Book summary: In the newly revised Second Edition of the Handbook of Archaeological Sciences, a team of more than 100 researchers delivers a comprehensive and accessible overview of modern methods used in the archaeological sciences. The book covers all relevant approaches to obtaining and analyzing archaeological data, including dating methods, quaternary paleoenvironments, human bioarchaeology, biomolecular archaeology and archaeogenetics, resource exploitation, archaeological prospection, and assessing the decay and conservation of specimens [...]

The present work addresses the fundamental question involving the modeling of subgrid-scale turbulence as a function of resolved field. A new-nonlinear model has been developed from the constitutive equation of subgrid stresses extending the Reynolds stress model proposed by Warsi. The time scale is expressed in terms of subgrid scale kinetic energy as opposed to strain rate tensor. Effort has been made to identify the terms appearing in the modeled subgrid stresses with "Reynolds term", "Leonard's term" and "cross term". The physical nature of these terms can be best understood from the triadic interactions in wave number space. Understanding these three terms leads to decouple the complex nature of the subgrid stresses. Modeling of these terms separately helps to capture the physics of the problem accurately. The turbulent field is assumed to be isotropic and Kolmogrov's hypothesis is used. The model coefficients are expressed as universal constants for Gaussian filter so as to satisfy the dissipation criteria in inertial subrange. Further dissipation term is assumed to be isotropic and equilibrium condition is used. Although the definition of the subgrid stress terms becomes less clear and separate for smooth filter, an attempt has been made to compare the stress terms with the exact definition obtained for sharp cut-off filter. An estimate of the backscatter of energy can be obtained from the Eddy-Damped Quasi Normal Markovian (EDQNM) theory. The model coefficients thus obtained are tested with results of plain homogeneous shear layer. The model results have been compared with the mixed-nonlinear model and Smagorinsky model. A priori test shows that new-nonlinear model has a good correlation with Smagorinsky model, which in turn has good correlation with experimental results, and has the behavior of the mixed-nonlinear model. The above model has been used for solving two-dimensional flow over backward facing step as a test case. The numerical model solves the vertically hydrostatic boundary layer equation. The top boundary is assumed to be a free surface. Terrain following coordinate system has been used. Because of the non-negativity of the subgrid scale dissipation term i.e. backscatter of energy, the nature of the solution is stochastic. The deterministic solution is obtained by clipping the dissipation term. The results are compared with the experimental data of Kim et al. Good agreement with the experimental data is obtained for the velocity profile and SGS kinetic energy. The reattachment point obtained is at 5.2h (h is the step height), which is less compared to 6h as suggested by other authors. This discrepancy may be due to the assumptions involved in the equations, which is being solved. The model is further extended for the diffusion of scalar variables and to include the buoyancy effect. It is implemented to explore the hydrostatic flow over three dimensional elliptical mountain ridges, where Boussinesq approximation is used for variable density. The flow characteristics have been studied for the various aspect ratios of the mountain and Froude?s number (Nh/U) based on Brunt-Vaisala frequency (N). The phenomenon of upstream blocking and Lee-vortices generation has been studied.

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Borehole induced structures seen in image logs from the Coso Geothermal Field, CA record variation in the azimuth of principal stress. Image logs of these structures from five boreholes were analyzed to quantify the stress heterogeneity for three geologically distinct locations: two boreholes within the Coso Geothermal Field (one in an actively produced volume), two on the margin of the Coso Geothermal Field and outside the production area, and a control borehole several tens of kilometers south of the Coso Geothermal Field. Average directions of Shmin and its standard deviation are similar along the eastern portion of the geothermal field at ~107 ± 28°; this is distinct from the western portion which has an azimuth of 081 ± 18° and also distinct from outside the geothermal field where the average azimuth is 092 ± 47°. These relationships suggest a correlation of stress orientation and heterogeneity with slip on the Coso Wash fault, suggesting that ~20 years of production has not affected the Shmin.orientation. The slope of power spectrum quantifies the length-scale dependence of stress rotations for the volume of the brittle crust penetrated by each borehole. Spectral analysis was applied to the depth variation of stress direction and it demonstrates that: (1) the data set contains distinct wavelengths of stress rotation, (2) that the relative power of these wavelengths in the total scaling of stress directions demonstrates a fractal distribution and (3) in a manner consistent with earthquakes causing the stress rotations. While the vertically averaged Shmin orientation for the three eastern boreholes varied by as little as 1°, the spectral slopes varied by 0.4 log (deg2 *m)(m) from the inside to the margin unproduced areas of the Coso Geothermal Field. The two boreholes inside the field had spectral slopes within one standard deviation, even though Shmin orientations were not parallel. These results suggest that at the kilometer length scale, the source of stress heterogeneity is dominated by proximity to recent fault slip, whereas the centimeter to meter stress heterogeneity is dominated by earthquake activity. / Geology

Slip on the geometrically complex Rhyolite Ridge Fault System and associated local stresses in the Desert Peak Geothermal Field in Nevada, were modeled with the boundary element method (BEM) implemented in Poly3D. The impact of uncertainty in the fault geometry at depth, the tectonic stresses driving slip, and the potential ranges of frictional strength resisting slip on the likely predictions of fracture slip and formation in the surrounding volume due to these local stresses were systematically explored and quantified. The effect of parameter uncertainty was evaluated by determining the frequency distribution of model predicted values. Alternatively, Bayesian statistics were used to determine the best fitting values for parameters within a probability distribution derived from the difference of the model prediction from the observed data. This approach honors the relative contribution of uncertainties from all existing data that constrains the fault parameters. Lastly, conceptual models for different fault geometries and their evolution were heuristically explored and the predictions of local stress states were compared to available measurements of the local stresses, fault and fracture patterns at the surface and in boreholes, and the spatial extent of the geothermal field. The complex fault geometry leads to a high degree of variability in the locations experiencing stress states that promote fracture, but such locations generally correlate with the main injection and production wells at Desert Peak. In addition, the strongest and most common stress concentrations occur within relays between unconnected fault segments, and at bends and intersections in faults that connect overlapping fault segments associated with relays. The modeling approach in this study tests the conceptual model of the fault geometry at Desert Peak while honoring mechanical constants and available constraints on driving stresses and provides a framework that aids in geothermal exploration by predicting the spatial variations in stresses likely to cause and reactivate fractures necessary to sustain hydrothermal fluid flow. This approach also quantifies the relative sensitivity of such predictions to fault geometry, remote stress, and friction, and determines the best fitting model with its associated probability. / Geology

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The transport of material in geophysical fluid flows is a problem with important implications for fields as diverse as: agriculture, aviation, human health, disaster response, and weather forecasting. Due to the unsteady nature of geophysical flows, predicting how material will be transported in these systems can often be challenging. Tools from dynamical systems theory can help to improve the prediction of material transport by revealing important transport structures. These transport structures reveal areas of the flow where fluid parcels, and thus material transported by those parcels, are likely to converge or diverge. Typically, these transport structures have been uncovered by the use of Lagrangian diagnostics. Unfortunately, calculating Lagrangian diagnostics can often be time consuming and computationally expensive. Recently new Eulerian diagnostics have been developed. These diagnostics are faster and less expensive to compute, while still revealing important transport structures in fluid flows. Because Eulerian diagnostics are so new, there is still much about them and their connection to Lagrangian diagnostics that is unknown. This dissertation will fill in some of this gap and provide a mathematical bridge between Lagrangian and Eulerian diagnostics. This dissertation is composed of three projects. These projects represent theoretical, numerical, and experimental advances in the understanding of Eulerian diagnostics and their relationship to Lagrangian diagnostics. The first project rigorously explores the deep mathematical relationship that exists between Eulerian and Lagrangian diagnostics. It proves that some of the new Eulerian diagnostics are the limit of Lagrangian diagnostics as integration time of the velocity field goes to zero. Using this discovery, a new Eulerian diagnostic, infinitesimal-time Lagrangian coherent structures is developed. The second project develops a methodology for estimating local Eulerian diagnostics from wind velocity data measured by a fixed-wing unmanned aircraft system (UAS) flying in circular arcs. Using a simulation environment, it is shown that the Eulerian diagnostic estimates from UAS measurements approximate the true local Eulerian diagnostics and can predict the passage of Lagrangian diagnostics. The third project applies Eulerian diagnostics to experimental data of atmospheric wind measurements. These are then compared to Eulerian diagnostics as calculated from a numerical weather simulation to look for indications of Lagrangian diagnostics. / Doctor of Philosophy / How particles are moved by fluid flows, such as the oceanic currents and the atmospheric winds, is a problem with important implications for fields as diverse as: agriculture, aviation, human health, disaster response, and weather forecasting. Because these fluid flows tend to change over time, predicting how particles will be moved by these flows can often be challenging. Fortunately, mathematical tools exist which can reveal important geometric features in these flows. These geometric features can help us to visualize regions where particles are likely to come together or spread apart, as they are moved by the flow. In the past, these geometric features have been uncovered by using methods which look at the trajectories of particles in the flow. These methods are referred to as Lagrangian, in honor of the Italian mathematician Joseph-Louis Lagrange. Unfortunately, calculating the trajectories of particles can be a time consuming and computationally expensive process. Recently, new methods have been developed which look at how the speed of the flow changes in space. These new methods are referred to as Eulerian, in honor of the Swiss mathematician Leonhard Euler. These new Eulerian methods are faster and less expensive to calculate, while still revealing important geometric features within the flow. Because these Eulerian methods are so new, there is still much that we do not know about them and their connection to the older Lagrangian methods. This dissertation will fill in some of this gap and provide a mathematical bridge between these two methodologies. This dissertation is composed of three projects. These projects represent theoretical, numerical, and experimental advances in the understanding of these new Eulerian methods and their relationship to the older Lagrangian methods. The first project explores the deep mathematical relationship that exists between Eulerian and Lagrangian diagnostic tools. It mathematically proves that some of the new Eulerian diagnostics are the limit of Lagrangian diagnostics as the trajectory’s integration times is decreased to zero. Taking advantage of this discovery, a new Eulerian diagnostic is developed, called infinitesimal-time Lagrangian coherent structures. The second project develops a technique for estimating local Eulerian diagnostics using wind speed measures from a single fixed-wing unmanned aircraft system (UAS) flying in a circular path. Using computer simulations, we show that the Eulerian diagnostics as calculated from UAS measurements provide a reasonable estimate of the true local Eulerian diagnostics. Furthermore, we show that these Eulerian diagnostics can be used to estimate the local Lagrangian diagnostics. The third project applies these Eulerian diagnostics to real-world wind speed measurements. These results are then compared to Eulerian diagnostics that were calculated from a computer simulation to look for indications of Lagrangian diagnostics.

Including porosity introduces absorption into the previously developed scattering analysis for elastic spheres. Acoustic propagation in porous media has two distinct compressional modes, one in which the fluid and the structure move in phase with each other and the other in which they move in opposite phase. Expressions for the complex wavenumbers of both waves are derived, using the parameters for manganese nodules. A modal analysis with a pressure boundary condition indicates that the first kind of compressional wave is lightly attenuated and carries most of the energy of the coupled system. The second compressional wave is highly attenuated and effectively loses all of its energy in the first centimeter of the nodule. This second wave is very important for consideration of nodule-scale dimensions since it represents the dominant loss mechanism. A method was developed to form a single effective compressional wave attenuation for both compressional waves by employing a pressure and velocity boundary condition at the surface of the nodule and using a spatially integrated intensity match. An effective wave attenuation is generated for the compressional wave in the non-porous elastic model which accounts for porous attenuation and which is based on a parameter defined as travel distance L. If L is assumed to be proportional to nodule radius, the attenuation is approximated as constant for the frequency range of interest and is independent of nodule radius. An effective attenuation is predicted. The shear attenuation is found to exhibit a frequency squared form dependence for manganese nodules. However, shear attenuation is very small for ideal nodules and is negligible compared to the compressional loss. The elastic model of the nodule was numerically altered to accommodate complex wavenumbers in shear and compression. Four distinct regions of attenuation are observed in individual reflectivity, R_θ, versus ka plots and discussed. The importance of including attenuation is readily apparent from observing the transformation of the elastic non-porous results. Scattering experiments were performed on manganese nodules and experimental individual reflectivity versus ka plots were generated. Good agreement is found for the spherical Atlantic nodules using values in the third region of attenuation. From these experiments, an estimation of attenuation is made and compared with the theoretical prediction. The influence of attenuation on individual scattering and multiple scattering is investigated. Attenuation tends to shift the major bottom reflectivity, C_R, peak toward lower ka values. This affects the prediction of the acoustic response of manganese nodule deposits. / Master of Science

To facilitate its objective of high-resolution imaging of the Earth's crust and upper mantle, The Program for Array Seismic Studies of the Continental Lithosphere (PASSCAL) has initiated studies into developing instrumentation capable of achieving that goal. The requirements include portable sensors capable of resolving seismic signals to 100 second periods. To test the feasibility of obtaining useful long-period seismic data from a portable array, prototype instruments were installed in hand excavated shallow holes (postholes) at several sites in various geologic settings across the continental United States. Three of the sites were near established seismic vaults and comparisons between posthole installation and vault installation were made. Results from this study indicate that posthole installation of long-period sensors may indeed be feasible: eight out of the 12 sites occupied had long-period background noise levels low enough to resolve 100-second surface waves generated from a magnitude 5.0 earthquake 30 degrees distant from the recording station. At periods less than 10 seconds, background noise recorded from postholes was no more than 3 dB. higher than that recorded in vaults. At 100 seconds, vertical noise was 11 to 16 dB. higher than that recorded in vaults and horizontal noise was 4 to 22 dB. higher. Across all posthole installations, as compared to Peterson’s Low Noise Model, vertical and horizontal noise at 100 seconds averaged 27 and 45 dB. higher, respectively. Sites should be located directly on bedrock, where possible. If this is not possible, they should be in well compacted inorganic soil with a low moisture content. Immediately after installation at a potential site, a noise sample should be analyzed in the field to test the suitability of the site. / Master of Science