A study of the geology of the Vaalbank and Lady Frere areas in the Karoo Basin of South Africa using gravity, magnetic and gamma-ray spectrometry data: implications of groundwater potential
- Authors: Khalimashe, Sinesihle , Gwavava, Oswald
- Date: 2020
- Subjects: Gamma ray astronomy
- Language: English
- Type: Thesis , Masters , MSc (Geology)
- Identifier: http://hdl.handle.net/10353/11983 , vital:39124
- Description: The Vaalbank and Lady Frere areas belong to the Elliot, Molteno and Burgersdorp Formations, that are part of the sedimentary succession of the Beaufort Group in the Karoo Basin of South Africa. There is Quaternary alluvium covering the mudstone, sandstone and shale rocks of the Beaufort Group. Dolerite and gabbro sills of the Karoo age have intruded the whole area. A number of investigations were carried out for the study namely field observations, petrographic, X-ray diffraction, airborne gamma-ray spectrometry, aeromagnetic and gravity analyses. Twenty four rock samples were collected in the field from fresh outcrops of the Karoo dolerites, Burgersdorp and Molteno formations. The measured densities and porosities show that the Karoo dolerite suite has the highest average dry density of 2.771 g/cm3 and the lowest average porosity of 3%. The Burgersdorp Formation has an intermediate average density of 2.458 g/cm3 and an intermediate average porosity of 5.4%. The Molteno Formation has the lowest average density of 2.190 g/cm3 and the highest average porosity of 14.5%. Petrographic and geochemical investigations were carried on 19 rocks samples collected in the field to determine the mineralogy character using microscopic and XRD analyses. Both petrographic and X-ray diffraction analyses revealed that the sandstones of the study area are composed of quartz as their primary mineral and feldspars as the secondary mineral. The dolerite consists of euhedral structured minerals such as magnetite, pyroxene, plagioclase and amphibole. The gamma ray maps show high spectrometric values are associated with the Burgersdorp Formation, alluvium cover and dolerite dykes. The low spectrometric values are associated with dolerite sills and ring complexes. The boundaries of the sill/ring complexes are clearly delineated by the K/U ratio and ternary maps. The magnetic maps show ring like patterns of magnetic high anomalies that are due to the sills/ring complexes whilst the numerous, narrow, linear magnetic highs are due to faults and dolerite dyke swarms. The majority of the dykes trend in a NW-SE direction and a few dykes are in a NE-SE direction. The magnetic power spectrum indicates four depths of the magnetic sources at average depths of 0.13 km, 1.60 km, 2.83 km and 12.40 km. The magnetic depth iii slices maps show that both the circular/ring like and linear anomalies extend from shallow to deeper depth of 12.4 km. The gravity map is dominated by a long wavelength gravity anomaly that increases from about -120 mGals in the northwestern corner of the study area to -110 mGals in the southeastern corner of the study area. Results from 2½D gravity modelling show that this long wavelength anomaly is due to a horizontal Moho at a depth of 47 km in the study area, which shallows outside the study area near the coast. Superimposed on it are short wavelength gravity anomalies due to low density sediments and high density dolerite intrusions. The simple 2½D models generated from five profiles traversing the study area reveal that the sediments of the Karoo Supergroup extend from the surface down to a depth 5 km below sea level attaining a maximum thickness of about 6½ km. These sediments are dykes, sills and ring complexes. The dykes and sills/ring complexes identified from gamma ray spectrometry, magnetic and gravity data results are likely to be associated with fractures, joints, cracks and fissures in the host rocks, which form preferential pathways for groundwater transmission. Hence, they could be suitable targets for groundwater.
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Classification of Distinct Fuzzy Subgroups of the Dihedral Group Dp nq for p and q distinct primes and n ∈ N
- Authors: Nxala, Baphumelele Ellen
- Date: 2018
- Subjects: Fuzzy mathematics Fuzzy sets
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10353/14516 , vital:39997
- Description: In this dissertation, we classify distinct fuzzy subgroups of the dihedral group Dpnq, for p and q distinct primes and n ∈ N, under a natural equivalence relation of fuzzy subgroups and a fuzzy isomorphism. We aim to present formulae for the number of maximal chains and the number of distinct fuzzy subgroups of this group. Our study will include some theory on non-abelian groups since the classification of distinct fuzzy subgroups of this group relies on the crisp characterization of maximal chains. We give the definition of a natural equivalence relation introduced by Murali and Makamba in [67] which we will use in this study. Based on this definition, we introduce two counting techniques that we will use to compute the number of distinct fuzzy subgroups of Dpnq. In this dissertation, we use the criss-cut counting technique as our primary method of enumeration, and the cross-cut method serves as a means of verifying results we obtain from our primary method. To classify distinct fuzzy subgroups of this group, we begin by investigating the dihedral groups Dpnq, for p and q distinct primes and specific values of n = 2 and 3 to observe a trend. We classify the flags of these groups using the characterization of flags introduced in [93]. From this characterization, we then present formulae for the number of distinct fuzzy subgroups attributed to the flags of Dp 2q and Dp 3q . To generalise results for Dpnq, for p and q distinct primes and n ∈ N, we characterize the flags of this group and classify them as either cyclic, mdcyclic for 1 ≤ m ≤ n, or b-cyclic. Finally, we establish a general formula for the number of distinct fuzzy subgroups obtainable from these flags. We conclude by comparing results obtained from using our general formula to those obtained by other researchers for the same group. Based on the results from this study, we give an outline of future research work
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