The Pennell Coast continental shelf is isolated from West Antarctic Ice Sheet drainage; for an ice sheet to ground in this region it must flow over the Transantarctic Mountains from East Antarctica. Features observed indicate that ice grounded on the Pennell shelf. Cores from the shelf sampled till, a pelletized unit, glacial-marine sediments, contourite deposits, and diatomaceous muds. The timing of ice sheet grounding is revealed by radiocarbon dates that indicate the ice sheet was grounded on the shelf during the Last Glacial Maximum and has a retreat history that differs from nearby drainage areas. Comparison to sea-level curves suggests that melting ice from the region contributed to the Holocene sea-level rise and that formation of that ice contributed to the fall in sea level immediately prior to the Last Glacial Maximum. Comparison between the Pennell Coast and drainage outlets of the West Antarctic Ice Sheet allows examination of controls on ice sheet behavior. There is a consistent pattern of erosional features on the crystalline bedrock of the inner shelf, mega-scale glacial lineations on the sedimentary strata of the outer shelf, and drumlins between the two. The troughs in the areas of sedimentary substrate are interpreted to have been occupied by fast-flowing ice and those in the areas of crystalline substrate by slower-moving ice. The Pennell shelf differs in that it has both crystalline and sedimentary substrates but no drumlins or lineations. Possible reasons for this difference include the size of the drainage basin, the narrow continental shelf, and the high sand content of the tills. Core and seismic data were used to conduct an analysis of the west Louisiana outer shelf depositional systems formed during the last glacial-eustatic cycle. Differences in deltaic deposition in the area illustrate the complex relationship between depositional patterns and sea-level change. Particularly salient is the difference between the two primary sequence boundaries. The oldest sequence boundary is a major erosional surface. The youngest sequence boundary is characterized by much smaller channels and is primarily an interfluve feature. The observed variations in each system can be used to refine sequence-stratigraphic models.

The Strange Lake deposit is located on the Quebec-Labrador border. This large deposit of Zr, Y, REE, Nb and Be mineralization is hosted by a Late Proterozoic high-level stock that was intruded into high-grade graphitic gneisses. The intrusive rocks consist of leucocratic and melanocratic peralkaline granites. The occurrence of plastically deformed melanocratic xenoliths in the leucogranite and vice versa indicate that the two granite types were intruded coevally. / The stock is extensively altered, especially in the north. Early alteration is manifested by the replacement of arfvedsonite with aegirine. Later alteration involved an exchange of calcium for sodium. Zr, Ti, Y, REE, Nb, Be are concentrated in Ca-bearing minerals that, together with quartz, commonly pseudomorph Na-bearing minerals. Hematite typically coats the rare-metal enriched minerals. / Pseudomorph outlines are frequently delineated by trains of fluid inclusions. / A model is proposed in which the intrusion of a peralkaline granite to high crustal levels initiated a meteoric water-dominated hydrothermal system in the adjacent gneisses.

The Superior Province is the Earth’s largest Archean craton. Its western portion in Canada represents the nucleus of the North American continent, and has a lineated structure with well-preserved supracrustal rock sequences, mineral resources, and greenstone-granite terranes. Its strong east-west tectonic fabric is most commonly attributed to the formation and widespread accretion of island arcs and accretionary prisms ~ 2.6 Ga ago (Lucas et al., 1998). The Superior Province is underlain by lithospheric mantle that exhibits strong regional variations in anisotropy and velocity structure (Darbyshire et al., 2007). The stratigraphy, velocity structure and thickness of the crust and upper-mantle beneath the western Superior Province, were examined through the analysis of seismic discontinuities on the radial and transverse components of P-wave receiver functions. Global earthquakes that occurred between 2003 and 2008 and recorded by 13 broadly spaced FedNor/POLARIS and CNSN three-component broadband seismic stations across western Ontario were used to create receiver functions. Receiver functions were calculated using a panel deconvolution approach (using inter-trace regularization constraints) to improve signal-to-noise ratio. Inversion for lithospheric parameters was carried out through a directed Monte-Carlo search method that uses the neighbourhood algorithm of Sambridge (1999). The receiver function data show indications of crustal and mantle layering. Generally, it was observed that in the western Superior Province, seismic stations in the southern portion of the study area (south of ~ 51° N): LDIO, EPLO, PNPO, TIMO and NANO reveal a uniform crust, but a complicated and layered mantle; whereas stations in the northern portion of the study area (north of ~ 51° N): KASO, RLKO, SILO, VIMO and PKLO reveal a more uniform mantle layer, but a stratified crust. The only exception is ATKO, which displays dominant crustal layering, but is located south of ~ 51° N. Other observations include: crustal discontinuities which lose continuity laterally, possibly due to subducting structures and/or regions of velocity gradients, and lobes of opposite polarities on the radial and transverse components of the receiver functions, which are indicative of either azimuthal anisotropy or dipping interfaces. Inversion of the receiver function data showed: 1) that crustal thickness beneath the western Superior Province varies between 39 and 46 km, similar to results from other studies such as Darbyshire et al. (2007), 2) a ubiquitous, anisotropic 15-20 km thick sub-Moho layer similar to results from studies such as Musacchio et al. (2004) and 3) two 20-25 km thick, anisotropic uppermost mantle layers observed only beneath certain stations. Modeling of the data for dip and anisotropy showed that observed back-azimuthal variation at stations with dominant crustal layering, is mainly in response to NE-SW dipping layer interfaces; while in the mantle, inherent azimuthal anisotropy is interpreted to result from frozen fabric due to regional tectonic stresses. Unlike other geophysical studies (Ferguson et al., 2005; Frederiksen et al., 2007; Darbyshire and Lebedev, 2009) in the western Superior Province that reflect the Province’s regional E-W fabric, the NE-SW anisotropic results from this study are in response to small-scale, local structures.

The objective of this thesis is to investigate the importance of melt migration in shaping major characteristics of geological features associated with the partial melting of the upper mantle, such as sea-floor spreading, continental flood basalts and rifting. The partial melting produces permeable partially molten rocks and a buoyant low viscosity melt. Melt migrates through the partially molten rocks, and transfers mass and heat. Due to its much faster velocity and appreciable buoyancy, melt migration has the potential to modify dynamics of the upwelling partially molten plumes. I develop a 2-D, two-phase flow model and apply it to investigate effects of melt migration on the dynamics and melt generation of upwelling mantle plumes and focusing of melt migration beneath mid-ocean ridges. Melt migration changes distribution of the melt-retention buoyancy force and therefore affects the dynamics of the upwelling plume. This is investigated by modeling a plume with a constant initial melt of 10% where no further melting is considered. Melt migration polarizes melt-retention buoyancy force into high and low melt fraction regions at the top and bottom portions of the plume and therefore results in formation of a more slender and faster upwelling plume. Allowing the plume to melt as it ascends through the upper mantle also produces a slender and faster plume. It is shown that melt produced by decompressional melting of the plume migrates to the upper horizons of the plume, increases the upwelling velocity and thus, the volume of melt generated by the plume. Melt migration produces a plume which lacks the mushroom shape observed for the plume models without melt migration. / Melt migration forms a high melt fraction layer beneath the sloping base of the impermeable oceanic lithosphere. Using realistic conditions of melting, freezing and melt extraction, I examine whether the high melt fraction layer is able to focus melt from a wide partial melting zone to a narrow region beneath the observed neo-volcanic zone. My models consist of three parts; lithosphere, asthenosphere and a melt extraction region. It is shown that melt migrates vertically within the asthenosphere, and forms a high melt fraction layer beneath the sloping base of the impermeable lithosphere. Within the sloping high melt fraction layer, melt migrates laterally towards the ridge. In order to simulate melt migration via crustal fractures and cracks, melt is extracted from a melt extraction region extending to the base of the crust. Performance of the melt focusing mechanism is not significantly sensitive to the size of melt extraction region, melt extraction threshold and spreading rate. In all of the models, about half of the total melt production freezes beneath the cooling base of the lithosphere, and the rest is effectively focused towards the ridge and forms the crust. / To meet the computational demand for a precise tracing of the deforming upwelling plume and including the chemical buoyancy of the partially molten zone in my models, a new numerical method is developed to solve the related pure advection equations. The numerical method is based on Second Moment numerical method of Egan and Mahoney [1972] which is improved to maintain a high numerical accuracy in shear and rotational flow fields. In comparison with previous numerical methods, my numerical method is a cost-effective, non-diffusive and shape preserving method, and it can also be used to trace a deforming body in compressible flow fields.

We investigate the nonlinear development of a forced wave packet in the presence of a critical layer in a shear flow. Two different geophysical flows are considered: vertically propagating internal gravity wave packets in a stratified shear flow and Rossby wave packets propagating toward the equator in a zonal flow. Most previous analyses of these phenomena have dealt with spatially periodic, monochromatic waves. These studies observed that, in the initial linear stages, the disturbance is absorbed at the critical layer, but subsequently, the linear theory breaks down and nonlinear phenomena such as wave breaking and reflection result. For a more realistic representation of wave activities in the atmosphere, we employ a forcing in the form of a spatially localized wave packet, rather than a monochromatic wave. We solve the nonlinear equations numerically using a pseudo-spectral Fourier approximation and a high order compact finite difference scheme. / It is found that the spatial localization delays the onset of the nonlinear breakdown in the critical layer, the absorption of the disturbance continues for large time and there is an outward flux of momentum in the zonal or horizontal direction. For the Rossby wave packet problem, we also derive an approximate analytical solution for the special case of long waves. According to this solution, the total length of the packet increases with time, as seen in the numerical simulations. In the gravity wave packet problem, the horizontal extent of the packet increases with time, but there appears to be a different mechanism for this: the part of the disturbance that spreads out is centered at the zero wave number. The region over which the packet interacts with the mean flow increases in length with time. We observe also that the prolonged absorption of the disturbance stabilizes the solution to the extent that it is always convectively stable; the local Richardson number remains positive well into the nonlinear regime. In this sense, our results differ from those in the case of monochromatic forcing in which significant regions with negative Richardson number appear.

In exploration seismics and non-destructive evaluation, acoustic, elastic and electro-magnetic waves sensitive to inhomogeneities in the medium under investigation are used to probe its interior. Waves multiply scattered by the inhomogeneities carry significant information but, due to their non-linear relation with the inhomogeneities, are notoriously dificult to image or invert for subsurface structure. Recently, however, this paradigm may have been broken as it was shown that high-order multiply scattered acoustic waves can be time-reversed and focused onto their original source location through arbitrary, unknown, inhomogeneous media using a so-called time-reversal mirror: in a first step, the multiply scattered waves are recorded on an array of transducers partially surrounding the medium, in the second step the recorded wavefields are time-reversed and reemitted into the medium (i.e., the time-reversal mirror acts as a linear boundary condition on the medium injecting the time-reversed, multiply scattered wave- field). The multiply scattered waves retrace their paths through the medium and focus on the original source location. In another development the full waveform Green's function between two (passive) receivers has been observed to emerge from crosscorrelation of multiply scattered coda waves. This process is called interferometry. The principal aim of this thesis is to explore the relation between time-reversal and interferometry and to apply the resulting insights to forward modelling of wave propagation in the broader context of inversion. A secondary aim is to see if the seismological receiver function method can be applied to a reflection setting in ways that are both dynamically and kinematically correct. These aims are achieved through: (1) Derivation of an integral representation for the time-reversed wavefield in arbitrary points of an inhomogeneous medium [first, for the acoustic case, based on the Kirchhoff-Helmholtz integral, then for the elastic case based on the Betti-Rayleigh reciprocity theorem]. Evaluation of these integral representations for points other than the original source point will be shown to give rise to the Green's function between the two points. Physically intuitive explanations will be given as to why this is the case. (2) Application of ordinary reciprocity to the integral representation for the time-reversed wavefield to get an expression in terms of sources on the surrounding surface only. This gives rise to an efficient and flexible forward modeling algorithm. By illuminating the medium from the surrounding surface and storing full waveforms in as many points in the interior as possible, full waveform Green's functions between arbitrary points in the volume can be computed by cross correlation and summation only. (3) Derivation of an exact, interferometric von Neumann type boundary condition for arbitrary interior perturbed scattering problems. The exact bound- ary condition correctly accounts for all orders of multiple scattering, both inside the scattering perturbation(s) and between the perturbations and the background model and thus includes all so-called higher-order, long-range interactions. (4) A comprehensive study of the receiver function method in a reflection setting, both kinematically and dynamically. All presented results are verified and illustrated by numerical (finite-difference) modelling. Overall, the results in this thesis demonstrate that, while the original instabilities associated with direct inversion remain, multiply scattered waves can be used in an industrial context { both in real-life experiments and in forward modelling { in ways that are stable. The presented advances in forward modelling are argued to have a significant impact on inversion as well, albeit indirectly.

<p> Possible sea-floor spreading anomalies are indentified in marine magnetic surveys conducted in the eastern Gulf of Mexico. A symmetric pattern of lineated anomalies can be correlated with the geomagnetic time scale using previously proposed opening histories for the Gulf of Mexico basin. Lineated magnetic anomalies are characterized by amplitudes of up to 30 nT and wavelengths of 45-55 km, and are correlatable across 12 different ship tracks spanning a combined distance of 6,712 km. The magnetic lineations are orientated in a NW-SE direction with 3 distinct positive lineations on either side of the inferred spreading ridge anomalies. The magnetic anomalies were forward modeled with a 2 km thick magnetic crust composed of vertically bounded blocks of normal and reverse polarity at a model source depth of 10 km. Remnant magnetization intensity and inclination are 1.6 A m^-1 and 0.2&deg; respectively, chosen to best fit the magnetic observed amplitudes and, for inclination, in accord with the nearly equatorial position of the Gulf of Mexico during Jurassic seafloor spreading. The current magnetic field is modeled with declination and inclination of and 0.65&deg; and 20&deg; respectively. Using a full seafloor spreading rate of 1.7 cm/yr, the anomalies correlate with magnetic chrons M21 to M10. The inferred spreading direction is consistent with previous suggestions of a North-East to South-West direction of sea-floor spreading off the west coast of Florida beginning 149 Ma (M21) and ending 134 Ma (M10). The opening direction is also consistent with the counter-clockwise rotation of Yucatan proposed in past models.</p>

<p> The depositional environment of the middle to late Eocene Oberlin sand of Northwest Oberlin Field and Pilgrim Church Field in central Allen Parish, Louisiana, was investigated. The depositional environment of the Oberlin sand has been interpreted from observations of spontaneous potential log signatures, conventional core reports, paleontological reports, shape of isochore maps, coherency extraction attribute, amplitude extraction attribute, and multiple seismic and subsurface cross sections. Focus is centered on the juxtaposition of component sand bodies and their proximity to the interdistributary and prodelta environments. Sand bodies include distributary channels, distributary mouth bars, crevasse subdeltas and shelfal bars and are interpreted to be the products of lower deltaic and shelf processes. The results of this study are based on seismic analysis, display techniques and subsurface maps calibrated to well logs, models, and recognition criteria of modern and ancient depositional environments previously described in the regional literature. The integration of all available data provides an objective and systematic approach detailing the origin, lateral extent, geometry and architecture of the Oberlin sand in the lower deltaic plain and shelf environments. The results of this study may be applicable to similar age sands on trend with the study area. Understanding of sand component types of the lower deltaic and shelf environments is vital to exploration success and development optimization of hydrocarbon bearing reservoirs.</p>

The Superior Province is the Earth’s largest Archean craton. Its western portion in Canada represents the nucleus of the North American continent, and has a lineated structure with well-preserved supracrustal rock sequences, mineral resources, and greenstone-granite terranes. Its strong east-west tectonic fabric is most commonly attributed to the formation and widespread accretion of island arcs and accretionary prisms ~ 2.6 Ga ago (Lucas et al., 1998). The Superior Province is underlain by lithospheric mantle that exhibits strong regional variations in anisotropy and velocity structure (Darbyshire et al., 2007). The stratigraphy, velocity structure and thickness of the crust and upper-mantle beneath the western Superior Province, were examined through the analysis of seismic discontinuities on the radial and transverse components of P-wave receiver functions. Global earthquakes that occurred between 2003 and 2008 and recorded by 13 broadly spaced FedNor/POLARIS and CNSN three-component broadband seismic stations across western Ontario were used to create receiver functions. Receiver functions were calculated using a panel deconvolution approach (using inter-trace regularization constraints) to improve signal-to-noise ratio. Inversion for lithospheric parameters was carried out through a directed Monte-Carlo search method that uses the neighbourhood algorithm of Sambridge (1999). The receiver function data show indications of crustal and mantle layering. Generally, it was observed that in the western Superior Province, seismic stations in the southern portion of the study area (south of ~ 51° N): LDIO, EPLO, PNPO, TIMO and NANO reveal a uniform crust, but a complicated and layered mantle; whereas stations in the northern portion of the study area (north of ~ 51° N): KASO, RLKO, SILO, VIMO and PKLO reveal a more uniform mantle layer, but a stratified crust. The only exception is ATKO, which displays dominant crustal layering, but is located south of ~ 51° N. Other observations include: crustal discontinuities which lose continuity laterally, possibly due to subducting structures and/or regions of velocity gradients, and lobes of opposite polarities on the radial and transverse components of the receiver functions, which are indicative of either azimuthal anisotropy or dipping interfaces. Inversion of the receiver function data showed: 1) that crustal thickness beneath the western Superior Province varies between 39 and 46 km, similar to results from other studies such as Darbyshire et al. (2007), 2) a ubiquitous, anisotropic 15-20 km thick sub-Moho layer similar to results from studies such as Musacchio et al. (2004) and 3) two 20-25 km thick, anisotropic uppermost mantle layers observed only beneath certain stations. Modeling of the data for dip and anisotropy showed that observed back-azimuthal variation at stations with dominant crustal layering, is mainly in response to NE-SW dipping layer interfaces; while in the mantle, inherent azimuthal anisotropy is interpreted to result from frozen fabric due to regional tectonic stresses. Unlike other geophysical studies (Ferguson et al., 2005; Frederiksen et al., 2007; Darbyshire and Lebedev, 2009) in the western Superior Province that reflect the Province’s regional E-W fabric, the NE-SW anisotropic results from this study are in response to small-scale, local structures.

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.