ALBERT

Description: Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2002

Description: One of the major problems in wireless communications is compensating for the time-varying intersymbol interference (ISI) due to multipath. Underwater acoustic communications is one such type of wireless communications in which the channel is highly dynamic and the amount of ISI due to multipath is relatively large. In the underwater acoustic channel, associated with each of the deterministic propagation paths are macro-multipath fluctuations which depend on large scale environmental features and geometry, and micro-multipath fluctuations which are dependent on small scale environmental inhomogeneities. For arrivals which are unsaturated or partially saturated, the fluctuations in ISI are dominated by the macro-multipath fluctuations resulting in correlated fluctuations between different taps of the sampled channel impulse response. Traditional recursive least squares (RLS) algorithms used for adapting channel equalizers do not exploit this structure. A channel subspace post-filtering algorithm that treats the least squares channel estimate as a noisy time series and exploits the channel correlation structure to reduce the channel estimation error is presented. The improvement in performance of the algorithm with respect to traditional least squares algorithms is predicted theoretically, and demonstrated using both simulation and experimental data. An adaptive equalizer structure that explicitly uses this improved estimate of the channel impulse response is discussed. The improvement in performance of such an equalizer due to the use of the post-filtered estimate is also predicted theoretically, and demonstrated using both simulation and experimental data.

Description: This research was supported by an ONR Graduate Traineeship Award Grant #N00014-00-10049.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2000.

Description: Geometrically compliant mooring systems that change their shape to accommodate deformations are common in oceanographic and offshore energy production applications. Because of the inherent geometric nonlinearities, analyses of such systems typically require the use of a sophisticated numerical model. This thesis describes one such model and uses that model along with experimental results to develop simpler forms for understanding the dynamic response of geometrically compliant moorings. The numerical program combines the box method spatial discretization with the generalized- a method for temporal integration. Compared to other schemes commonly employed for the temporal integration of the cable dynamics equations, including box method, trapezoidal rule, backward differences, and Newmark’s method, the generalized-a algorithm has the advantages of second-order accuracy, controllable numerical dissipation, and improved stability when applied to the nonlinear problem. The numerical program is validated using results from laboratory and field experiments. Field experiment and numerical results are used to develop a simple model for dynamic tension response to vertical motion in geometrically compliant moorings. As part of that development, the role of inertia, drag, and stiffness in the tension response are explored. For most moorings, the response is dominated by inertial and drag effects. The simple model uses just two terms to accurately capture these effects, including the coupling between inertia and drag. The separability of the responses to vertical and horizontal motions is demonstrated and a preliminary model for the response to horizontal motions is presented. The interaction of the mooring line with the sea floor in catenary moorings is considered. Using video and tension data from laboratory experiments, the tension shock condition at the touchdown point and its implications are observed for the first time. The lateral motion of line along the bottom associated with a shock during unloading may be a significant cause of chain wear in the touchdown region. Results from the laboratory experiments are also used to demonstrate the suitability of the elastic foundation approach to modeling sea floor interaction in numerical programs.

Description: During my initial three years of study I was supported by an Office of Naval Research Graduate Fellowship. More recently, including the time spent on the research described in this thesis, I have been supported by the Office of Naval Research under grant numbers N00014-92-J-1269 and N00014-97-1-0583.

Description: Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2001

Description: The interaction between the eddy field and the mean flow near the Gulf Stream is studied here using satellite altimeter measurements and an eddy resolving numerical modeL. The eddy vorticity flux in the quasigeostrophic framework is obtained from the stream function standard deviation and spatial correlation function assuming the correlation function is homogeneous. An analytical expression is found for the stream function correlation using the altimetric and numerical data. Cases when the correlation function is anisotropic are compared to the isotropic case previously studied by Hogg (1993), who found that the eddy vorticity flux drives two counter rotating gyres on either side of the stream. The anisotropy can be important in the eddy vorticity flux, even when its departure from the isotropic case is smalL. Meridional or zonal anisotropies can drive recirculation gyres similar in strength and position to the ones driven by the isotropic case. The results when including anisotropy in the diagonal direction suggest that the homogenoeus assumption may not be valid.

Description: This work was founded in part by a Fulbright/CONACyT fellowship and a J. Seward Johnson Fellowship through the Education Offce in WHOI.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2003

Description: Inertial terms dominate the single-gyre ocean model and prevent western-intensification when the viscosity is small. This occurs long before the oceanically-appropriate parameter range. It is demonstrated here that the circulation is controlled if a mechanism for ultimate removal of vorticity exists, even if it is active only in a narrow region near the boundary. Vorticity removal is modeled here as a viscosity enhanced very near the solid boundaries to roughly parameterize missing boundary physics like topographic interaction and three dimensional turbulence over the shelf. This boundary-enhanced viscosity allows western-intensified mean flows even when the inertial boundary width, is much wider than the frictional region because eddies flux vorticity from within the interior streamlines to the frictional region for removal. Using boundary-enhanced viscosity, western-intensified calculations are possible with lower interior viscosity than in previous studies. Interesting behaviors result: a boundary-layer balance novel to the model, calculations with promise for eddy parameterization, eddy-driven gyres rotating opposite the wind, and temporal complexity including basin resonances. I also demonstrate that multiple-gyre calculations have weaker mean circulation than single-gyres with the same viscosity and subtropical forcing. Despite traditional understanding, almost no inter-gyre flux occurs if no-slip boundary conditions are used. The inter-gyre eddy flux is in control only with exactly symmetric gyres and free slip boundaries. Even without the inter-gyre flux, the multiple-gyre circulation is weak because of sinuous instabilities on the jet which are not present in the single-gyre model. These modes efficiently flux vorticity to the boundary and reduce the circulation without an inter-gyre flux, postponing inertial domination to much smaller viscosities. Then sinuous modes in combination with boundary-enhanced viscosity can control the circulation.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2000

Description: The variability of salt transport determines the variation of the length of the salinity intrusion and the large-scale density gradient in an estuary. This thesis contains three studies that address salt transport and the salt balance. The variation of salt transport with the depth, the along-channel salinity gradient, and the amplitude of the tidal velocity is investigated with analytic and numerical models. The results indicate that salt transport increases dramatically during stratified periods when vertical mixing is weak. Analysis of salt transport from observations in the Hudson Estuary show that stratified periods with elevated estuarine salt transport occur in five-day intervals once a month during apogean neap tides. Oscillatory salt transport, which is hypothesized to be primarily caused by lateral exchange and mixing of salt, appears to play a more minor role in the salt balance of the estuary. The salt balance of the estuary adjusts very little to the spring-neap modulation of salt transport but adjusts rapidly to pulses of freshwater flow. A simple model is used to investigate the process and time scales of adjustment of the salt balance by connecting variations of salt transport to the variations of freshwater flow and vertical mixing. The results show the length of the salinity intrusion adjust via advection to rapid and large increases in freshwater flow. The salinity intrusion adjusts more rapidly to the spring-neap cycle of tidal mixing the higher the freshwater flow.

Description: The National Science Foundation provided support through a National Science Foundation Graduate Fellowship and NSF Grant OCE94-15617. Grants from the Hudson River Foundation (HRF Grant 006j96A) and the Office of Naval Research (Grant Number N00014-97-1-0134) have also contributed towards the work in this thesis. This work is also partially the result of research sponsored by NOAA National Sea Grant College Program Office, Department of Commerce, under Grant No. NA46RG0470, Woods Hole Oceanographic Institution (WHOI) Sea Grant project no. R/O-30.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2007

Description: The first part of the dissertation investigates the application of the theory of large random matrices to high-dimensional inference problems when the samples are drawn from a multivariate normal distribution. A longstanding problem in sensor array processing is addressed by designing an estimator for the number of signals in white noise that dramatically outperforms that proposed by Wax and Kailath. This methodology is extended to develop new parametric techniques for testing and estimation. Unlike techniques found in the literature, these exhibit robustness to high-dimensionality, sample size constraints and eigenvector misspecification. By interpreting the eigenvalues of the sample covariance matrix as an interacting particle system, the existence of a phase transition phenomenon in the largest (“signal”) eigenvalue is derived using heuristic arguments. This exposes a fundamental limit on the identifiability of low-level signals due to sample size constraints when using the sample eigenvalues alone. The analysis is extended to address a problem in sensor array processing, posed by Baggeroer and Cox, on the distribution of the outputs of the Capon-MVDR beamformer when the sample covariance matrix is diagonally loaded. The second part of the dissertation investigates the limiting distribution of the eigenvalues and eigenvectors of a broader class of random matrices. A powerful method is proposed that expands the reach of the theory beyond the special cases of matrices with Gaussian entries; this simultaneously establishes a framework for computational (non-commutative) “free probability” theory. The class of “algebraic” random matrices is defined and the generators of this class are specified. Algebraicity of a random matrix sequence is shown to act as a certificate of the computability of the limiting eigenvalue distribution and, for a subclass, the limiting conditional “eigenvector distribution.” The limiting moments of algebraic random matrix sequences, when they exist, are shown to satisfy a finite depth linear recursion so that they may often be efficiently enumerated in closed form. The method is applied to predict the deterioration in the quality of the sample eigenvectors of large algebraic empirical covariance matrices due to sample size constraints.

Description: I am grateful to the National Science Foundation for supporting this work via grant DMS-0411962 and the Office of Naval Research Graduate Traineeship award

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2007

Description: Oceanic spreading centers are sites of magmatic, tectonic, and hydrothermal processes. In this thesis I present experimental and seismological constraints on the evolution of these complex regions of focused crustal accretion and extension. Experimental results from drained, triaxial deformation experiments on partially molten olivine reveal that melt extraction rates are linearly dependent on effective mean stress when the effective mean stress is low and non-linearly dependent on effective mean stress when it is high. Microearthquakes recorded above an inferred magma reservoir along the TAG segment of the Mid-Atlantic Ridge delineate for the first time the arcuate, subsurface structure of a long-lived, active detachment fault. This fault penetrates the entire oceanic crust and forms the high-permeability pathway necessary to sustain long-lived, high-temperature hydrothermal venting in this region. Long-lived detachment faulting exhumes lower crustal and mantle rocks. Residual stresses generated by thermal expansion anisotropy and mismatch in the uplifting, cooling rock trigger grain boundary microfractures if stress intensities at the tips of naturally occurring flaws exceed a critical stress intensity factor. Experimental results coupled with geomechanical models indicate that pervasive grain boundary cracking occurs in mantle peridotite when it is uplifted to within 4 km of the seafloor. Whereas faults provide the high-permeability pathways necessary to sustain high-temperature fluid circulation, grain boundary cracks form the interconnected network required for pervasive alteration of the oceanic lithosphere. This thesis provides fundamental constraints on the rheology, evolution, and alteration of the lithosphere at oceanic spreading centers.

Description: Research was funded by a MIT Presidential Fellowship and NSF grants OCE-0095936, OCE-9907224, OCE-0137329, OCE-6892222, and OCE-6897400.

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution December 1997

Description: A new tomographic technique is employed to investigate the structure and dynamics of the Pacific upper mantle. We invert band-center travel times of ScS reverberations and frequency-dependent travel times of direct S phases, upper-mantle guided waves such as SS and SSS, and the R1 and G1 surface waves for the 2D composite structure in the plane of two Pacific corridors. The frequency-dependent travel times of the turning and surface waves are measured from all three components of ground motion as phase delays relative to a radially-anisotropic, spherically-symmetric oceanic mantle model, and their 2D Fréchet kernels are constructed by a coupled-mode algorithm. The travel times of the primary ScSn and sScSn phases and their first-order reverberations from the 410 and 660 discontinuities are measured as individual phases and the 2D Fréchet kernels for these band-limited signals are calculated using the paraxial ray approximation. The model parameters include shear-speed variations throughout the mantle, perturbations to radial shear-wave anisotropy in the uppermost mantle, and the topography of the 410 and 660 discontinuities. We construct vertical tomograms through two mantle corridors: one between the Tonga subduction zone and Oahu, Hawaii, which traverses the central Pacific Ocean; and the other between the Ryukyu subduction zone and Oahu, which samples the northern Philippine Sea, the western Pacific, and the entire Hawaiian swell. Tests demonstrate that the data sets for the two corridors resolve the lateral structure in the upper mantle with a scale length of a few hundreds kilometers and greater but that the resolving power decreases rapidly in the lower mantle. The model for the Tonga-Hawaii corridor reveals several interesting features, the most significant being a regular pattern of high and low shear velocities in the upper mantle between Tonga and Hawaii. These variations, which are well resolved by the data set, have a horizontal wavelength of 1500 km, a vertical dimension of 700 km, and an amplitude of about 3%, and they show a strong positive correlation with seafloor topography and geoid-height variations along this corridor. The geoid highs correspond to a series of northwest-trending swells associated with the major hotspots of the Society, Marquesas, and Hawaiian Islands. Where these swells cross the corridor, they are underlain by high shear velocities throughout the uppermost mantle, so it is unlikely that their topography is supported by thermal buoyancy. This result is substantiated by the model from the Ryukyu-Hawaii corridor, which exhibits a prominent, fast region that extends beneath the entire Hawaiian swell. This anomaly, which resides in the uppermost 200-300 km of the mantle, is also positively correlated with the undulations of the Hawaiian-swell height. The other dominant features in the Ryukyu-Hawaii model include the high-velocity subducting slabs beneath the Ryukyu and Izu-Bonin seismic zones, which extend throughout the entire upper mantle; a very low-velocity in the uppermost 160 km of the mantle beneath the northern Philippine Sea, which is ascribed to the presence of extra water in this region; and a pronounced minimum in the amount of radial anisotropy near Hawaii, which is also seen along the Tonga-Hawaii corridor. A joint inversion of the data from the two corridors reveals the same anomaly pattern and clearly demonstrates that the swells in the Central Pacific are underlain by fast velocities. It is therefore implied that the topography of the swells in the central Pacific is supported by a chemical buoyancy mechanism which is generated by basaltic volcanism and the formation of its low-density peridotitic residuum. While the basaltic depletion mechanism can produce high shear velocities in the uppermost 200 km, it cannot explain the depth extent of the fast anomalies beneath the swells which, along Tonga-Hawaii corridor, extend well into the transition zone. It is therefore hypothesized that the central Pacific is underlain by a system of convective rolls that are confined above the 660-km discontinuity. It is likely that these rolls are predominantly oriented in the direction of plate motion (like "Richter rolls ") but the limited depth of the fast anomaly beneath the Hawaiian swell (200-300 km) suggests that their pattern is probably more complicated. Nevertheless, this convection pattern appears to be strongly correlated with the locations of the Tahitian, Marquesan, and Hawaiian hotspots, which raises interesting questions for Morgan's hypothesis that these hotspots are the surface manifestations of deep-mantle plumes.

Description: This research was supported by the National Science Foundation under grant EAR- 9628351 and by the Defense Special Weapons Agency under grant DSW A-F49620-95-1- 0051.

Description: Submitted in partial fulfillment of the requirements of the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2004

Description: Laterally extensive, well-developed clinoforms have been mapped in Early Cretaceous deposits located in the northeastern 27,000 km2 of the Colvile Basin, North Slope of Alaska. Using public domain 2-D seismic data, well logs, core photographs, and grain size data, depositional geometries within the Nanushuk and Torok formations were interpreted in order to constrain the transport conditions associated with progradation of the shoreline and construction of the continental margin out of detritus shed from the ancestral Brooks Range. Using STRATA, a synthetic stratigraphic modeling package, constructional clinoform geometries similar to those preserved in the North Slope clinoform volume (32,400 km3) were simulated. Sediment flux, marine and nonmarine diffusivities, and basin subsidence were systematically varied until a match was found for the foreset and topset slopes, as well as progradation rates over a 6 milion year period. The ability of STRATA to match the seismically interpreted geometries allows us to constrain measures of possible water and sediment discharges consistent with the observed development of the Early Cretaceous c1inoform suite. Simulations indicate that, in order to reproduce observed geometries and trends using constant input parameters, the subsidence rate must be very small, only a fraction of the most likely rate calculated from the seismic data. Constant sediment transport parameters can successfully describe the evolution of the prograding margin only in the absence of tectonic subsidence. However, further work is needed to constrain the absolute magnitude of these values and determine a unique solution for the NPR-A clinoforms.

Description: The tides of coastal embayments derive their energy from the ocean tides rather than from the direct action of lunar and solar gravitational forces. They are considered to be part of co-oscilating systems in which the period is determined by the tide in the outer sea, while the detailed character of the motion depends on the size and form of the enclosed basin (Defant, 1925; Doodson and Warburg, 1941). In narrow basins of simple form in which the influence of the earth's rotation is small, the motions resemble standing waves. Ideally, such waves are characterized by the simultaneous rise and fall of level on either side of a nodal line at which no change in elevation takes place. The elevation at high water increases with distance from the nodal line and slack water coincides with high and low water. The properties of tides due to standing waves may be deduced by assuming the motion to result from a primary progressive wave moving up the channel which undergoes complete reflection at a barrier. Mathematically, this situation may be treated as the interference of two identical progressive waves moving in opposite directions and so related that both waves are in phase at the barrier. This treatment of standing waves assumes the presence of total reflection, the absence of damping and the absence of effects of the earth's rotation. Since these conditions are not realized in natural tidal basins, the standing wave concept leads to oversimplification. In coastal embayments the most striking departure from the expectations of the standing wave concept is the discrepancy between times of high water and slack water, which may be great near the mouths of the larger bays and sounds. High water does not occur simultaneously within such enclosures but is earlier near the sea. Commonly, the nodal line is represented merely by a region in which the tidal range is small. These are effects which can be explained if damping of the primary and reflected waves by frictional or other effects is taken into account. According to these concepts, the problem of tidal behavior in embayments is to determine numerically the properties of the primary and reflected waves so as to account for the observed relations of amplitude and stream velocity of the actual tide and to correlate these numerical properties with the geographical form of the embayment. In the present paper an attempt is made to treat the tidal behavior in such a way that the observed changes in elevation and motion of the water along the path of the wave may be used to determine the distribution of phase of the primary and reflected waves along the channel and to measure the damping. The relations between the several aspects of a wave as it advances along a channel of uniform depth and width have been developed theoretically so as to show the times of high water and slack water, the range of the tide, and the phase relations of the primary and reflected waves along the channel for any degree of damping. By expressing the relationship of the several aspects of a reflected wave in a form in which the wave period is taken as the unit of time and distance is given in terms of the related phase changes, it is possible to eliminate the purely geographical dimensions and to obtain a wholly general description of the tide which may be used to indicate how any given channel distorts the behavior of the wave as it advances. In the case of irregular channels, in order to justify the application of relations deduced for uniform channels, in which the change in phase of the primary and reflected waves and their damping is proportional to the distance traveled and in which the velocity of the waves is constant, it is necessary to make the following assumptions: 1. That the effect of irregularities in cross section is to alter the velocity of the primary and reflected waves; i.e., to distort the geographical distribution of phase differences. 2.That damping is proportional to the phase change in the waves rather than to the distance traveled. 3. That the damping coeffcient, as defined, is constant along the length of the channel.