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In this thesis, gravity and surface tension-driven water waves are investigated by designing an experimental setup to track wave patterns using a 300 fps high speed camera. This is done to reproduce the theoretical diagram of the dispersion relation for surface waves in different teaching contexts. Surface waves are dispersive, i.e. the phase speed depends on the wavelength.Initially, the background theory for surface waves is presented and the differences between gravity and surface tension-driven waves are described. The conditions for deep and shallow water are also studied. Thereafter, a literature study is conducted to study similar experiments. Test experiments are then carried out where both direct and indirect methods of observing the waves are examined to determine which method generates the best images.The water waves in the experiment are generated by dropping a 1.6 cm marble and a 4 mm water droplet into a 35 cm diameter hexagonal tank filled with 1–10 cm deep water. The waves are recorded from above and illuminated by backlighting with a 10 W LED panel. The experimental results show that a 1.6 cm marble generates wavelengths in the 0.4–3.5 cm range. Moreover, for a 4 mm water droplet, wavelengths in the range of 0.4–2.5 cm are generated.

Phased microphone arrays are valuable tools for aeroacoustic measurements that can measure the directivity of multiple acoustic sources. However, when deployed in closed test-section wind tunnels, the acoustics suffer due to intense pressure fluctuations contained in the wall-bound turbulent boundary layer. Furthermore, phased microphone arrays require many sensors distributed over a large aperture to ensure good spatial resolution over a wide frequency range. Microphone arrays of such large count are not always feasible due to constraints in space and cost. This thesis describes an alternative approach for measuring single broadband acoustic sources that uses an acoustic metasurface. The metasurface is comprised of a meandering channel of quarter-wave cavities and an array of equally spaced half-wave open through-cavities. A series of tests were conducted in Virginia Tech's Anechoic Wall-Jet Tunnel where combinations of a wall-bound turbulent jet-flow and a single broadband acoustic source were used to excite the metasurface and produce acoustic surface waves. Measurements of the acoustic surface waves were performed using two methods: a pair of traversing microphones scanning the pressure field along the length of the metasurface 0.25 mm beneath its bottom face, and an array of unequally spaced microphones embedded inside the metasurface. Spectral analysis on the measurements revealed that the inclusion of multiple through-cavities leads to constructive reinforcement of select acoustic surface waves as a function of the acoustic source location. In the case of the embedded microphones, acoustic beamforming was applied in order to extract spatial information. This reinforcement was observed during measurements made with both flow and acoustic excitation, up to Wall-Jet Tunnel nozzle exit speeds of 40 m/s beyond which it was no longer seen. A series of quiescent measurements made with a range of speaker locations constituted a calibration for the metasurface which was used to locate an unknown broadband acoustic source within an The Root-Mean-Square (RMS) error of 1.06 degrees. / Master of Science / Phased microphone arrays are valuable tools for aeroacoustic measurements that can measure the directivity of multiple acoustic sources within a sound field. When used in conjunction with signal processing techniques, such as delay-and-sum beamforming, a researcher or engineer can obtain an intuitive view of the sound field and distinguish between multiple sources over a wide frequency range. However, these microphone arrays often utilize dozens of microphones which raises the array's complexity and cost. Furthermore, when a phased microphone array is mounted flush to the wall of a wind tunnel test section, it is submerged under a turbulent boundary layer which imposes intense pressure fluctuations on the microphones making it difficult to identify acoustic sources. Boundary layers form at the interface between a fluid and solid interface. This thesis describes experimentation performed in the Virginia Tech Anechoic Wall-Jet Tunnel on a new type of pressure sensing microphone array that leverage acoustic metamaterial technology. The acoustic metamaterial shields the microphones from the flow, lessening the influence of the turbulent boundary layer on the measurement. The focus in this thesis is on the novel array's ability to locate a single broadband acoustic source using as few as six microphones. The metasurface was installed in the Wall-Jet Tunnel test plate such that an array of evenly spaced through-cavities are flush to the surface. The through-cavities communicate the pressure field on top of the test surface to a meandering channel of interconnected closed cavities below. Near the resonant depth frequencies of the closed cavities, acoustic surface waves form which are evanescent pressure waves that are bound to the surface or structure that support them. The interference between the acoustic surface waves generated at each through-cavity leads to reinforced acoustic surface waves which are sensitive to the direction of a broadband source. In all, an acoustic metamaterial was tested under a variety of conditions such as: Wall-Jet Tunnel flow speed, speaker location, and the number of through-cavities open. The performance of the novel array and future plans are discussed.

This research is focused on the application of both new and established seismic interferometry techniques to a single area: the Altiplano in the Andes region. This area has already been widely studied in terms of its geological evolution. Nevertheless, a single accepted theory has not yet been developed to explain why the topography of the Andes incorporates such a large area of low relief at this altitude. The Altiplano is therefore an interesting zone to study. This research introduces and analyses new concepts and methodologies, such as retrieving surface and body waves between earthquakes by using interferometry. Nevertheless, several factors, such as the quality of recordings, the separation between sources, and the velocity gradient of the medium, had to be taken into account for body and surface wave retrieval. This research also analysed the retrieval of body waves by means of seismic interferometry applied to coda wave arrivals. Results show that due to the attenuation of S waves produced by the zone of partial molten material, when using S coda waves, seismic interferometry does not achieve the objective of wave retrieval. On the other hand, P coda waves gave good results. Also, the combined methodology of interferometry by cross-correlation and convolution was shown to account for the behaviour of the retrieved waves and provided an indication of how the distribution of sources affects the Green’s functions estimates for body waves in this area. Another point covered by this research was the analysis of passive recordings in order to retrieve surface and body waves. Results indicate that surface and body waves could be retrieved. However, in order to retrieve body waves, special circumstances are required, such as lateral continuity of the Moho, a relative strong Moho impedance contrast, and simplicity of the geologic structure because these factors will contribute to a strong signal like that obtained in critical reflections making interferometry results more successful.

This thesis applies a fully nonlinear Bayesian inversion methodology to estimate shear-wave velocity (Vs) profiles and uncertainties from surface-wave dispersion data extracted from ambient seismic noise. In the inversion, the Vs profile is parameterized using a Bernstein polynomial basis, which efficiently characterizes general depth-dependent gradients in the soil/sediment column. Bernstein polynomials provide a stable parameterization in that small perturbations to the model parameters (basis-function coefficients) result in only small perturbations to the Vs profile. The inversion solution is defined in terms of the marginal posterior probability for Vs as a function of depth, estimated using Metropolis-Hastings sampling with parallel tempering. This methodology is validated via inversion of synthetic dispersion data as well as previously-considered data inverted using different parameterizations. The approach considered here is better suited than layered modelling approaches in applications where smooth gradients in geophysical parameters are expected, and/or the observed data are diffuse and not sensitive to fine-scale discrete layering (such as surface-wave dispersion). The Bernstein polynomial representation is much more general than other gradient-based models such that the form of the gradients are determined by the data, rather than by subjective parameterization choice. The Bernstein inversion methodology is also applied to dispersion data processed from passive array recordings collected in the coastal community of Kitimat, British Columbia. The region is the proposed site of several large-scale industrial development projects and has great economic and environmental significance for Canada. The inversion results are consistent with findings from other geophysical studies in the region and are used in a site-specific seismic hazard analysis. The level of ground-motion amplification expected to occur during an earthquake due to near-surface Vs structure is probabilistically quantified, and predicted to be significant compared to reference (hard ground) sites. / Graduate

A lingering question in Cordilleran tectonics is how high plateaus form in the absence of continental collision. The type example of an active Cordilleran high plateau is found in the Central Andes of Peru, Bolivia, Argentina, and Chile. Along this section of the South American Cordillera, tectonics are primarily driven by subduction of the oceanic Nazca Plate beneath the continental South American Plate. Extending over 1,800 km along the active continental margin, the Central Andean Plateau (CAP) reaches a maximum width of around 400 km with several peaks in excess of 6 km. Numerous morphotectonic subdivisions of the CAP highlight the complex along-strike variability of the Plateau providing a natural laboratory for investigating the relative contribution of tectonic processes involved in building and maintaining Cordilleran high plateaus. The scale of this problem extends far beyond the scope of any one geoscientific discipline requiring a multidisciplinary approach. Our contribution to this scientific problem and the focus of the work presented in this dissertation is to better understand the current lithospheric and uppermost mantle structure along the CAP. This is achieved by integrating recent advances in seismic imaging techniques with a growing availability of high-quality seismic data into three distinct studies across the South American continent. In the first study, we present a shear-wave velocity model for the crust below the Altiplano-Puna Volcanic Complex (APVC). The target of this study is to constrain the crustal volume of a large magma reservoir inferred to exist below the APVC. When combined with geological and petrological constraints, the large-volume magma reservoir imaged in this study suggests a significant magmatic contribution to the growth of the Plateau in excess of one kilometer over the last ten million years. In addition to the tectonic contributions of this work, we introduce a new method of jointly inverting surface-wave dispersion data and receiver functions to generate a three-dimensional velocity model. In the second study, we combine Rayleigh-wave dispersion data from ambient noise and earthquake-generated surface waves to invert for a shear-wave velocity model of the lithosphere and uppermost mantle below the Bolivian Orocline. The target of this study is to identify any possible mantle contributions to the uplift history along the northern CAP. The highlight of this study is a high-velocity feature that extends from the base of the crust to ~120 km depth below the Altiplano basin. We interpret this feature using a simple isostatic model and suggest it is responsible for the relatively low topography of the Altiplano basin. In the third and final study, we extend the seismic model of the APVC crust to cover the entire Puna Plateau (southern CAP). The target of this study is to assess the uniqueness of the APMB and to look for additional magma reservoirs in the crust. A highlight of this work is the nearly one-to-one spatial correlation between the long-wavelength topography, ignimbrite deposits, long-wavelength Bouguer gravity anomalies, and four additional mid-crustal low-velocity zones imaged in the southern Puna Plateau. When placed in the context of existing geological and petrological constraints, we suggest the contribution of magmatic addition as an uplift mechanism in Cordilleran systems is much larger than is currently accepted.

The uppermost crustal velocity structure of the Goldstream Valley, central Alaska is investigated using a series of five explosions that were detonated in schist bedrock and recorded at >120 local stations to develop 1-D and 3-D models of the upper crust. Simple refraction analyses reveal that both P- and S-wave arrival times are azimuth dependent, with the fastest velocities in the southeast and northeast directions. The Swave velocity structure of the upper crust is also determined through multiple filter analysis and a damped, least squares inversion of 0.2-2 sec period Rg waves. The shear wave velocity model from the surface-wave analysis is combined with the refraction analysis results to develop 1-D P- and S-wave models to a depth of 2 km. In order to better constrain P- and S-wave velocity variations both laterally and with depth throughout the Goldstream Valley, 3-D velocity models are produced using a numerical simulation model. / Thesis (MS) — Boston College, 2008. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Geology and Geophysics.

The standard model of the thermal and chemical structure of cratons has been scrutinized in recent years as additional data have been collected. Recent seismological and petrological studies indicate that the notion of cratonic lithosphere as a thick thermal boundary layer with a very depleted and dehydrated composition may be too simplistic and does not fully explain all aspects of the seismological and petrological observations. We hypothesized that the cratonic lithosphere may be more complicated and designed an experiment to investigate its thermal, chemical, and mineralogical properties using a global database of fundamental mode Rayleigh surface waves. To test this hypothesis, the phase velocities of Rayleigh wave that travel paths primarily over cratons were selected. A 1-D global craton phase velocity profile was generated from these observations and compared to predicted phase-velocity curves using two different forward modeling techniques. With the first approach, profiles of shear velocity were generated based on educated guesses of upper mantle temperatures using geotherms. With the second approach, profiles of shear velocity were generated using random permutations about 1-D global model STW105. In total 5,625 geotherm and 80,000 random 1-D forward models were generated for comparison. Each shear velocity model was converted to phase velocity and compared to the observed range of cratonic phase velocities, defined as within one standard deviation of the mean. This method was able to constrain shear velocity in cratons relatively well though the 1-D profiles deviate at depths shallower than 100 km. Shear velocity is faster than PREM/STW105 to depths greater than 200 km with constantly increasing velocity with depth in the random model and a low velocity layer at 100-150 km.

The Wiggins-Holmes extension of the generalized Melnikov method (GMM) is applied to weakly damped parametrically excited cross waves with surface tension in a long rectangular wave channel in order to determine if these cross waves are chaotic. The Lagrangian density function for surface waves with surface tension is simplified by transforming the volume integrals to surface integrals and by subtracting the zero variation integrals. The Lagrangian is written in terms of the three generalized coordinates (or, equivalently the three degrees of freedom) that are the time-dependent components of the velocity potential. A generalized dissipation function is assumed to be proportional to the Stokes material derivative of the free surface. The generalized momenta are calculated from the Lagrangian and the Hamiltonian is determined from a Legendre transformation of the Lagrangian. The first order ordinary differential equations derived from the Hamiltonian are usually suitable for the application of the GMM. However, the cross wave equations of motion must be transformed in order to obtain a suspended system for the application of the GMM. Only three canonical transformations that preserve the dynamics of the cross wave equations of motion are made because of an extension of the Herglotz algorithm to nonautonomous systems. This extension includes two distinct types of the generalized Herglotz algorithm (GHA). The system of nonlinear nonautonomous evolution equations determined from Hamilton's equations of motion of the second kind are averaged in order to obtain an autonomous system. The unperturbed system is analyzed to determine hyperbolic saddle points that are connected by heteroclinic orbits The perturbed Hamiltonian system that includes surface tension satisfies the KAM nondegeneracy requirements; and the Melnikov integral is calculated to demonstrate that the motion is chaotic. For the perturbed dissipative system with surface tension, the Melnikov integral is identically zero implying that a higher dimensional GMM is necessary in order to demonstrate by the GMM that the motion is chaotic. However, numerical calculations of the largest Liapunov characteristic exponent demonstrate that the perturbed dissipative system with surface tension is also chaotic. A chaos diagram is computed in order to search for possible regions of the damping parameter and the Floquet parametric forcing parameter where chaotic motions may exist. / Graduation date: 1999

Thesis (Ph. D.)--Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1982. / Vita. Bibliography: leaves 321-326.