Numerical methods have been used to predict the eigenperiods and eigenfunctions of the Earth’s Slichter modes, known as the Slichter triplets. In order to test the validity of our method, we have also computed the frequencies and displacement eigenfunctions of some of the inertial modes of the Earth’s fluid core. We use a Galerkin method to integrate the Three Potential Description (3PD) for a neutrally, stratified and rotating fluid core of a modified Preliminary Reference Earth Model (PREM). Moreover, the same mathematical tool is used for the computation of the frequencies and displacement amplitudes of the Slichter modes. In the Galerkin formulation of the 3PD, using the divergence theorem, we make use of the natural character of the boundary conditions to reduce the order of derivatives from second to first. To compute the frequencies of the Slichter modes, we solve simultaneously the equations of the inner core motion and the dynamics of the fluid core as described above. The results are compared to those in previous studies and it is shown that in the case of the inertial modes they agree well, which proves the validity of the approach. For the Slichter modes, however, it is shown that the results are significantly different from previous work for a similar Earth model. We have also plotted the displacement eigenfunctions for the motion of the fluid in the fluid core during the Slichter oscillations. It is shown that the pattern of motion is consistent with the motion of the inner core, which serves as a second test of the validity of our results. / x, 105 leaves : ill. ; 29 cm

Convection in the Earth's mantle is a complicated phenomenon that causes various tectonic activities and affects mantle evolution on geologic time scales (billions of years). It is a subject as yet not fully understood. The early success of the high Rayleigh number constant viscosity theory was later tempered by the absence of plate motion when the viscosity is more realistically strongly temperature dependent. A similar problem arises if the equally strong pressure dependence of viscosity is considered, since the classical isothermal core convection theory would then imply a strongly variable mantle viscosity, which is inconsistent with results from postglacial rebound studies. We consider a mathematical model for Rayleigh-Bénard convection in a basally heated layer of a fluid whose viscosity depends strongly on both temperature and pressure, defined in an Arrhenius form. The model is solved numerically for extremely large viscosity variations across a unit aspect ratio cell, and steady solutions are obtained. To improve the efficiency of numerical computation, we introduce a modified viscosity law with a low temperature cut-off. We demonstrate that this simplification results in markedly improved numerical convergence without compromising accuracy. Continued numerical experiments suggest that narrow cells are preferred at extreme viscosity contrasts. We are then able to determine the asymptotic structure of the solution, and it agrees well with the numerical results. Beneath a stagnant lid, there is a vigorous convection in the upper part of the cell, and a more sluggish, higher viscosity flow in the lower part of the cell. We then offer some comments on the meaning and interpretation of these results for planetary mantle convection.

M. S.

Arc magmatism is sustained by the complex interactions between the subducting slab, the overriding plate, and the mantle wedge. Partial melting of mantle peridotite is achieved by fluid-induced flux melting and decompression melting due to upward flow. The distribution of melting is sensitive to temperature, the pattern of flow, and the pressure in the mantle wedge. The arc front is the surface manifestation of partial melting in the mantle wedge and is characterized by a narrow chain of active volcanoes that migrate in time. The conventional interpretation is that changes in slab dip angle lead to changes in the arc front position relative to the trench. We explore an alternative hypothesis: evolution of the overlying plate, specifically thickening of the arc root, causes arc front migration. We investigate the effects of varying crustal morphology and viscous decoupling of the shallow slab-mantle interface on melt production using 2D numerical models involving a stationary overriding plate, a subducting plate with prescribed motion, and a dynamic mantle wedge. Melt production is quantified using a hydrous melting parameterization. We conclude: 1) Localized lithospheric thickening shifts the locus of melt production trenchward while thinning shifts melting landward. 2) Inclined LAB topography modulates the asthenospheric flow field, producing a narrow, well-defined arc front. 3) Thickening of the overriding plate exerts increased torque on the slab, favoring shallowing of the dip angle. 4) Viscous decoupling produces a cold, stagnant forearc mantle but promotes arc front melting due to reduction in the radius of corner flow, leading to higher temperatures at the coupling/decoupling transition.

No description available.

L’éon Archéen est marqué par un phénomène majeur dans l’histoire de la terre :la stabilisation de du manteau lithosphérique continental. Bien que le rôle réel de cette stabilisation en tant qu’acteur dans la géodynamique archéenne ne soit pas encore parfaitement établi, elle a joué un rôle important, par la suite, dans le développement et la préservation de la croûte continentale stabilisée sous la forme de cratons. L’isolement de cette lithosphère par rapport à l’asthénosphère convective a dû également avoir une incidence importante sur l’évolution du manteau et sur son régime thermique. Comprendre les processus qui ont formé et modifié le manteau lithosphérique sub-cratonique à l’Archéen est donc essentiel pour appréhender l’évolution géodynamique du globe terrestre. L’origine et l’histoire de ce manteau lithosphérique restent encore très controversées car bien qu’il ait été épargné depuis deux milliards d’années de toute tectonique active, les roches qui le constituent ont subi des rééquilibrages chimiques et/ou modaux suite à un ou plusieurs événements métasomatiques. Ce travail s’inscrit en grande partie dans cette problématique avec une étude détaillée des équilibres existant entre les différentes phases minéralogiques des péridotites inclues dans les kimberlites de Thaba Putsoa et de Letseng-la-Terrae (Lesotho). L’étude de ces équilibres minéralogiques nous permet de déterminer les phases qui résultent (ou ont été modifiées) d’un phénomène métasomatique, et inversement d’en apprendre sur la nature de celui-ci. Le traitement des données pétrographiques, géochimiques et thermodynamiques a établi que la partie du manteau lithosphérique archéen échantillonnée à Letseng et de Thaba Putsoa ne peut pas être considérée comme homogène et à l’équilibre. On démontre qu’au moins deux épisodes de métasomatisme aux caractéristiques chimiques distinctes ont affecté successivement ces roches. Bien que trois grandes familles de péridotites ont été décrites, l’hypothèse d’un protolithe commun de type harzburgite subcalcique a été proposée pour l’ensemble de la lithosphère archéenne profonde. Ceci implique que tous les clinopyroxènes présents dans ces péridotites soient d'origine secondaire. La question de la validité des modèles thermodynamiques reposant sur le principe d’un équilibre du clinopyroxène avec les autres minéraux se pose dès lors. Cela nous a conduits dans la seconde partie de la thèse à commencer le développement d’un nouvel outil thermodynamique se basant sur une phase minérale plus stable comme l’orthopyroxène. Pour ce faire, un nouveau protocole d'inversion a été proposé permettant la détermination d'un modèle de solution fiable pour cette phase. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

A research report submitted In partial fulfilment for the degree Master of Science (Geographical Information Systems & Remote Sensing). to the School of Geography, Archaeology & Environmental Studies, University of the Witwatersrand, Johannesburg , July 2017 / The nature of urban development experienced by mining towns across the world has been a subject of concern among urban planners because of its transitory nature. Most times mining towns develop gloriously into booming urban centres that create employment, generate wealth and satisfaction. All these fades into oblivion as soon as the mines get depleted. Mining towns often go through a number of urban processes which have been considered an expression of ‘infrastructural violence’ especially in the earlier stage of urban growth, and continually persists throughout the town’s life span. This research sought to reconstruct the history of urban development in the mining town of Virginia, Free State, and to quantify the manifestations of infrastructural violence throughout its timeline using GIS and remote sensing. Hence, land use and land cover maps were produced from aerial photographs, topographical maps and Landsat images through manual on-screen digitizing and classification using supervised support vector machine algorithms. Land use change detection analysis was conducted on the produced images using the cross classification and tabulation tool of QGIS 2.18.4 and the post classification tool of ENVI 5.3. Landscape metrics were employed to calculate the dimensions of growth and change experienced by all the land use classes during the timeline under study. Results obtained from this study confirmed the thoughts and findings of several theories vis a vis the nature of mining towns. Results reveal a rapid growth in the urban formal land use class up until 1995 with urban expansion and sprawl happening in the years between 1986 and 1995 with metrics of CA, NP and ED multiplying to twice their initial values ten years earlier. The urban informal land use class also experienced its subtle growth throughout the timeline of the study with its own urban expansion also happening between 1986 and 1995 with double increase in CA, NP and ED metric values. However, unlike the formal class that experienced decline after this period of urban expansion, the informal class continued to experience growth up until the end of the study period. Infrastructural violence was measured using the fractal dimension index (AWMPFD) of the landscape metrics for the formal and informal LU class. The results reveal continuous fragmentation throughout the period of study but with higher values in the years in which urban development started. / LG2018

Reprocessing of the United States Geological Survey's seismic reflection profile along Interstate 64 (I64) across Virginia with a data extension to 14-sec two-way travel time has provided a stacked section suitable for an integrated interpretation of refraction, earthquake, and blast analyses done by previous workers as well as gravity modelling done in this study. The seismic reflection profile shows a highly reflective upper crust which is consistent with an allochthonous Blue Ridge Province, possibly with underlying thrust sheets, and a basal decollement at about 9 km (3 sec) depth. Immediately east of the Blue Ridge province, the Appalachian structures plunge to up to 12 km (4 sec) depth where their interpretation on the section becomes ambiguous. The Evington Group, Hardware Terrane, and Chopawamsic metavolcanic rocks exposed in the Piedmont Province correspond to numerous reflections which appear to overlie a shallowly (10° to 15°) west-dipping, highly reflective zone dipping from 1.5 sec beneath the Goochland Terrane to 5 sec beneath the Evington Group rocks. Some of the overlying reflections apparently root in this zone which is therefore interpreted to include decollement surfaces along which the overlying rocks were transported. Grenville basement rocks are interpreted to underlie this zone and form autochthonous basement beneath the entire western portion of the profile because relatively few reflections originate from within this region. The Goochland granulite terrane is interpreted as a nappe structure which has overridden a portion of the Chopawamsic metavolcanic rocks. The Goochland terrane is bounded on the east' on the section by a broad zone of east-dipping (20° to 45°) reflections which may penetrate to Moho depths and are possibly correlative with similar events seen on other Appalachian lines. The 164 section contains a layered sequence of reflections at about 9 to 12 sec extending about 70 km west from Richmond, Virginia whose base coincides almost exactly with the Mohorovicic Discontinuity (Moho) interpreted from earlier refraction work. The deep reflections are thus believed to be lower crustal layering forming a 5 to 10 km thick Moho transition zone which is believed to persist across the state. The density contrast of 0.25 gm/cm³ between the lower crust and upper mantle derived from gravity modelling, the seismic transition zone, and the presence of intrusive rocks of lower crust-upper mantle origin at the surface are consistent with partial melting and contamination of the lower crust with upper mantle material. The refraction data and gravity modelling are consistent with a crust which thins from about 52 km beneath the Appalachian mountains to about 35 km beneath Richmond, Virginia, and rethickens by up to 10 km beneath the zone of east-dipping events east of Richmond. The pervasiveness of the zone of east-dipping events on other seismic reflection lines and the continuity of the adjacent Piedmont gravity high suggest that a similar crustal profile occurs along the length of the Appalachians. / Ph. D.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: The sodic and leucocratic Tonalite, Trondhjemite and Granodiorite (TTG) granitoid series of rocks characterise Paleo- to Meso- Archaean felsic continental crust, yet are uncommon in the post-Archaean rock record. Consequently, petrogenetic studies on these rocks provide valuable insight into the creation and evolution of Earth’s early continental crust. The highpressure (HP)-type of Archaean TTG magmas are particularly important in this regard as their geochemistry requires that they are formed by high-pressure melting of a garnet-rich eclogitic source. This has been interpreted as evidence for the formation of these magmas by anatexis of the upper portions of slabs within Archaean subduction zones. In general, TTG magmas have been assumed to arise through fluid-absent partial melting of metamafic source rocks. Therefore, very little experimental data on fluid-present eclogite melting to produce Archaean TTG exist, despite the fact that water drives magmatism in modern arcs. Consequently, this study experimentally investigates the role of fluid-present partial melting of eclogite-facies metabasaltic rock in the production of Paleo- to Meso-Archaean HP-type TTG melts. Experiments are conducted between 1.6 GPa and 3.0 GPa and 700 ºC and 900 ºC using natural and synthetic eclogite, and gel starting materials of low-K2O basaltic composition. Partial melting of the natural and synthetic eclogite occurred between 850 ºC and 870 ºC at pressures above 1.8 GPa, and the melting reaction is characterised by the breakdown of sodic clinopyroxene, quartz and water: Qtz + Cpx1 + H2O ± Grt1 = Melt + Cpx2 ± Grt2. The experimental melts have the compositions of sodic peraluminous trondhjemites and have compositions that are similar to the major, trace and rare earth element composition of HPtype Archaean TTG. This study suggests that fluid-present eclogite melting is a viable petrogenetic model for this component of Paleo- to Meso-Archaean TTG crust. The nature of the wet low-K2O eclogite-facies metamafic rock solidus has been experimentally defined and inflects towards higher temperatures at the position of the plagioclase-out reaction. Therefore, the results indicate that a crystalline starting material is necessary to define this solidus to avoid metastable melting beyond temperatures of the Pl + H2O + Qtz solidus at pressures above plagioclase stability. Furthermore, this study uses numerical and metamorphic models to demonstrate that for reasonable Archaean mantle wedge temperatures within a potential Archaean subduction zone, the bulk of the water produced by metamorphic reactions within the slabs is captured by an anatectic zone near the slab surface. Therefore, this geodynamic model may account for HP-type Archaean TTG production and additionally provides constraints for likely Archaean subduction. The shape of the relevant fluid-present solidus is similar to the shape of the pressure-temperature paths followed by upper levels of the proposed Archaean subducting slab, which makes water-fluxed slab anatexis is very dependant on the temperature in the mantle wedge. I propose that cooling of the upper mantle by only a small amount during the late Archaean ended fluid-present melting of the slab. This allowed slab water to migrate into the wedge and produce intermediate composition magmatism which has since been associated with subduction zones. / AFRIKAANSE OPSOMMING: Die reeks natruimhoudende en leukokraties Tonaliet, Trondhjemiet en Granodioriet (TTG) felsiese stollingsgesteentes is kenmerkend in die Paleo- tot Meso-Argeïkum felsiese kontinentale kors, maar is ongewoon in die post-Argeïese rots rekord. Gevolglik, petrogenetiese studies op hierdie rotse verskaf waardevolle insig in die skepping en evolusie van die aarde se vroeë kontinentale kors. Die hoë-druk (HD)-tipe van die Argeïkum TTG magmas is veral belangrik in hierdie verband as hulle geochemie vereis dat hulle gevorm word deur hoë druk smelting van 'n granaat-ryk eklogitiese bron. Dit word interpreteer as bewys vir die vorming van hierdie magmas deur smelting van die boonste gedeeltes van die blaaie in Argeïese subduksie sones. TTG magmas in die algemeen, is veronderstel om op te staan deur middel van water-afwesig gedeeltelike smelting van metamafiese bron rotse. Daarom bestaan baie min eksperimentele data op water-teenwoordig eklogiet smelting om Argeïkum TTG te produseer, ten spyte van die feit dat water magmatisme dryf in moderne boë. Gevolglik is hierdie studie ‘n eksperimentele ondersoek in die rol van water-teenwoordig gedeeltelike smelting van eklogiet-fasies metamafiese rots in die produksie van Paleo- tot Meso-Argeïkum HD-tipe TTG smelte. Eksperimente word uitgevoer tussen 1.6 GPa en 3.0 GPa en 700 ºC en 900 ºC met behulp van natuurlike en sintetiese eklogiet, en gel begin materiaal van lae-K2O basaltiese samestelling. Gedeeltelike smelting van die natuurlike en sintetiese eklogiet het plaasgevind tussen 850 ºC en 870 ºC te druk bo 1.8 GPa, en die smeltings reaksie is gekenmerk deur die afbreek van natruimhoudende klinopirokseen, kwarts en water: Qtz + Cpx1 + H2O ± Grt1 = Smelt + Cpx2 ± Grt2. Die eksperimentele smelte het die komposisies van natruimhoudende trondhjemites en is soortgelyk aan die hoof-, spoor- en seldsame aard element samestelling van HD-tipe Argeïkum TTG. Hierdie studie dui daarop dat water-teenwoordig eklogiet smelting 'n lewensvatbare petrogenetiese model is vir hierdie komponent van Paleo- tot Meso-Argeïkum TTG kors. Die aard van die nat lae-K2O eklogietfasies metamafiese rock solidus is eksperimenteel gedefinieër en beweeg na hoër temperature by die posisie van die plagioklaas-out reaksie. Daarom dui die resultate daarop dat 'n kristallyne materiaal nodig is om hierdie solidus te definieër en metastabiele smelting buite temperature van die Pl + H2O + Qtz solidus druk bo plagioklaas stabiliteit te vermy. Verder maak hierdie studie gebruik van numeriese en metamorfiese modelle om aan te dui dat die grootste deel van die water geproduseer deur metamorfiese reaksies binne die blaaie bestaan vir redelike Argeïkum mantel wig temperature binne 'n potensiële Argeïkum subduksie sone, en word opgevang deur 'n smelting sone naby die blad oppervlak. Daarom kan hierdie geodinamies model rekenskap gee vir HD-tipe Argeïkum TTG produksie en dit bied ook die beperkinge vir waarskynlik Argeïese subduksie. Die vorm van die betrokke waterteenwoordig solidus is soortgelyk aan die vorm van die druk-temperatuur paaie gevolg deur die boonste vlakke van die voorgestelde Argeïkum subderende blad, wat water-vloeiing blad smeltingbaie afhanklik maak van die temperatuur in die mantel wig. Ons stel voor dat afkoeling van die boonste mantel met slegs 'n klein hoeveelheid gedurende die laat Argeïese, die water-vloeiing smelting van die blad beëindig. Dit het toegelaat dat die blad water in die wig migreer en intermediêre samestelling magmatisme produseer wat sedert geassosieer word met subduksie sones.

Global paleogeography exerts a first order control on both the deep and surficial components of the Earth system. Temporal and spatial constraints on the Mozambique Belt of Eastern Africa are needed to understand its crustal evolution and its role in assembly of Gondwana. This thesis provides detailed data on the timing, sources and nature of tectono-thermal events responsible for magmatism in the Mozambique Belt in southern Malawi. An integrated approach of petrography, geochemistry, radiogenic isotopes, and single zircon geochronology has been used to determine spatial and temporal constraints and to better constrain models of the assembly of East and West Gondwana, which occurred along the Mozambique Belt. In particular the thesis attempts to address key unresolved questions about the number and timing of accretionary pulses within the orogen. LA-ICP-MS single zircon U-Pb results show tectono-thermal events in four periods: Mesoproterozoic from 1128 ± 30 Ma to 1033 ± 20 Ma; Neoproterozoic (956 ± 12 Ma – 594 ± 65 Ma); Cambrian (530 ± 3 Ma – 515 ± 12 Ma); and Cretaceous (118 ± 2 Ma). Metamorphism is dated from a charnockitic gneiss that yielded a lower intercept age of 515 ± 18 Ma. The granitoids are intermediate to acidic with relative enrichment in LILEs and depletion in HFSEs with moderately negative anomalies in Th, Nb, P, Zr and Ti. REE spider plots show enrichment in LREEs and depleted HREEs with negative Eu anomalies. The meta-granites are largely metaluminous with a few peraluminous, I-type granites belonging to the calc-alkaline series. Radiogenic isotope data reveals slight differences with older, Mesoproterozoic rocks showing positive ɛNd and ɛHf values signifying derivation from depleted mantle material, whilst the younger rocks display negative epsilon values suggestive of crustal material recycling and mixing for their source and origins. Granitoids of southern Malawi display characteristics consistent with derivation in a continental Andean type arc with some aspects of the chemistry resembling tonalite-trondhjemite-granite (TTG) suites mapped in the Mozambique Belt in Kenya, Tanzania, Mozambique, and Antarctica although the data are not sufficiently compelling to assign the Malawi rocks to classic TTGs.