To simplify the complex total magnetic field intensity (T) on datasets obtained from locations close to the geomagnetic Equator (inclinations |α| ≤ 20°) such datasets are routinely reduced-to-equator (RTE), since they cannot be stably reduced-to-pole (RTP). RTE anomalies tend to have small amplitudes and exhibit azimuth-based anisotropy, unlike RTP anomalies. Anisotropy describes the dependence of the amplitude and shape of an RTE anomaly on the strike direction of its source. For example, an East-West striking contact/fault will generate a strong RTE anomaly response whereas a North-South striking equivalent will not. Where adjacent sources occur, anisotropy causes interference between anomalies, displacing anomalies relative to their sources. This makes using magnetic data to map structures in regions that are close to the geomagnetic equator difficult or potentially of limited value. This thesis develops a strategy to interpret RTE datasets and applies it to determine the basement structure in NE Nigeria where |α| ≤ 8°. This area has >50% of the basement concealed beneath Cretaceous and Quaternary sediments of the Benue Trough and Chad basin, respectively. The aim of the study is to structurally map the basement underlying the Benue and Chad rifted basins in NE Nigeria, by tracing and determining the depths of basement faults and associated structures.
The first-order derivative-based "Tilt-Depth" method has been evaluated to determine its effectiveness
when applied to RTE datasets to determine the location and depth of structures. The method was tested first using RTE and RTP equivalents of synthetic datasets obtained from profiles across East-West striking, 2D contacts at various depths, inclinations of effective magnetisation (ϕ), and dips (d). RTP datasets were used throughout as reference models. Errors in "Tilt-Depth" method estimates were invariant to changes in depth, but sensitive to changes in ϕ and d of sources. At error limits of 0-20%, the method effectively estimates locations and depths of 2D contacts when dip is within the 75 ≤ d° ≤ 105 range, inclination of remanent magnetisation relative to induced magnetisation is within the 155 ≤ β° ≤ 205 range (magnetisations are collinear), and Koenigsberger ratio (Q) of remanent to induced magnetisation amplitudes ≤ 1. Relationships between Q, α , β and ϕ suggests that the simplification of remanence-laden anomalies due to magnetisations being collinear results from deviations of ϕ from α of ≤12° when Q≤1. Similar deviations occur between ϕ and α , for all β values, when Q≤0.2. Hence, remanent
magnetisation is negligible for RTP or RTE datasets when a priori information suggests Q≤0.2.
The "Tilt-Depth" method was further tested for anisotropy-induced anomaly interference effects using RTP or RTE of the Complex “Bishop” Model (CBM) and Tanzania grids. The CBM grid contains 2D contacts of various strikes and three-dimensional (3D) sources with non-2D contacts at various depths (all precisely known), and satisfy the d, ϕ and Q requirements above. The Tanzania grid presented a real dataset from a Karoo rift basin, where more randomly striking 2D contacts occur at unknown depths. For comparison, the second vertical derivative, analytic signal amplitude, local wavenumber, and the horizontal gradient magnitudes of Ѳ (HGM(Ѳ)) and (HGM()) methods were also tested using these grids. Locations estimated from all these methods show that: (1) Sources of all shapes and strikes are correctly imaged on RTP grids; (2) North-South striking 2D contacts are not imaged at all on RTE datasets, but can be inferred from linear alignments of stacked short wavelength East-West striking anomalies; (3) 2D contacts with strikes ranging from N045 to N135° are correctly imaged on RTE datasets; (4) Anomalies from poorly isolated 2D contacts with N±020° strikes interfere to further complicate RTE datasets, making it difficult to correctly image these sources; and (5) RTE anomalies from 3D sources tend to smear in an East-West direction, extending such anomalies well past edges of their sources along this direction. These North-South striking non-2D edges are not imaged at all, whilst their East-West striking non 2D (Northern and Southern edges are correctly imaged.
Depths estimated for 2D and non-2D contacts with strikes ranging from N045 toN135° from RTP and RTE of the CBM grids, using the local wavenumber, analytic signal amplitude and |Ѳ| = 27°- based “Tilt-Depth" methods show that: (1) "Tilt-Depth” and local wavenumber methods underestimate the actual depth of sources, while the analytic signal amplitude method provided both severely underestimated and overestimated depths. Thus, “Tilt-Depth” and local wavenumber estimates were easier to utilise and interpret; (2) "Tilt-Depth" and local wavenumber methods underestimate 2D contacts from RTP and RTE grids by up to 25 and 35% of their actual depths, respectively; (3) 'Tilt-Depth" and local wavenumber methods, respectively, underestimate depths of East-West striking non-2D edges of 3D sources by about 35 and 30% from the RTP grid; and (4) "Tiit-Depth" method consistently underestimates non-2D contacts from RTE grids by up to 40%.
Using knowledge gained from the above tests, all the methods were applied to a NE Nigeria (RTE) dataset, to delineate basement structures in the area. The dataset was a 1 km upward-continued grid with 1 km x 1 km cell size, and extended well beyond NE Nigeria into Niger, Chad and Cameroon Republics. While basement depths were estimated from the dataset using the "Tilt-Depth" and local wavenumber methods only, these methods and the second vertical derivative, analytic signal amplitude, local wavenumber, as well as the horizontal gradient magnitudes of Ѳ (HGM(Ѳ)) and (HGM()) methods, were used to map source edge locations.
A basement structure map of NE Nigeria was obtained using the above methods and found not to be dominated by North-South striking faults. Instead the basement is dissected mainly by near vertical,
NE-SW trending faults against which NW-SE or E-W trending faults terminate. The relationship between these inferred faults, basement horsts, volcanic plugs, and basement depressions, and outcrop information suggests that rifting was episodic as the mainly NorthEast directed rift propagation direction was occasionally deflected by transcurrent faults to relieve differential stresses built up from wall rock and/or crustal resistance. Apparent stress relief features include the Yola basin, flood basalts, Lamurde Anticline and Kaltungo Inlier. A number of isolated depocenters, mainly half grabens, with sediment thickness exceeding 11km seem to occur in NE Nigeria. Outside these depocenters, basement occur at depths generally shallower than 0.5 km, except where intra-basinal horsts occur, at depths shallower than 2.5 km. These depths agree well with well information and seismic data interpretation, and show the SW Chad basin depocenter to be isolated from adjoining basins in Cameroon, Chad and Niger Republics.
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