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.

ABSTRACTThis paper interprets aeromagnetic data for a deep basin section of the Karroo rift in south‐east Tanzania. We use a novel integrated approach involving the application of advanced derivatives to define structure and the tilt‐depth method to determine and map the depth to basement. In the latter case we use the result of both reduced to pole and reduced to equator data to help constrain the shape and depth of the basin. We show that for a reduced to pole aeromagnetic data set, the generalized form of the local phase, called the tilt derivative, is an effective means of providing an initial (first pass) mapping of a sedimentary basin in terms of its fault structure, dip direction of faults and depth to basement. Since the amplitude of the tilt derivative does not contain information on the strength of the geomagnetic field nor magnetization (other than inclination) of the causative body, the susceptibility contrast across faults/contacts is derived from the analytic signal derivative. We also investigate how effective the tilt derivative and tilt‐depth method are for structural and depth to basement mapping in regions close to the magnetic equator, where the reduction to pole transform is often unstable; this is done using the same Tanzania data set transformed to the pole and the equator. We find that the tilt derivative applied to the reduction to equator data cannot be used to map the structure because of the effects of magnetic anisotropy, which results in the magnetic response of structures varying with strike azimuth. To overcome this anisotropy problem the analytic signal and/or local wavenumber derivatives, which are for all practical purposes independent of inclination, provide the best means of defining the major structural trends. We also find that the tilt‐depth method provides coherent depth to basement estimates for both reduced to pole and reduced to equator data. For the deep basin sections of the Karroo rift, there is a sparsity of tilt‐depth results from both the reduced to pole and reduced to equator data sets. However, each set of results has a different spatial coverage, so when combined they provide a better spatial sampling of the long wavelength magnetic character of the basin and thus improve the constraints on the minimum curvature gridding method to map the shape and depth of the basin.

We compute the depth to the top of magnetic basement using the Tilt-Depth method from the best available magnetic anomaly grids covering the continental USA and Australia. For the USA, the Tilt-Depth estimates were compared with sediment thicknesses based on drilling data and show a correlation of 0.86 between the datasets. If random data were used then the correlation value goes to virtually zero. There is little to no lateral offset of the depth of basinal features although there is a tendency for the Tilt-Depth results to be slightly shallower than the drill depths. We also applied the Tilt-Depth method to a local-scale, relatively high-resolution aeromagnetic survey over the Olympic Peninsula of Washington State. The Tilt-Depth method successfully identified a variety of important tectonic elements known from geological mapping. Of particular interest, the Tilt-Depth method illuminated deep (3 km) contacts within the non-magnetic sedimentary core of the Olympic Mountains, where magnetic anomalies are subdued and low in amplitude. For Australia, the Tilt-Depth estimates also give a good correlation with known areas of shallow basement and sedimentary basins. Our estimates of basement depth are not restricted to regional analysis but work equally well at the micro scale (basin scale) with depth estimates agreeing well with drill hole and seismic data. We focus on the eastern Officer Basin as an example of basin scale studies and find a good level of agreement between previously-derived basin models. However, our study potentially reveals depocentres not previously mapped due to the sparse distribution of well data. This example thus shows the potential additional advantage of the method in geological interpretation. The success of this study suggests that the Tilt-Depth method is useful in estimating the depth to crystalline basement when appropriate quality aeromagnetic anomaly data are used (i.e. line spacing on the order of or less than the expected depth to basement). The method is especially valuable as a reconnaissance tool in regions where drillhole or seismic information are either scarce, lacking, or ambiguous.

The Tilt‐depth‐dip‐ΔK method described here is based on the buried 2D vertical contact model and provides a relatively simple means of interpreting magnetic data to estimate location and strike of geological contacts/faults, depth to basement, direction of fault throw (or direction from high to low susceptibility) as well as susceptibility contrast. Determining these spatially derived parameters provides a rapid means of evaluating magnetic data and ultimately mapping the depth to basement and structure. The method is particularly applicable for sedimentary basins lacking intra‐sedimentary volcanics. The method relies on the spatial visualization of the results by the interpreter to estimate and identify only those parameters that are least affected by anomaly interference caused by neighboring structures. The Tilt‐depth‐dip‐ΔK method thus provides an important alternative interpretation approach over moving window methods, such as Euler, where the solutions lose their physical link with their causative anomalies. The vertical contact model used is found to be robust and can thus cater for a wide range of geological conditions.