on the Antarctic Bottom Water, which crosses the equator in the western Atlantic ocean, where the bathymetry forms an almost-westward channel. Cross-equatorial flow is strongly constrained by potential vorticity conservation, which requires fluid to acquire a large relative vorticity in order to move between hemispheres. Including the complete Coriolis force accounts for the fact that fluid crossing the equator in an eastward/westward channel experiences a smaller change in angular momentum, and therefore acquires less relative vorticity. Our analytical and numerical solutions for shallow water flow over idealised channel topography show that the non-traditional component of the Coriolis force facilitates cross-equatorial flow through an almost-westward channel.
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Devlin, Adam Thomas. "On the variability of Pacific Ocean tides at seasonal to decadal time scales| Observed vs modelled." Thesis, Portland State University, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10128376.
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Ocean tides worldwide have exhibited secular changes in the past century, simultaneous with a global secular rise in mean sea level (MSL). The combination of these two factors contributes to higher water levels, and may increase threats to coastal regions and populations over the next century. Equally as important as these long-term changes are the short-term fluctuations in sea levels and tidal properties. These fluctuations may interact to yield locally extreme water level events, especially when combined with storm surge. This study, presented in three parts, examines the relationships between tidal anomalies and MSL anomalies on yearly and monthly timescales, with a goal of diagnosing dynamical factors that may influence the long-term evolution of tides in the Pacific Ocean. Correlations between yearly averaged properties are denoted tidal anomaly trends (TATs), and will be used to explore interannual behavior. Correlations of monthly averaged properties are denoted seasonal tidal anomaly trends (STATs), and are used to examine seasonal behavior. Four tidal constituents are analyzed: the two largest semidiurnal (twice daily) constituents, M2 and S2, and the two largest diurnal (once daily) constituents, K1 and O1.
Part I surveys TATs and STATs at 153 Pacific Ocean tide gauges, and discusses regional patterns within the entire Pacific Ocean. TATs with statistically significant relations between MSL and amplitudes (A-TATs) are seen at 89% of all gauges; 92 gauges for M2, 66 for S2, 82 for K1, and 59 for O1. TATs with statistically significant relations between tidal phase (the relative timing of high water of the tide) and MSL (P-TATs) are observed at 55 gauges for M2, 47 for S2, 42 for K1, and 61 for O1. Significant seasonal variations (STATs) are observed at about a third of all gauges, with the largest concentration in Southeast Asia. The effect of combined A-TATs was also considered. At selected stations, observed tidal sensitivity with MSL was extrapolated forward in time to the predicted sea level in 2100. Results suggest that stations with large positive combined A-TATs produce total water levels that are greater than those predicted by an increase in MSL alone, increasing the chances of high-water events.
Part II examines the mechanisms behind the yearly (TAT) variability in the Western Tropical Pacific Ocean. Significant amplitude TATs are found at more than half of 26 gauges for each of the two strongest tidal constituents, K1 (diurnal) and M2 (semidiurnal). For the lesser constituents analyzed (O1 and S2), significant trends are observed at ten gauges.
Part III analyzes the seasonal behavior of tides (STATs) at twenty tide gauges in the Southeast Asian waters, which exhibit variation by 10 – 30% of mean tidal amplitudes. A barotropic ocean tide model that considers the seasonal effects of MSL, stratification, and geostrophic and Ekman velocity is used to explain the observed seasonal variability in tides due to variations in monsoon-influenced climate forcing, with successful results at about half of all gauges. The observed changes in tides are best explained by the influence of non-tidal velocities (geostrophic and Ekman), though the effect of changing stratification is also an important secondary causative mechanism.
From the results of these surveys and investigations, it is concluded that short-term fluctuations in MSL and tidal properties at multiple time scales may be as important in determining the state of future water levels as the long-term trends. Global explanations for the observed tidal behavior have not been found in this study; however, significant regional explanations are found at the yearly time scale in the Solomon Sea, and at the seasonal time scale in Southeast Asia. It is likely that tidal sensitivity to annual and seasonal variations in MSL at other locations also are driven by locally specific processes, rather than factors with basin-wide coherence. (Abstract shortened by ProQuest.)
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Swaters, Gordon Edwin. "On the stability and propagation of barotropic modons in slowly varying media." Thesis, [S.l. : s.n.], 1985. http://catalog.hathitrust.org/api/volumes/oclc/13002210.html.
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Ritzer, Jason Andreas. "The Topography, Gravity, and Tectonics of the Terrestrial Planets." Case Western Reserve University School of Graduate Studies / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=case1278603504.
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Cattaneo, L. "CHARACTERIZATION OF THE SUBSURFACE THROUGH JOINT HYDROGEOLOGICAL AND GEOPHYSICAL INVERSION." Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/239175.
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Characterization of the subsurface heterogeneity, monitoring groundwater dynamics, modelling flow and transport in the subsoil are of paramount importance for protection of groundwater quality, design of remediation plans, control of restoration activities. One of the key physical parameters that control groundwater flow and solute transport is hydraulic conductivity. Both hydraulic conductivity and electrical resistivity depend on porosity, water content and textural properties. Moreover, the difficulties of directly and effectively measure hydraulic conductivity makes the possibility of predicting it from geophysical measurements very attractive. Hydrogeophysics provides useful complementary techniques, both for hydrostratigraphic and hydrogeological characterization and for monitoring. It provides a minimally invasive approach to obtaining spatially-continuous data-sets, at a relatively high temporal and spatial sampling density. The general-purpose objective of this work is the development of a modelling tool for the subsurface characterization, in order to improve studies on groundwater flow and contaminant transport, with the specific goal of obtaining a spatial 3D parameter distribution of hydraulic conductivity and electrical resistivity. Such a tool profits from DC geoelectrical and hydraulic collected data, which are used in a joint geophysical and hydrological data inversion, with an approach similar to the Ensemble Kalman Filter.
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Habana, Nlingilili Oarabile Kgosietsile. "Gravity Recovery by Kinematic State Vector Perturbation from Satellite-to-Satellite Tracking for GRACE-like Orbits over Long Arcs." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1578042687104082.
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Booth, Richard J. S. "Miscible flow through porous media." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:542d3ec1-2894-4a34-9b93-94bc639720c9.
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This thesis is concerned with the modelling of miscible fluid flow through porous media, with the intended application being the displacement of oil from a reservoir by a solvent with which the oil is miscible. The primary difficulty that we encounter with such modelling is the existence of a fingering instability that arises from the viscosity and the density differences between the oil and solvent. We take as our basic model the Peaceman model, which we derive from first principles as the combination of Darcy’s law with the mass transport of solvent by advection and hydrodynamic dispersion. In the oil industry, advection is usually dominant, so that the Péclet number, Pe, is large. We begin by neglecting the effect of density differences between the two fluids and concentrate only on the viscous fingering instability. A stability analysis and numerical simulations are used to show that the wavelength of the instability is proportional to Pe^−1/2, and hence that a large number of fingers will be formed. We next apply homogenisation theory to investigate the evolution of the average concentration of solvent when the mean flow is one-dimensional, and discuss the rationale behind the Koval model. We then attempt to explain why the mixing zone in which fingering is present grows at the observed rate, which is different from that predicted by a naive version of the Koval model. We associate the shocks that appear in our homogenised model with the tips and roots of the fingers, the tip-regions being modelled by Saffman-Taylor finger solutions. We then extend our model to consider flow through porous media that are heterogeneous at the macroscopic scale, and where the mean flow is not one dimensional. We compare our model with that of Todd & Longstaff and also models for immiscible flow through porous media. Finally, we extend our work to consider miscible displacements in which both density and viscosity differences between the two fluids are relevant.
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Wagner, Gregory LeClaire. "On the coupled evolution of oceanic internal waves and quasi-geostrophic flow." Thesis, University of California, San Diego, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10128416.
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Oceanic motion outside thin boundary layers is primarily a mixture of quasi-geostrophic flow and internal waves with either near-inertial frequencies or the frequency of the semidiurnal lunar tide. This dissertation seeks a deeper understanding of waves and flow through reduced models that isolate their nonlinear and coupled evolution from the Boussinesq equations. Three physical-space models are developed: an equation that describes quasi-geostrophic evolution in an arbitrary and prescribed field of hydrostatic internal waves; a three-component model that couples quasi-geostrophic flow to both near-inertial waves and the near-inertial second harmonic; and a model for the slow evolution of hydrostatic internal tides in quasi-geostrophic flow of near-arbitrary scale. This slow internal tide equation opens the path to a coupled model for the energetic interaction of quasi-geostrophic flow and oceanic internal tides.
Four results emerge. First, the wave-averaged quasi-geostrophic equation reveals that finite-amplitude waves give rise to a mean flow that advects quasi-geostrophic potential vorticity. Second is the definition of a new material invariant: Available Potential Vorticity, or APV. APV isolates the part of Ertel potential vorticity available for balanced-flow evolution in Eulerian frames and proves necessary in the separating waves and quasi-geostrophic flow. The third result, hashed out for near-inertial waves and quasi-geostrophic flow, is that wave-flow interaction leads to energy exchange even under conditions of weak nonlinearity. For storm-forced oceanic near-inertial waves the interaction often energizes waves at the expense of flow. We call this extraction of balanced quasi-geostrophic energy 'stimulated generation' since it requires externally-forced rather than spontaneously-generated waves. The fourth result is that quasi-geostrophic flow can encourage or 'catalyze' a nonlinear interaction between a near-inertial wave field and its second harmonic that transfers energy to the small near-inertial vertical scales of wave breaking and mixing.
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Trinh, Phuong-Thu. "3D Multi-parameters Full Waveform Inversion for challenging 3D elastic land targets." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAU033/document.
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L’imagerie sismique du sous-sol à partir de données terrestres est très difficile à effectuer due à la complexité 3D de la proche surface. Dans cette zone, les ondes sismiques sous forme d’un paquet compact de phases souvent imbriquées sont dominées par des effets élastiques et viscoélastiques, couplés aux effets dus à la surface libre qui génèrent des ondes de surface de grande amplitude et dispersives.L’interaction des ondes sismiques avec une topographie plus ou moins complexe dans un contexte de fortes hétérogénéités de la proche surface induit d’importantes conversions des ondes avec de fortes dispersions d’énergie. Il est donc nécessaire de prendre en compte à la fois une représentation tridimensionnelle précise de la topographie et une physique correcte qui rend compte de la propagation du champ d’onde dans le sous-sol au niveau de précision réclamé par l’imagerie sismique. Dans ce manuscrit, nous présentons une stratégie d’inversion des formes d’onde complètes (FWI en anglais) efficace, autonome et donc flexible, pour la construction de modèles de vitesse à partir de données sismiques terrestres, plus particulièrement dans les environnements dits de chevauchements d’arrière pays(foothills en anglais) aux variations de vitesse importantes.Nous proposons une formulation efficace de cette problématique basée sur une méthode d’éléments spectraux en domaine temporel sur une grille cartésienne déformée, dans laquelle les variations de topographie sont représentées par une description détaillée de sa géométrie via une interpolation d’ordre élevé. La propagation du champ d’onde est caractérisée par une élasticité linéaire anisotrope et par une atténuation isotrope du milieu: cette deuxième approximation semble suffisante pour l’imagerie crustale considérée dans ce travail. L’implémentation numérique du problème direct inclut des produits matricevecteurefficaces pour résoudre des équations élastodynamiques composant un système différentielhyperbolique du second ordre, pour les géométries tridimensionnelles rencontrées dans l’exploration sismique. Les expressions explicites des gradients de la fonction écart entre les données et les prédictions sont fournies et inclut les contributions de la densité, des paramètres élastiques et des coefficients d’atténuation. Ces expressions réclament le champ incident venant de la source au même temps de propagation que le champ adjoint. Pour ce faire, lors du calcul du champ adjoint à partir de l’instant final, le champ incident est recalculé au vol à partir de son état final, de conditions aux bords préalablement sauvegardées et de certains états intermédiaires sans stockage sur disques durs. Le gradient est donc estimé à partir de quantités sauvegardées en mémoire vive. Deux niveaux de parallélisme sont implémentés, l’un sur les sources et l’autre sur la décomposition du domaine pour chaque source, cequi est nécessaire pour aborder des configurations tridimensionnelles réalistes. Le préconditionnement de ce gradient est réalisé par un filtre dit de Bessel, utilisant une implémentation différentielle efficace fondée sur la même discrétisation de l’espace du problème direct et formulée par une approche d’éléments spectraux composant un système linéaire symétrique résolu par une technique itérative de gradient conjugué. De plus, une contrainte non-linéaire sur le rapport des vitesses de compression et de cisaillement est introduite dans le processus d’optimisation sans coût supplémentaire: cette introductions’avére nécessaire pour traiter les données en présence de faibles valeurs de vitesse proche de la surface libre.L’inversion élastique multi-paramètres en contexte de chevauchement est illustrée à travers des exemples de données synthétiques dans un premier temps, ce qui met en évidence les difficultés d’une telle reconstruction…Seismic imaging of onshore targets is very challenging due to the 3D complex near-surface-related effects. In such areas, the seismic wavefield is dominated by elastic and visco-elastic effects such as highly energetic and dispersive surface waves. The interaction of elastic waves with the rough topography and shallow heterogeneities leads to significant converted and scattering energies, implying that both accurate 3D geometry representation and correct physics of the wave propagation are required for a reliable structured imaging. In this manuscript, we present an efficient and flexible full waveform inversion (FWI) strategy for velocity model building in land, specifically in foothill areas.Viscoelastic FWI is a challenging task for current acquisition deployment at the crustal scale. We propose an efficient formulation based on a time-domain spectral element method (SEM) on a flexible Cartesian-based mesh, in which the topography variation is represented by an accurate high-order geometry interpolation. The wave propagation is described by the anisotropic elasticity and isotropic attenuation physics. The numerical implementation of the forward problem includes efficient matrix-vector products for solving second-order elastodynamic equations, even for completely deformed 3D geometries. Complete misfit gradient expressions including attenuation contribution spread into density, elastic parameters and attenuation factors are given in a consistent way. Combined adjoint and forward fields recomputation from final state and previously saved boundary values allows the estimation of gradients with no I/O efforts. Two-levels parallelism is implemented over sources and domain decomposition, which is necessary for 3D realistic configuration. The gradient preconditioning is performed by a so-called Bessel filter using an efficient differential implementation based on the SEM discretization on the forward mesh instead of the costly convolution often-used approach. A non-linear model constraint on the ratio of compressional and shear velocities is introduced into the optimization process at no extra cost.The challenges of the elastic multi-parameter FWI in complex land areas are highlighted through synthetic and real data applications. A 3D synthetic inverse-crime illustration is considered on a subset of the SEAM phase II Foothills model with 4 lines of 20 sources, providing a complete 3D illumination. As the data is dominated by surface waves, it is mainly sensitive to the S-wave velocity. We propose a two-steps data-windowing strategy, focusing on early body waves before considering the entire wavefield, including surface waves. The use of this data hierarchy together with the structurally-based Bessel preconditioning make possible to reconstruct accurately both P- and S-wavespeeds. The designed inversion strategy is combined with a low-to-high frequency hierarchy, successfully applied to the pseudo-2D dip-line survey of the SEAM II Foothill dataset. Under the limited illumination of a 2D acquisition, the model constraint on the ratio of P- and S-wavespeeds plays an important role to mitigate the ill-posedness of the multi-parameter inversion process. By also considering surface waves, we manage to exploit the maximum amount of information in the observed data to get a reliable model parameters estimation, both in the near-surface and in deeper part.The developed FWI frame and workflow are finally applied on a real foothill dataset. The application is challenging due to sparse acquisition design, especially noisy recording and complex underneath structures. Additional prior information such as the logs data is considered to assist the FWI design. The preliminary results, only relying on body waves, are shown to improve the kinematic fit and follow the expected geological interpretation. Model quality control through data-fit analysis and uncertainty studies help to identify artifacts in the inverted models
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Al-Attar, David. "Theoretical problems in global seismology and geodynamics." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:e700e8df-49d0-47e0-8929-cd254c5416c1.
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In Chapter 2, we consider the hydrostatic equilibrium figure of a rotating earth model with arbitrary radial density profile. We derive an exact non-linear partial differential equation describing the equilibrium figure. Perturbation theory is used to obtain approximate forms of this equation, and we show that the first-order theory is equivalent to Clairaut's equation. In Chapter 3, a method for parametrizing the possible equilibrium stress fields of a laterally heterogeneous earth model is described. In this method a solution of the equilibrium equations is first found that satisfies some desirable physical property. All other solutions can be written as the sum of this equilibrium stress field and a divergence-free stress tensor field whose boundary tractions vanish. In Chapter 4, we consider the minor vector method for the stable numerical solution of systems of linear ordinary differential equations. Results are presented for the application of the method to the calculation of seismic displacement fields in spherically symmetric, self-gravitating earth models. In Chapter 5, we present a new implementation of the direct solution method for calculating normal mode spectra in laterally heterogeneous earth models. Numerical tests are presented to demonstrate the validity and effectiveness of this method for performing large mode coupling calculations. In Chapter 6, we consider the theoretical basis for the viscoelastic normal mode method which is used in studies of seismic wave propagation, post-glacial rebound, and post-seismic deformation. We show how the time-domain solution to the viscoelastodynamic equation can be written as a normal mode sum in a rigorous manner.
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Reid, Fiona J. L. "Velocity and attenuation structure of the mantle : constraints from differential properties of shear waves." Thesis, University of Oxford, 1999. http://ora.ox.ac.uk/objects/uuid:83796f01-c45f-4d84-9c4c-04e084ac135f.
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Although much progress has been made in determining the three dimensional distribution of seismic wave velocities in the Earth, substantially less is known about the three dimensional distribution of intrinsic attenuation. In this study variations in attenuation and shear velocity of the Earth's mantle are constrained using measurements of differential travel time and attenuation. The data are broadband displacement SH seismograms filtered to have energy in the period range 8 to 20 s. Broadband data are used as they should allow a more accurate estimation of body wave attenuation to be made. The seismograms are obtained from over 600 globally distributed earthquakes of magnitude, Mw, 5.5 or greater. Two new methods for determining differential travel times and differential t* values from multiple S phases are presented. The first of these, referred to as the "waveform fitting method" is used to analyse approximately 4300 SS and S waveforms and around 1000 SSS and SS waveforms resulting in differential SS-S and SSS-SS travel times, and corresponding values of differential attenuation represented by t*. The second method, referred to as the "spectral ratio method" is used to analyse approximately 3200 SS and S and around 900 SSS and SS waveforms. The differential travel times and t* values are inverted to obtain models of the lateral variation of shear velocity and lateral variation of q(mu) where q(mu) =1/Q(mu). The models explain the data well but have limited depth resolution. The velocity models show good correlation with previous studies, in particular, low velocities are observed underlying spreading ridges and convergent margins and high velocities are observed under continental regions. The q(mu) model shows shield regions to be less attenuating than PREM, with ridges appearing as highly attenuating features. Models of shear velocity and attenuation are also obtained by combining the body wave dataset of this study with the surface wave datasets of Van Heijst (1997) and Selby (1998).
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Hu, Xuanyu. "Comparison of Ellipsoidal and Spherical Harmonics for Gravitational Field Modeling of Non-Spherical Bodies." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1339607441.
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Theodoridis, John Apostolis 1972. "Borehole electromagnetic prospecting for weak conductors." Monash University, School of Geosciences, 2004. http://arrow.monash.edu.au/hdl/1959.1/5225.
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Groby, Jean-Philippe. "Modélisation de la propagation des ondes élastiques générées par un séisme proche ou éloigné à l'intérieur d'une ville." Phd thesis, Université de la Méditerranée - Aix-Marseille II, 2005. http://tel.archives-ouvertes.fr/tel-00115636.
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Nous ne pouvons ni prévoir, ni lutter contre un séisme. Nous ne pouvons que tenter de limiter les dégâts et désastres humains qu'ils occasionnent au sein des zones urbaines. Celles-ci, pour des raisons purement pratiques (culture et eau) sont souvent construites sur des bassins sédimentaires ou lacustres. Or, ces sites, de part les caractéristiques physiques de leur sous-sol, sont parmi les plus dangereux lorsqu'un séisme les touche (Mexico en 1985, Izmit en 1999...).La compréhension des mécanismes et phénomènes mis en jeu constitue la première étape pour l'élaboration de moyens d'action visant à limiter les effets des séismes en zone urbaine. Ceux-ci peuvent être classés en deux catégories principales qui vont interagir fortement entre elles. D'une part, les mécanismes et phénomènes liés à "l'histoire" de l'onde touchant le milieu urbain, et d'autre part ceux de l'interaction, au sein de ce milieu urbain, de l'onde incidente et des bâtiments.
Nous montrons, analytiquement et numériquement, que l'excitation d'une configuration par une onde plane en incidence verticale ne fournit pas une représentation correcte ni de la réponse, ni des phénomènes lorsque l'épicentre est localisé loin de la ville. A la limite, une telle excitation peut être employée pour l'étude de séismes touchant des villes telle que Nice, mais en aucun cas pour celle de séismes touchant des villes comme Mexico. Dans ce second cas, nous montrons que certaines des caractéristiques de la coda étaient présentes avant l'entrée dans la ville et que ces caractéristiques sont dues à l'excitation des modes réels de la configuration sur un parcours régional.
Nous dégageons ensuite, toujours analytiquement et numériquement, les mécanismes majeurs de l'interaction de cette onde avec les bâtiments qui induisent une modification notable du champ de déplacement dans la ville, conduisant un effet encore plus dévastateur (surtout dans le cas des mouvements anti-plans).
Cette étude constitue une preuve analytique de l'importance et de la complémentarité de ces deux classes de mécanismes dans la compréhension des phénomènes qui, nous l'espérons, un jour se traduira par des actions concrètes sur l'urbanisme, de façon à compléter les mesures déjà mises en oeuvre pour limiter les dégâts et désastres humains lors d'un sisme.
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Martínez-Alvarado, Oscar. "A POD-Galerkin approach to the atmospheric dynamics of Mars." Thesis, University of Oxford, 2007. http://ora.ox.ac.uk/objects/uuid:9cbd0528-323e-486f-abbe-5a6b36a510b1.
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The observation of less chaoticity and enhanced interannual periodicity of transient waves in the Martian atmosphere in comparison with that of the Earth suggests the hypothesis of a low-dimensional underlying atmospheric attractor. Grounded on this hypothesis, two questions can be asked: is there a small set of atmospheric modes, measured and classified by a suitable norm, capable of describing the atmosphere of Mars? If this set exists, are those atmospheric modes able to reproduce the dynamical behaviour of the atmosphere of Mars? The answer to these questions, constituting the central focus of this thesis, has led to the first application of POD-Galerkin methods to a state-of-the-art Mars general circulation model. The proper orthogonal decomposition (POD) as a method for extracting coherent structures, called empirical orthogonal functions (EOFs), provided a means to answer the first question in the positive. An important amount of atmospheric total energy (TE) was found to be concentrated in a few EOFs (e.g., 90% TE in 20 EOFs). The most energetic EOFs were identified with atmospheric motions such as thermal tides and transient waves. The Galerkin projection of the hydrostatic primitive equations onto the span of the EOFs provided a systematic method to establish physically plausible interactions between the most energetic EOFs. These interactions were complemented with closure schemes representing interactions with unresolved modes. This requirement proved to be essential in order to obtain bounded behaviour. In the diagnostic analysis, represented by the POD alone, increasing the number of EOFs directly leads to a better approximation of the atmospheric state. In contrast, the dynamic reconstruction of the atmospheric evolution does not depend only on the number of included EOFs. Other important factors to obtain realistic evolution are the inclusion of every mode involved in the description of a particular kind of motion (diurnal tide, semidiurnal tide or transients) and the retention of higher order modes that may interact strongly with the modes of interest. Once these conditions are satisfied the behaviour of the reduced models is greatly improved. Implications of these findings for future work are discussed.
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Wisely, Beth, and Beth Wisely. "Geophysical and Hydrogeologic Investigations of Two Primary Alluvial Aquifers Embedded in the Southern San Andreas Fault System: San Bernardino and Upper Coachella Valley." Thesis, University of Oregon, 2012. http://hdl.handle.net/1794/12427.
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This study of alluvial aquifer basins in southern California is centered on observations of differential surface displacement and the search for the mechanisms of deformation. The San Bernardino basin and the Upper Coachella Valley aquifers are bound by range fronts and fault segments of the southern San Andreas fault system. I have worked to quantify long-term compaction in these groundwater dependent population centers with a unique synthesis of data and methodologies using Interferometric Synthetic Aperture Radar (InSAR) and groundwater data. My dissertation contributes to the understanding of alluvial aquifer heterogeneity and partitioning. I model hydrogeologic and tectonic interpretations of deformation where decades of overdraft conditions and ongoing aquifer development contribute to extreme rapid subsidence.
I develop the Hydrogeologic InSAR Integration (HII) method for the characterization of surface deformation in aquifer basins. The method allows for the separation of superimposed hydraulic and/or tectonic processes in operation. This formalization of InSAR and groundwater level integration provides opportunities for application in other aquifer basins where overdraft conditions may be causing permanent loss of aquifer storage capacity through compaction.
Sixteen years of SAR data for the Upper Coachella Valley exhibit rapid vertical surface displacement (#8804; 48mm/a) in sharply bound areas of the western basin margin. Using well driller logs, I categorize a generalized facies analysis of the western basin margin, describing heterogeneity of the aquifer. This allowed for assessment of the relationships between observed surface deformation and sub-surface material properties.
Providing the setting and context for the hydrogeologic evolution of California's primary aquifers, the mature San Andreas transform fault is studied extensively by a broad range of geoscientists. I present a compilation of observations of creep, line integrals across the Pacific-North America Plate Boundary, and strain tensor volumes for comparison to the Working Group 2007 (UCERF 2) seismicity-based deformation model. I find that the moment accumulation across the plate boundary is consistent with the deformation model, suggesting fault displacement observations within the plate boundary zone accurately capture the strain across the plate boundary.
This dissertation includes co-authored materials previously published, and also includes unpublished work currently under revisions for submission to a technical journal.
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van, den Bremer T. S. "The induced mean flow of surface, internal and interfacial gravity wave groups." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:e735afe7-a77d-455d-a560-e869a9941f69.
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Although the leading-order motion of waves is periodic - in other words backwards and forwards - many types of waves including those driven by gravity induce a mean flow as a higher-order effect. It is the induced mean flow of three types of gravity waves that this thesis examines: surface (part I), internal (part II) and interfacial gravity waves (part III). In particular, this thesis examines wave groups. Because they transport energy, momentum and other tracers, wave-induced mean flows have important consequences for climate, environment, air traffic, fisheries, offshore oil and other industries. In this thesis perturbation methods are used to develop a simplified understanding of the physics of the induced mean flow for each of these three types of gravity wave groups. Leading-order estimates of different transport quantities are developed. For surface gravity wave groups (part I), the induced mean flow consists of two compo- nents: the Stokes drift dominant near the surface and the Eulerian return flow acting in the opposite direction and dominant at depth. By considering subsequent orders in a separation of scales expansion and by comparing to the Fourier-space solutions of Longuet-Higgins and Stewart (1962), this thesis shows that the effects of frequency dis- persion can be ignored for deep-water waves with realistic bandwidths. An approximate depth scale is developed and validated above which the Stokes drift is dominant and below which the return flow wins: the transition depth. Results are extended to include the effects of finite depth and directional spreading. Internal gravity wave groups (part II) do not display Stokes drift, but a quantity analogous to Stokes transport for surface gravity waves can still be developed, termed the “divergent- flux induced flow” herein. The divergent-flux induced flow it itself a divergent flow and induces a response. In a three-dimensional geometry, the divergent-flux induced flow and the return flow form a balanced circulation in the horizontal plane with the former transporting fluid through the centre of the group and the latter acting in the opposite direction around the group. In a two-dimensional geometry, stratification inhibits a balanced circulation and a second type of waves are generated that travel far ahead and in the lee of the wave group. The results in the seminal work of Bretherton (1969b) are thus validated, explicit expressions for the response and return flow are developed and compared to numerical simulations in the two-dimensional case. Finally, for interfacial wave groups (part III) the induced mean flow is shown to behave analogously to the surface wave problem of part I. Exploring both pure interfacial waves in a channel with a closed lid and interacting surface and interfacial waves, expressions for the Stokes drift and return flow are found for different configurations with the mean set-up or set-down of the interface playing an important role.
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Groshong, Kimberly Ann. "Modeling the Effect of Calcium Concentration and Volumetric Flow Rate Changes on the Growth of Rimstone Dam Formations Due to Calcium Carbonate Precipitation." University of Akron / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=akron1220067458.
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Talebi, Hassan. "On the spatial modelling of mixed and constrained geospatial data." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2018. https://ro.ecu.edu.au/theses/2279.
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Spatial uncertainty modelling and prediction of a set of regionalized dependent variables from various sample spaces (e.g. continuous and categorical) is a common challenge for geoscience modellers and many geoscience applications such as evaluation of mineral resources, characterization of oil reservoirs or hydrology of groundwater. To consider the complex statistical and spatial relationships, categorical data such as rock types, soil types, alteration units, and continental crustal blocks should be modelled jointly with other continuous attributes (e.g. porosity, permeability, seismic velocity, mineral and geochemical compositions or pollutant concentration). These multivariate geospatial data normally have complex statistical and spatial relationships which should be honoured in the predicted models.
Continuous variables in the form of percentages, proportions, frequencies, and concentrations are compositional which means they are non-negative values representing some parts of a whole. Such data carry just relative information and the constant sum constraint forces at least one covariance to be negative and induces spurious statistical and spatial correlations. As a result, classical (geo)statistical techniques should not be implemented on the original compositional data. Several geostatistical techniques have been developed recently for the spatial modelling of compositional data. However, few of these consider the joint statistical and/or spatial relationships of regionalized compositional data with the other dependent categorical information.
This PhD thesis explores and introduces approaches to spatial modelling of regionalized compositional and categorical data. The first proposed approach is in the multiple-point geostatistics framework, where the direct sampling algorithm is developed for joint simulation of compositional and categorical data. The second proposed method is based on two-point geostatistics and is useful for the situation where a large and representative training image is not available or difficult to build. Approaches to geostatistical simulation of regionalized compositions consisting of several populations are explored and investigated. The multi-population characteristic is usually related to a dependent categorical variable (e.g. rock type, soil type, and land use). Finally, a hybrid predictive model based on the advanced geostatistical simulation techniques for compositional data and machine learning is introduced. Such a hybrid model has the ability to rank and select features internally, which is useful for geoscience process discovery analysis.
The proposed techniques were evaluated via several case studies and results supported their usefulness and applicability.
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Williams, Paul David. "Nonlinear interactions of fast and slow modes in rotating, stratified fluid flows." Thesis, University of Oxford, 2003. http://ora.ox.ac.uk/objects/uuid:5365c658-ab60-41e9-b07b-0f635909835e.
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This thesis describes a combined model and laboratory investigation of the generation and mutual interactions of fluid waves whose characteristic scales differ by an order of magnitude or more. The principal aims are to study how waves on one scale can generate waves on another, much shorter scale, and to examine the subsequent nonlinear feedback of the short waves on the long waves. The underlying motive is to better understand such interactions in rotating, stratified, planetary fluids such as atmospheres and oceans. The first part of the thesis describes a laboratory investigation using a rotating, two-layer annulus, forced by imposing a shear across the interface between the layers. A method is developed for making measurements of the two-dimensional interface height field which are very highly-resolved both in space and time. The system's linear normal modes fall into two distinct classes: 'slow' waves which are relatively long in wavelength and intrinsic period, and 'fast' waves which are much shorter and more quickly-evolving. Experiments are performed to categorize the flow at a wide range of points in the system's parameter space. At very small background rotation rates, the interface is completely devoid of waves of both types. At higher rates, fast modes only are generated, and are shown to be consistent with the Kelvin-Helmholtz instability mechanism based on a critical Richardson number. At rotation rates which are higher still, baroclinic instability gives rise to the onset of slow modes, with subsequent localized generation of fast modes superimposed in the troughs of the slow waves. In order to examine the generation mechanism of these coexisting fast modes, and to assess the extent of their impact upon the evolution of the slow modes, a quasi-geostrophic numerical model of the laboratory annulus is developed in the second part of the thesis. Fast modes are filtered out of the model by construction, as the phase space trajectory is confined to the slow manifold, but the slow wave dynamics is accurately captured. Model velocity fields are used to diagnose a number of fast wave radiation indicators. In contrast to the case of isolated fast waves, the Richardson number is a poor indicator of the generation of the coexisting fast waves that are observed in the laboratory, and so it is inferred that these are not Kelvin-Helmholtz waves. The best indicator is one associated with the spontaneous emission of inertia-gravity waves, a generalization of geostrophic adjustment radiation. A comparison is carried out between the equilibrated wavenumbers, phase speeds and amplitudes of slow waves in the laboratory (which coexist with fast modes), and slow waves in the model (which exist alone). There are significant differences between these wave properties, but it is shown that these discrepancies can be attributed to uncertainties in fluid properties, and to model approximations apart from the neglect of fast modes. The impact of the fast modes on the slow modes is therefore sufficiently small to evade illumination by this method of inquiry. As a stronger test of the interaction, a stochastic parameterization of the inertia-gravity waves is included in the model. Consistent with the laboratory/model intercomparison, the parameterized fast waves generally have only a small impact upon the slow waves. However, sufficiently close to a transition curve between two different slow modes in the system's parameter space, it is shown that the fast modes can exert a dominant influence. In particular, the fast modes can force spontaneous transitions from one slow mode to another, due to the phenomenon of stochastic resonance. This finding should be of interest to the meteorological and climate modelling communities, because of its potential to affect model reliability.