No description available.

No description available.

No description available.

No description available.

No description available.

A 10 km x 10 km study area in the western Bushveld Complex, south of the Pilanesberg Complex, was selected for testing the inversion of vertical component gravity (Gz) data to determine the geometry of the Bushveld Complex/Transvaal Supergroup contact. This contact has a density contrast of ~0.350 g.cm-3 making it a suitable target for gravity inversion. The resulting 3D gravity model agrees well with the 3D seismic interpretation, indicating that the depths determined from the seismic data are appropriate. The gravity inversion could be extended laterally to investigate regions without seismic data coverage. This methodology may prove useful where upwellings in the floor of the Bushveld Complex distort seismic data, but can be imaged by gravity inversions. The Gz dataset was created from converted Airborne Gradient Gravity (AGG) data, combined with upward continued ground Gz gravity data, providing extensive coverage. This combined dataset was used in an interactive, iterative 3D gravity inversion methodology used to model the geometry of the Bushveld Complex/Transvaal Supergroup contact and densities of the Bushveld Complex, Transvaal Supergroup and Iron-Rich Ultramafic Pegmatoids (IRUPs). The resulting 3D gravity model provides an acceptable first-pass model of the Bushveld Complex/Transvaal Supergroup contact. In the shallow south-west region of the study area, the steeply dipping contact was determined from borehole intersections. 3D seismic data was the only constraint towards the north-east, where the contact flattens out to a sub-parallel contact, at ~2 000 m depth. In the north-western section, the Bushveld Complex/Transvaal Supergroup contact is fault-bounded by a conjugate set of the Rustenburg Fault, causing the Bushveld to onlap the Transvaal sediments. In the southern region, the contact changes as the conjugate fault dies out, and the Bushveld Complex becomes layered/sub-parallel to Transvaal sediments. This, and other geological features (e.g. faulting, folding, dykes), can be explained in relation to the regional tectonic history, relating to motion along the Thabazimbi-Murchison Lineament (TML). Pre-Bushveld emplacement NW-SE far-field stress caused NW trending extensional features in the region (e.g. Rustenburg Fault). Re-orientation of the compressive force to NE-SW, in syn- to post-emplacement, caused compressive features in the region (e.g. open folds with axes trending NW). Ground gravity data (100 m x 100 m station- and line-spacing) were also inverted to obtain a 3D model of the overburden, constrained by borehole data. However, the inversion failed to satisfy the gravity data and borehole data simultaneously, relating to difficulties in modelling the regional gravity field and the gradational nature of the weathered contact. Several rapid variations in overburden thickness were mapped, with particular success in the high frequency ground gravity survey (30 m x 30 m station- and line-spacing) with the identification of a deeply weathered (~10 m deep) channel relating to an mapped fault.

The dynamics of the atmosphere and ocean are dominated by slowly evolving, large-scale motions. However, fast, small-scale motions in the form of inertia-gravity waves are ubiquitous. These waves are of great importance for the circulation of the atmosphere and oceans, mainly because of the momentum and energy they transport and because of the mixing they create upon breaking. So far the study of inertia-gravity waves has answered a number of questions about their propagation and dissipation, but many aspects of their generation remain poorly understood. The interactions that take place between the slow motion, termed balanced or vortical motion, and the fast inertia-gravity wave modes provide mechanisms for inertia-gravity wave generation. One of these is the instability of balanced flows to gravity-wave-like perturbations; another is the so-called spontaneous generation in which a slowly evolving solution has a small gravity-wave component intrinsically coupled to it. In this thesis, we derive and study a simple model of inertia-gravity wave generation which considers the evolution of a small-scale, small amplitude perturbation superimposed on a large-scale, possibly time-dependent °ow. The assumed spatial-scale separation makes it possible to apply a WKB approach which models the perturbation to the flow as a wavepacket. The evolution of this wavepacket is governed by a set of ordinary differential equations for its position, wavevector and its three amplitudes. In the case of a uniform flow (and only in this case) the three amplitudes can be identifed with the amplitudes of the vortical mode and the two inertia-gravity wave modes. The approach makes no assumption on the Rossby number, which measures the time-scale separation between the balanced motion and the inertia-gravity waves. The model that we derive is first used to examine simple time-independent flows, then flows that are generated by point vortices, including a point-vortex dipole and more complicated flows generated by several point vortices. Particular attention is also paid to a flow with uniform vorticity and elliptical streamlines which is the standard model of elliptic instability. In this case, the amplitude of the perturbation obeys a Hill equation. We solve the corresponding Floquet problem asymptotically in the limit of small Rossby number and conclude that the inertia-gravity wave perturbation grows with a growth rate that is exponentially small in the Rossby number. Finally, we apply the WKB approach to a flow obtained in a baroclinic lifecycle simulation. The analysis highlights the importance of the Lagrangian time dependence for inertia-gravity wave generation: rapid changes in the strain field experienced along wavepacket trajectories (which coincide with fluid-particle trajectories in our model) are shown to lead to substantial wave generation.

Master of Science - Science / The giant graviton part of the AdS/CFT dictionary is expanded from consideration of N = 4 super Yang-Mills theory with U(N) gauge group to the case of an SU(N) gauge group. Candidate duals to giant gravitons for the U(N) case were found by Corley, Jevicki and Ramgoolam [4] to be Schur polynomials of the Lie algebra. In this dissertation, computational generalisation of the U(N) result is achieved, and a set of linearly independent operators in one-to-one correspondence with the half-BPS representations of the SU(N) gauge theory given. These tools allow the rst elucidation of bulk and boundary degrees of freedom via the dual eld theory, exploiting the usefulness of giant gravitons as probes of the geometry.

A free-air gravity anomaly map of the continental margin of Peru between 12° and 18° S. Lat. shows a -110 to -220 mgl anomaly associated with the Peru-Chile Trench, a -60 mgl anomaly over the Pisco Basin on the continental shelf, and -120 mgl anomaly over the Mollendo (or Arequipa) Basin on the upper continental slope. Anomalies observed over the continental slope and shelf consist of slope and basin anomalies superposed on a very large, broad regional anomaly. The approximately zero mgl anomaly observed in the region of the Nazca Ridge indicates the ridge is isostatically compensated. A structural model constrained by the observed gravity anomalies and seismic refraction data indicates that compensation is due to a crust approximately 8 km thicker and about 0. 04 g/cm³ less dense than the oceanic crust on either side of the Nazca Ridge. Gravity anomalies are consistent with mass distributions expected at the Peru-Chi1e Trench as a consequence of subduction of the Nazca Ridge and the Nazca Plate. Crustal and subcrustal cross sections constrained by free-air gravity anomalies, seismic refraction data, and geologic information indicate approximately 2 km of crustal thinning seaward of the trench on the southeast side of the Nazca Ridge but no crustal thinning on the northwest side of the ridge. Crustal thickness increases from approximately 10 km near the trench to about 25 to 30 km under the southwestern flank of the Andes and to approximately 70 km under the Andes. The crust is inferred to be 33 km thick under the Amazon Basin. A cross section north of the Nazca Ridge suggests a rupture of the crust at depth under the coast mountains, and earthquake hypo centers projected onto this cross section indicate a relatively shallow, nearly horizontal Benioff zone under the Andes and the Amazon Basin. A cross section south of the Nazca Ridge does not show these features, hence a different subduction process on each side of the Nazca Ridge is indicated. Free-air gravity anomalies indicate a structural high extending northwest from 17° S. Lat, along the coast, the Paracas Peninsula and nearly 100 km offshore along the edge of the continental shelf. Computations based on gravity data suggest the Pisco Basin immediately east of this structural high contains approximately 2. 2 km of sediment. A similar computation for the Mollendo Basin yields a sediment thickness of approximately 1.4 km. Gravity anomaly patterns are consistent with uplift beneath the continental shelf edge and upper slope and suggest a continental margin composed of compacted, dewatered sediments of both continental and oceanic origin. / Graduation date: 1976

Graduation date: 1981