
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)11965-2
10.1016/j.heliyon.2024.e35934
e35934
Research Article
Gravity and magnetism of southern Africa in relation to Craton structures and belts
Osborne kubeka Zenzele kubhekazenzele@yahoo.com

China University of Geosciences (Beijing), School of Geophysics and Information Technology, No.29, Xueyaun Road, Haidan District, Beijing, China
23 8 2024
15 9 2024
23 8 2024
10 17 e3593419 11 2023
6 8 2024
6 8 2024
© 2024 The Author(s)
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
The general tectonic structural architecture of southern Africa is an ensemble comprised of Kalahari Craton, a vast range of mosaics of the best-preserved geological Belts, and exposed crustal blocks. In the region, demarcation of geological boundaries, tracing of magnetic and gravitational bodies, and detrending lineaments are essential to understanding the structural limits. The study presents the prevalent gravitational and magnetic investigation of major geological Belts, enhancing edges of Cratons, and evaluation of surface invariants to improve the geological understanding and evaluate the correlation of structures with the general structural tectonic framework. The utilized filter methods in the gravity maps are the Directional derivatives along x, y, and z-directions, the Modulus tensor, the Total horizontal derivative, and the Tilt angle techniques.

The phase-based filters used in the magnetic section include the Total horizontal derivative, Analytical signal, Tilt angle method, Tilt of total horizontal derivative, Theta method, Horizontal tilt angle method, Enhanced tilt filter, and Enhanced total derivative of the tilt angle. The Directional derivatives of the gravity field and the Modulus of the gravity gradient tensor demarcate the boundaries of geological structures. The Total horizontal derivative method gives an immediate and easy-to-read image of the linear structures and fault systems. The signal cluster on the Analytical signal and Tilt angle maps delineate the boundaries of causative geological sources. The Theta map is comparable with the enhanced total derivative of the tilt angle. The Tilt of the total horizontal derivative, Theta map, and Enhanced tilt filter accentuate the traces of magnetic bodies, including the Cratons. The study finds regional lineaments surrounding the Cratons and concentrated along the geological Belts. The approach of using joint elegant filters is effective and increases the certainty of the interpretation.

Keywords

Filters
Magnetic anomaly
Gravity anomaly
Southern Africa
Craton
Belt
==== Body
pmc1 Introduction

The regional scale magnetic and gravity surveys are tools to acquire information about the large-scale distribution of body sources in mosaic geologic environments and deformed geological-tectonic settings to enhance the geological understanding and interpretation of structures in the framework of geological knowledge of the study region [[1], [2], [3]]. Several geophysical techniques exist today, including gravity and magnetic imaging, which all form a large part of the geophysical investigation. The potential field data acquired in exploration record the trend of subsurface distribution of different rock types [4]. In magnetic data processing, the end limit of magnetic rocks and structural discontinuities can be delimited by drawing line segments in the magnetic anomaly map [5]. The gravity gradient is sensitive to causative geological structures and tends to present a higher spatial resolution that delineates the boundaries of buried gravitational bodies [1,6]. However, the multi-level sources in potential data impose a serious exploration challenge, making it difficult to distinguish between the deep and shallow source anomalies [5]. Data processing techniques have advanced over the years, leading to the development of various separation techniques. The new anomaly separation techniques include Fast Fourier Transform (FFT), Wavelet Filtering methods, and Singular Spectrum Analysis (SSA), all three of which are discussed by Ref. [7], as well as the Minimum-curvature technique by Ref. [8]. Other separation techniques include but are not limited to Polynomial fitting, Nonlinear filtering, Preferential continuation, Wavelet transform, Multiple-scale decomposition, Up and Down continuations, Wiener filtering, and Matching filtering [9,10].

The other challenge in potential data processing includes the multiple sources and geological noise present in the data, which causes superposition and hinders the analysis. Consequently, the interpretation of gravity and magnetic anomalies is a complex process. The gravity and magnetic maps demand different edge detection filters to bring subtle information and enhance different causative features. For simple investigations, local phase and derivative-based filters, both of which use a change in the signal intensity over gravity and magnetic anomaly bodies, serve as sufficient techniques to enhance structural visibility. For example, the horizontal and vertical derivatives of the potential fields are tools to locate the source bodies and delineate structural boundaries. The strength of vertical derivatives is the method's ability to narrow the width of the anomaly, whereas horizontal derivatives can enhance edges [[11], [12], [13]]. However, the horizontal and vertical derivatives may need to be combined to produce high-resolution filters in complex investigations. For instance Ref. [14], suggested a more elegant approach to the edge detection method by combining different gravity gradient tensors to provide more accurate and detailed information on the geological body. In geophysical data processing, some general filters are limited in utility. For example, despite the strength of the analytical signal to locate the maximum value over the edges of the body, the application of the analytical signal is limited by interference effects, as is true in many cases in which the detected edges from different bodies cannot be distinguished from the effects of adjacent causative bodies [15,16]. The other challenge in potential data processing is imposed by the local phase filters that cannot map the deep sources and yield a situation where the detected edges are "blurred" in the form of a halo. The demand for joint filters to delineate the bodies becomes apparent when conducting a study in a geologically complex region.

Previously, researchers [[17], [18], [19], [20], [21]] studied the region in southern Africa using seismic and gravitational methods. [22] studied the magnetic anomalies using total magnetic intensity and iso-magnetic map in the southeastern continental margin of South Africa. The regional crustal trends were studied using the spectral analysis of topographic and gravity data by Ref. [23]. [24] provided the crustal framework of southern Africa derived from magnetic and gravity data [25]. used the global field model to give a view of gravity changes in the region. In the seismic section [26], used the data derived from seismic receiver functions to study the crustal composition and delaminated the pre-existing lower crust in the region. The major lineaments related to ductile shear zones in southern Africa were studied by Ref. [27]. [28] investigated a correlation between the density of lineament-intersections and boreholes in the Northwest Province for geo-hydrological exploration, while [29] studied the 100 km long Thabazimbi–Murchison Lineaments. Despite the progress of the above studies and other geological observations, including the Vredefort impact structures investigation by Ref. [30], the sparse scale of seismic array installations and data resolution imposes limitations.

The lineaments, geological boundaries, main magnetic structures, and the trend of gravitational bodies in the region still need to be studied and correlated with the general structural tectonic framework. The study uses gravity and magnetism to conduct a prevalent investigation of regional scale lineaments and detrend structures related to major geological Belts, demarcates the edges of Craton structures, and evaluates the surface invariants to improve the geological understanding of the region of southern Africa. In the background, the study considers the structural interpretation map generated from geological observations on the structural limits as a basis for revealed crustal structures (Fig. 1). Since the region of southern Africa has distinct general tectonic structural architecture, complex geological set-up and features of structural arrangement on rocks the region provides a natural laboratory to test various geophysical data analysis methods.Fig. 1 The general geological framework of southern Africa (modified from James et al., 2003).

Fig. 1

2 Regional geology of southern Africa

The geological framework of southern Africa is composed of best-preserved crustal blocks, assembled in the Early–Late Archean and was subsequently modified by several major Precambrian and Phanerozoic tectono-thermal events [26,31]. The oldest known continental nucleus in southern Africa comprised two Cratons, namely the Kaapvaal Craton (3.2-2.5 Ga) and the Zimbabwe Craton (3.2-2.7 Ga), which are both separated by the sandwiched southwest-northeast trending Limpopo Belt (2.7–3.0 Ga). The Kaapvaal Craton is bounded in the South by the non-cratonic Namaqua-Natal Belt (Proterozoic) and in the West by the Kheise overthrust Belt (∼1.75 Ga). The Limpopo Belt is situated in the North of Kaapvaal Craton, while the intra-cratonic mafic layer, the Bushveld Complex, is located in the center of the Kaapvaal Craton [32]. The Zimbabwe Craton lies in the North of Kaapvaal Craton and is bounded in the southwest by the Okwa Belt (∼2.0 Ga). In the West of the Zimbabwe Craton lies the Magondi Belt (∼2 Ga). The Magondi Belt is enigmatic because of the complex tectonic and magmatic overprinting that occurred in the Archean basement during the Proterozoic. The Phanerozoic Cape Fold Belt is situated in the southernmost part of the African continent [33]. The details of regional tectonic evolution and geochemistry are beyond the scale of this paper. The summary is limited to the general geological framework (Fig. 1) and the main geological events that influenced the present-day general structural tectonic framework.

2.1 The Zimbabwe Craton

The Zimbabwe Craton comprises mainly of gneisses and granites as the dominant lithology. The gneisses form the base of sporadic patches of greenstone belts that are dated ∼3.5 to 2.6 Ga [34,35]. There have been several theories proposed to describe the link and relationship between the Kaapvaal Craton and the Zimbabwe Craton, but the consensus derived from the evaluation of cratonisation, dykes, and structural differences suggest the two cratons do not share history until 2.0 Ga [[35], [36], [37], [38]]. The two Cratons were formed due to two geologically distinct events: First, the formation of the early cratonic nucleus [37,39]. Second, the formation of magma gneisses and crust [40,41]. The crustal thickness in the Zimbabwe Craton ranges from 36 to 39 km on average, with sharp and simple Moho variation [26]. However, the crustal thicknesses increase drastically from 42 to 53 km closer to the border of the Limpopo Belt with complex Moho variation at the minimum depth of 33 km and show no evidence of the mid-crustal discontinuities [42].

2.2 The Kaapvaal Craton

The Kaapvaal Craton comprises of ∼3.2 Ga rock material with an average rock density of 2.86 g/ m3. The Kaapvaal Craton comprises ∼3.2 Ga rock material with an average rock density of 2.86 g/ m3. The average rock density suggests the felsic composition of the crust with rare mafic granulite xenolith [40]. The seismic results showed a large amplitude of Ps waves, clustering in the depth range of 34–37 km beneath the Zimbabwe Craton, while in the Kaapvaal Craton, it ranges from 33 to 45 km. The crustal thickness drastically increases closer to the Bushveld Complex and Magondi Belt in response to the widespread crustal modification that occurred during the Proterozoic [32,43].

2.3 The Limpopo Belt

The Limpopo Belt, sandwiched between the Kaapvaal and Zimbabwe Cratons is approximately 700 km long with a width ranging from 240 to 320 km. The anatomy of the Limpopo Belt consists of the northern Margin, Central Zone, and southern Margin [19,40]. The Central Zone is a deep zone formed by tectonic deformation that occurred during the collision of the Kaapvaal and Zimbabwe Cratons in the Archean, resulting in the uplift and exhumed strata that exposed high-grade metamorphic rocks [40]. The North Margin Zone has a 37 km thick crust adjacent to the Zimbabwe Craton, while the southern Margin is consistent with the thickness of the Kaapvaal Craton (40–42 km). The Moho is ambiguous, varying from 40 to 53 km, indicating structural complexity [32]. The crust is in excess of 40–45 km beneath Limpopo Belt's center [40].

2.4 The Kheis Belt and Bushveld Complex

The Bushveld Complex is situated in the northern part of the Kaapvaal Craton and was formed during the tectonic instability in the north-central Kaapvaal Craton at 2.05 Ga, which resulted in the intrusion of the Geologic Province. The tectonic event in the north-central Kaapvaal Craton produced deep Moho and downward crustal flexure [32,44]. The crust is thick along the crustal compensated zones beneath the Bushveld Complex and the Magondi Belt, and the thickness variation is related to the crustal disturbances and intrusion of 2.5 Ga Bushveld [32]. In contrast to the Bushveld Complex, the Kheis Belt is a relatively thin fold-thrust belt situated in the western margin of the Kaapvaal Craton, which formed in the Eburnean Age (1.8Ga) [45]. The rock layers in the Kheis Belt are relatively thin (<40 km) and contain more characteristics of rigid cratonic crust trending eastward [32]. The lithological framework of the Kheis Belt mainly constitutes an arenitic meta-sediment with an Archean basement [46]. Kheis Belt has been subjected to multiple tectonic processes, even though the exact time for each remains mysterious, as many researchers conclude different times, but the overall results indicate tectonic instability, which is marked by several deformational fabrics in the region [46,47].

2.5 The Grenvillian Namaqua-Natal Belt

The Grenvillian Namaqua-Natal Belt is an over 500 km long, North-West trending low-pressure granulite facies metamorphic zone situated adjacent to the South-Westof the Kaapvaal Craton [48,49]. The Grenvillian Namaqua-Natal Belt lies on the Craton decollement and consists of tectonostratigraphic terranes with the Paleoproterozoic debris that remains from the Columbia Supercontinent [50]. There are two events that formed the Grenvillian Namaqua-Natal Belt: the first event occurred in the Late Columbian tectonic, during Rodinian events, which deformed the upper mantle and entire crust [51]. The second event produced a basin filled with pilled sequences of volcano sediment [50]. The Namaqua tecto-genesis structurally piles up and thickens the crust to range from ∼20 to 25 km, with the Moho depth sharply reducing from 40 km at the center to ∼15 km at the continental edge [52].

2.6 The Cape Fold Belt

The Cape Fold Belt is situated in the southernmost margin of the continent, extending 1300 km long, and was formed in the Phanerozoic [53]. The deformation style and strain change drastically across the thin layers of the Cape Fold Belt [54]. There has been a serious discussion about the true thickness of the stratigraphic unit, and most models do not correspond with results from seismic surveys [55]. The limited understanding of the Cape Fold Belt restricts the provision of the tectonic framework. The Cape Fold Belt has a similar characteristic to the Grenvillian Namaqua-Natal Belt, except that the Cape Fold Belt is slightly thicker, with the crustal thickness ranging from ∼40 to 50 km, descending to ∼30 km near the South African coast.

3 Data description

3.1 Gravity data

The Bouguer gravity anomaly data [56] is extracted in an XYZ format from the ICGEM database at GFZ Potsdam via http://icgem.gfz-potsdam.de. The EIGEN-6C4 (European Improved Gravity model of the Earth by New Techniques) is the fourth release generation of the European Improved Gravity model of the Earth by New Techniques that has a high-resolution global gravity field model. The EIGEN-6C4 is a 1 × 1 minute resolution suitable for regional exploration. However, the model uses the standard Bouguer parameter of 2.67 g/ cm3 also does not take into consideration the density contrast between ice and rock. As such, the data is not suitable for areas covered by ice and the model is not accurate underneath the ocean. The study area under investigation is not covered by ice, nor is it covered by the ocean. The Bouguer gravity data is gridded to produce a Bougure gravity anomaly map (Fig. 2) using the Geosoft Oasis Montaj software, using the minimum curvature. Geosoft Oasis Montaj is a software that provides a platform for modeling and analysis of data for visualization and advanced understanding of the Earth's subsurface.Fig. 2 The gridded 1 × 1 minute Bouguer gravity anomaly map of the region of southern Africa. The Cape Fold Belt (CFB), Namaqua Natal Orogenic Belt (NNB), Limpopo Belt (LB), Kaapvaal Craton (KC), Zimbabwe Craton (ZC), Okwa Belt (OB), Magondi Belt (MB), Damaran Mobile Belt (DMB), Mozambique Mobile Belt (MMB), Lebombo Orogenic Belt (LOB), and Kheis Belt (KB).

Fig. 2

3.2 Magnetic data

The technique of delineating the edges of magnetic bodies is commonly used in magnetic data processing to interpret magnetic sources and understand the underlying subsurface geology. The magnetic data used in the magnetic section is based on the model publication by Ref. [57], which is a high-resolution lithospheric magnetic field model constructed based on a joint inversion of Swarm, WDMAM, CHAMP, and ground magnetic field data. The magnetic data used in the current study is specifically the magnetic data computed at the altitude of 50 km. The total magnetic data map (Fig. 3) is extracted in an XYZ format and gridded through Geosoft Oasis Montaj using the minimum curvature available on Geosoft. The minimum curvature gridding is a 2-D linear method available on Geosoft Oasis Montaj that uses the input data points to create a minimum curvature surface that fits the values.Fig. 3 The gridded magnetic anomaly map of Southern Africa. The CFB = Cape Fold Belt, NNB = Namaqua Natal Orogenic Belt, LB = Limpopo Belt, KC = Kaapvaal Craton, ZC = Zimbabwe Craton, OB= Okwa Belt, MB = Magondi Belt, and KB= Kheis Belt.

Fig. 3

4 Software description

After data collection, the next task requires visualization and data interpretation. The Geosoft Oasis Montaj, version 7.0.1 software provides a platform to process, visualize, and interpret specialized data for advanced understanding of the Earth's subsurface and subsea environments. The other tool used in the study includes Surfer software, version 13.6.618, a powerful platform for gridding and contouring. Also, Surfer software is an easy-to-use tool that allows the digitization and drawing of features into a final map.

5 Method(s)

5.1 Gravity data processing method

5.1.1 Gravity separation processes

To use the Bouguer gravity anomaly data to study geological structures at different depth levels, the effects of broader structures must first be separated from the effects caused by shallow body structures. The current monography utilizes the Upward continuation technique to separate the residual and regional gravity anomaly from the total Bouguer gravity anomaly. The key problem with the conventional upward continuation is that the continuation height must be known [9,58]. suggested a preferential continuation operator as the solution to the attenuation of gravity signals. The Upward continuation can minimally attenuate deep source wavelength signals from long wavelength signals if the separation height is correctly estimated [10]. In their model [59], presented that an optimum continuation height can be objectively calculated by cross-correlations. The current study uses a rather similar technique, constructing an interactive radially-averaged power spectrum filter to predict the optimum height. The height at which the Upward continuation is performed is 25 km. The upward continued regional gravity signal (Fig. 4a) is subtracted from the total observed anomaly signal to obtain the residual gravity anomaly signal (Fig. 4b).Fig. 4 Separated gravity field (a) Regional gravity, and (b) Residual gravity anomaly maps.

Fig. 4

5.1.2 The computation of gravity derivatives

[60] demonstrated that the vertical component of the gravity data can be transformed through Fast Fourier Transform techniques, which obey the Fourier Convolution theorem. In the current study, the separated residual node of the Bouguer gravity anomaly is processed through Euler 3-D convolution available on Geosoft Oasis Montaj to derive the directional derivatives along the x, y, and z axes. Since the First-order derivative has a high frequency, the derivative can provide more accurate and detailed information about the geological body [3]. The gravity nodes derived through Euler 3-D convolution are used to compute five independent gravity gradient tensors Txx, Txy, Txz,Tyz,andTzz. The goal of the directional derivatives technique is to be able to completely utilize potential data to extract the important boundaries of the scene of an image [61]. In order to combine the zero-crossings from different channels into primitive 'edge' elements that mark the transitions from the 'analytic' to the 'symbolic' analysis, the Directional derivatives THDx, THDy ,and THDz are computed through Geosoft Oasis Montaj. The parameters THDx, THDy , and THDz are directional derivatives along x, y, and z axes respectively, and are calculated using the following equations:

5.1.3 Computation of directional derivatives

The directional derivatives along x-direction(1) THDx=(Txy)2+(Tzx)2

The directional derivatives along y-direction(2) THDy=(Txy)2+(Tyz)2

The directional derivatives along z-direction(3) THDz=(Tzx)2+(Tyz)2

5.1.4 The Modulus of gravity gradient tensors

In order to obtain maximum information from gravity anomaly maps, the edge detection method utilizing nine components of the full gravity tensors, referred to as the Modulus of the gravity tensors, is necessary. The Modulus of gravity gradient tensors is the square root of the sum of all the tensors squared, which is expressed as the following equation:(4) Modulus=(Txx)2+(Txy)2+(Txz)2+(Tyy)2+(Tyx)2+(Tyz)2+(Tzz)2+(Tzx)2+(Tzy)2

5.1.5 The total horizontal derivative

The Total horizontal derivative (THD) of the gravity gradient tensor was proposed by Ref. [62], and the THD is now the commonly used edge detection filter for shallow causative bodies since it contains all the boundary details present in any single directional derivative term. The Total horizontal derivative of gravity gradient tensor is constructed by utilizing gravity gradient components Tx and Ty and is given by the following equation:(5) THD=(Tx)2+(Ty)2

Whereby Tx and Ty represent the gravitational tensors along the x and y orthogonal axes. THD is the Total horizontal derivative of the gravity tensor.

5.1.6 The tilt angle method

The Tilt angle method was first developed by Ref. [63] and is one of the conventional local phase filters widely used for resolution enhancement and detection of causative body edge. The Tilt angle is basically an automatic-gain-control filter with the size of an angle confined to a range between −π2 and π2 [64]. refined the Tilt angle and presents it using the following equation:(6) Tilt=tan−1[TzTHD]

Whereby Tz is the first derivative of the gravity field in a z-direction, THD is the Total horizontal derivative of the gravity field, and Tilt is the Tilt angle.

5.1.7 The structural map

The structural map (Fig. 6) is carried out through the correlation of the Tilt angle and the Total horizontal derivative maps, both calculated on the gravity data. The zero contour of the Tilt angle map is superimposed over the Total horizontal derivative through Geosoft Oasis Montaj, and the gravity lineaments are hand-picked on the suffer software. The Tilt angle technique responds well to the exploration since the amplitude is equal to zero at the edges of the gravitational body and can estimate the end of vertical contact sources [65].

5.2 Magnetic methods

5.2.1 The computation of magnetic tensor

The total magnetic data is processed using the Geosoft Oasis Montaj software by utilizing the Euler 3-D convolution to calculate the derivative of a magnetic tensor along the x, y, and z axes. In the study, various normalized derivative filters are constructed by calculations performed using the Grid math section available on Geosoft Oasis Montaj software. The filters constructed in the study are the Total horizontal derivative (Eq. (5)), Analytical signal (Eq. (7)), Tilt angle method (Eq. (6)), Tilt of total horizontal derivative (Eq. (8)), Theta map (Eq. (9)), Horizontal tilt angle method (Eq. (10)), Enhanced Tilt Filter (Eq. (11)), and Enhanced total horizontal derivative of the tilt angle (Eq. (12)).

5.2.2 The amplitude of analytical signal

The comprehensive literature on the utility of the Analytical signal technique is provided by Refs. [[11], [12], [13]]. In the study, the amplitude of the Analytic signal extended to the three-dimensional body is constructed using the following equation:(7) |AS(x,y)|=(Tx)2+(Ty)2+(Tz)2

Whereby Tx , Ty , and Tz represent the magnetic tensors along the x, y, and z orthogonal axes respectively. AS represent the amplitude of analytical signal of the magnetic tensors.

The Analytical signal map is constructed to enhance the effects of shallow sources and widen the anomalies' amplitude. The maxima of the analytical signal are very useful for delineating the edges of the sources because of the amplitude of the Analytical signal, which peaks over geological sources [13].

5.2.3 The total horizontal derivative of the tilt angle

To delineate the edges of the magnetic source, the study constructed the Total horizontal derivative of the Tilt angle. The Total horizontal derivative of the Tilt angle is independent of the geomagnetic field and trend. The method is based on the normalized amplitude of a horizontal gradient and shows the maximum values located at the edges of the magnetic structures. The major strength of tilt derivative is delineating shallow structures, but it is considered relatively ineffective for deep structures. The Total horizontal derivative of the Tilt Angle was proposed by Ref. [11], and the filter is presented by the following equation:(8) THDtilt=(tiltx)2+(tilty)2

Whereby THDtilt is the Total horizontal derivative of the Tilt. The tiltx and tilty are Tilt derivatives along x and y directions, respectively.

5.2.4 The Theta map

(9) [θ]=cos−1[THDSignal]

Whereby [θ] is Theta signal and THD is Total horizontal derivative. The Thetha map is also used to delineate the model edges of the shallow substructures.

5.2.5 The horizontal tilt angle method

The Horizontal tilt angle (HTA) method is the inverse of the tilt angle method. The HTA method is designed independently of traditional filters to control the magnetic data with a wide range of magnetic amplitude. The Horizontal tilt angle method performs equally well with both shallow and deep sources and is used to outline the edges of sub-basins. The high magnetic intensities occur at the edges of causative magnetic sources in the Horizontal tilt angle method. The Horizontal tilt angle method is presented using the following equation:(10) HTA=tan−1[THD(Tz)]

Whereby HTA is the Horizontal tilt angle, THD is the Total horizontal derivative and Tz is the first derivative of the field in the z direction.

5.2.6 The Enhanced Tilt Filter

The ratio of the vertical derivative to the Total horizontal derivative of the signal is proposed as an Enhanced tilt filter. The Enhanced tilt filter was proposed by Ref. [66], and the filter is presented using the following equation:(11) ETF=tan−1[k(Tz)(Tx)2+(Ty)2]

Whereby Tx , Ty , and Tz is the magnetic field along x,y and z orthogonal axes respectively. ETF is the Enhanced tilt filter. The parameter k is a dimensional correction factor sampled along dx and dy and does not affect the response of the Enhanced tilt filter.

5.2.7 The enhanced total horizontal derivative of the tilt angle

(12) ETHD=(∂ETFdx)2+(∂ETFdy)2

The ETF is the Enhanced tilt filter and ETHD is the Enhanced total derivative of the tilt angle.

The Enhanced total horizontal derivative of the tilt angle produces a sharp gradient on the edge of magnetic bodies and delineates the edges for structural interpretation of both shallow and deep bodies, providing clear resolutions. The method depends on geomagnetic inclination and declination. Generally, the higher intensities occur over the edges with gradually dropping amplitude and require that data is reduced to the pole.

5.3 Identification of magnetic structural lineaments

The objective of the magnetic survey is to understand the sub-surface geological setting using anomalies caused by magnetic susceptibility contrast. Magnetic lineament mapping is a crucial part of a magnetic investigation to understand the edges of geological bodies and the direction of structural trends to enhance the geological understanding [67,68]. The magnetic lineaments are straight to curvilinear structures distributed across geological bodies. The magnetic lineament indicates structural discontinuity, such as fold, shear zones, and lithological boundaries. Also, the density, orientation, and length of lineaments may reflect rock mass fracture patterns and foliation [67,69]. The extraction of lineament involves the interpretation of anomalies along the elongated zones of high magnetic gradients and linear magnetic lows caused by structural dynamics. For example, the linear magnetic lows on the map indicate fracture and shear zones, while folded basement ridges and choked fractures are delineated as linear magnetic highs [70].

The offset of identical magnetic anomalies indicates the transform movement of blocks, while high gradient magnetic anomalies indicate the dip-slip displacement of basement blocks. The positive nonlinear magnetic anomalies indicate isolated igneous intrusions within a sedimentary basin or mafic intrusion within a felsic country rock, while negative nonlinear magnetic anomalies occur in the demagnetized region. In the current study, the magnetic lineaments are traced out through the correlation of the zero contour Tilt angle map (Fig. 7c) and the Total horizontal derivative of the magnetic field map (Fig. 7a). The zero contour map of the Tilt angle is created through Geosoft Oasis Montaj software, and the Total horizontal derivative of the magnetic field is added into the section and exported. The lineaments are hand-picked by observing the trends and maximum amplitudes of the anomalies.

6 Results

6.1 The results from gravity data

6.1.1 The results from gravity separation

The regional gravity anomaly map (Fig. 4a) has a high gravity contrast and reflects the trend and geometry of deeply buried geological structures. The general trend on the regional gravity anomaly map has a low gravity signal in the continental interior with sporadic patches on zones of crustal variation (up to −222 mGal), and the gravity anomaly signal is high on the Ocean's basement (up to 155 mGal). The gravity anomaly signal is zero mGal at the continent-ocean boundary, demarcating the oceanic and continental crust. The gravity anomaly in the Cape Fold Belt and Namaqua Natal Orogenic Belt is uniform, with values ranging between −4 and −174 mGal. In the central Kaapvaal Craton, the gravity anomaly signal is ∼ −222 mGal and reaches ∼ −174 mGal at the eastern boundary. The gravity anomaly in the center of the Zimbabwe Craton is ∼ −206 mGal. In the western part of the continental interior, the gravity anomaly signal has two lobes of North-South elongated regional anomalies reaching up to ∼ −220 mGal.

The residual gravity anomaly map (Fig. 4b) shows the different textures influenced by shallow gravitational structures and contributes to understanding the sub-surface geology. In the Ocean basement, the residual gravity anomaly is dominantly positive with a gravity amplitude of over 14 mGal, while the continental interior has dominantly negative gravity anomalies (reaching −25 mGal) with a complex trend. The eastern boundaries of both Kaapvaal and the Zimbabwe Cratons on the residual gravity anomaly map are marked by a narrow North-South elongated strip of the strong amplitude of the gravitational signal (∼15 mGals). The western boundary on the interior has a long linear (moderate-high) gravitational anomaly structure aligning parallel to the continent-ocean boundary. The Cape Fold Belt has the dominantly negative gravity anomaly signal (−25 mGal) with a deep east-west trending gravitational depression at the boundaries of the Namaqua-Natal metamorphic Belt. Inside the Kaapvaal Craton, the gravity anomaly is dominantly negative, with irregular patches of high anomalies and strong gravity contrast at the eastern boundary. The Kheis Belt, the Magondi Belt, and the western Limpopo Belt are moderately negative in gravity anomalies.

6.1.2 The directional derivative filter maps

The directional derivatives of the gravity field along the x, y, and z directions (Fig. 5a, b, &c, respectively) eliminate the long wavelengths and preserve intermediate and short wavelengths that are essential to study the local sub-surface structures. The directional derivatives (Fig. 5a, b, &c) have high gravity contrast, with maximum values occurring at the continent-ocean boundaries. The gravity contrast in (Fig. 5a, b, &c) ranges between 6 and 1277 mGals, with high gravity signal clustered in the center of the Zimbabwe Craton and the western part of the Kaapvaal Craton. Furthermore, the strong amplitude gravity anomaly signal (∼1077 mGal) concentrates at the eastern boundary of the Zimbabwe Craton. Fig. 5b and c shows the gravity anomaly signal in the Cape Fold Belt concentrated in the western edge of the Belt and the linear gravity high (1077 mGal) structure in the east. The Cape Fold Belt in Fig. 5a has a strong amplitude of gravity anomaly signal distributed at the east and western edges of the Belt.Fig. 5 (a) The x-directional derivative map, (b) The y-directional derivative map, (c) The z-directional derivative map, (d) The Modulus of gravity gradient tensor map, (e) Total horizontal derivative map, and (f) Tilt Angle map.

Fig. 5

Fig. 6 The structural map of southern Africa based on gravity data interpretations. The CFB = Cape Fold Belt, NNB = Namaqua Natal Orogenic Belt, LB = Limpopo Belt, KC = Kaapvaal Craton, ZC = Zimbabwe Craton, OB= Okwa Belt, MB = Magondi Belt, and KB= Kheis Belt.

Fig. 6

Fig. 7 The magnetic anomaly maps derived from various filters (a) Total horizontal derivative, (b) Analytical signal anomaly, (c) Tilt angle map, (d) Total horizontal derivative of tilt angle, (e) Theta map, (f) Horizontal tilt angle map, (g) Enhanced tilt filter map, and (h) Enhanced total horizontal derivative of the tilt angle.

Fig. 7

The Modulus of the gravity gradient tensor map (Fig. 5d) has high gravity contrast with the gravity anomaly values varying from 37 to 3589 E. The maximum gravity values in Fig. 5d occur at the continent-ocean boundaries, the boundary of the Zimbabwe Craton, and concentrate on the western part of the Kaapvaal Craton. The Total horizontal derivative of the gravity tensors (Fig. 5e) accentuates the linear gravitational trends and demarcates the boundaries of the gravity-causative structures and fault systems. In the area, the Total horizontal derivative technique provides a clear resolution, with most features having strong amplitudes (80 E) localized along the surface of discontinuities. The Tilt angle map (Fig. 5f) emphasizes areas of weak gravitational features by equalizing the amplitude of anomalies. In the Tilt angle map, the continuous elongated zones of the Tilt angle reflect structural discontinuity in the bedrock.

6.2 The results from magnetic data

The Total horizontal derivative of the magnetic tensors map (Fig. 7a) has a magnetic contrast ranging from 17 to 155 nT/km with the distribution of linear magnetic high signal (155 nT/km) concentrated at the East and the western boundary of the Kaapvaal Craton. The magnetic high signal (155 nT/km) occurs at the boundaries of the Zimbabwe Craton, the boundary of the Kheis Belt - Kaapvaal Craton, and the interior of the Limpopo Belt. The analytical signal technique is based on the filter method that is independent of the magnetization direction. The magnetic contrast in Fig. 7b ranges between 58 and 356 nT/km, with high magnetic signals clustered in the center of the Zimbabwe Craton and the western part of the Kaapvaal Craton. The Tilt angle map (Fig. 7c) is constructed based on a method that avoids the structural index of the field source body. The Theta angle map (Fig. 7e) is based on a normalization of the horizontal gradient and delineates the shapes and magnetic contacts of 2-D bodies. The Horizontal tilt angle map (Fig. 7f) is constructed based on the method that normalizes the amplitude of the horizontal derivative. The Enhanced tilt filter map (Fig. 7g) is constructed based on the filter method that avoids the analytic singularity existing in the solution of the derivatives by controlling the dimensional correction factor.

7 Discussion

7.1 Discussion on gravity data

The strong amplitude of the regional gravity anomaly (Fig. 4a) signal in the Ocean's basement indicates the presence of high-density material influenced by the basaltic Ocean crust [71,72]. In contrast to the high-density Oceanic crust, the continental crust is composed of average low-density material of different lithology, which is reflected by low gravity signal. The regional gravity anomaly signal over the central Kaapvaal Craton is high compared to the gravity anomaly signal over the Zimbabwe Craton. The two patches of low gravity anomaly signal observed in the western part of the continental interior correspond to the position of Angola-Congo Craton and the Damaran Mobile Belt (see tectonic boundaries by Refs. [73,74]). The Congo Craton and the Damaran Mobile Belt are not part of the study, and the interpretation is only used as a reference. The regional field mapped the geometry of the regional structures, but the details on regional fields still hinder the complete analysis of geological Belts in the study region.

The residual gravity anomalies in (Fig. 4b) vary from −250 to over 14 mGal, indicating a clear gravity signal contrast in the region, which could be regarded as a sufficiently clear indicator to distinguish the effects of causative sub-surface geological sources. The sporadic distribution and irregular gravitational signal patches in the continental interior are attributed to rapid variation in local sub-surface geology in the study area. The residual gravity anomaly demarcated and marked with strong gravity amplitude the eastern boundaries of the Kaapvaal and the Zimbabwe Cratons. The study objective is to investigate the gravity anomalies related to Cratons and geological Belts, and Fig. 4b shows that the position where the major geological Belts are situated does not reveal useful information. These observations might suggest the limit of the field separation method or strictly indicate that the geological Belts in the region are caused by the even more shallow structures. The Cape Fold Belt, Namaqua Natal Orogenic Belt, and Limpopo Belt in the study area demand the application of enhanced filters.

In the study, little effort was directed to interpretations of individual gravity tensor components. However, during the research, it is observable that the second derivative of the gravitational tensor Tzz (see appendix) revealed more information compared to other tensor derivatives. For current work, different gravity tensor components are combined to form a single filter for better data visualization and clear sub-surface structures. The Directional derivatives of the gravity field (Fig. 5 a–c) and the Modulus of the gravity gradient tensor (Fig. 5d) contain information about the variation in lateral density distribution for three directions and assist in locating the boundaries of geological structures. In Fig. 5(a–d), the gravity anomaly signal also delineates the eastern boundary and the end limit of the Kaapvaal and the Zimbabwe Cratons. In the Kaapvaal Craton, the gravitational high anomaly signal clusters over the east section.

However, the western boundaries of both Cratons are different, characterized by poor gravity contrast. The Modulus of gravity anomaly tensor yields results similar to the three Directional derivatives of the field but with high resolution. The Total horizontal derivative map (Fig. 5e) gives an immediate and easy-to-read image of the boundaries of the gravity sources with an ensemble of maxima delineating the boundary of the causative structures by producing linear structures of narrow and elongated signal bandwidths. In the west of the Cape Fold Belt, the parallel lines of gravity-high signals may indicate structural discontinuity (possible fault due to further continental break). It is possible to use individual filter methods (Fig. 5a–e) as separate datasets to quantify structural features. However, the danger of this approach is the likelihood of not being able to visualize the whole picture, leading to misinterpretation of a signature pattern not common to all datasets. Despite the differences in petrophysical properties of rocks constituting different geological belts, the gravity data does not provide details about the orientation of the Belts. Instead, the Namaqua-Natal metamorphic, Limpopo, and Cape Fold Belts have consistently local low amplitude gravity anomaly signals.

7.2 The discussion on magnetic anomaly maps

The magnetic section uses different edge detection techniques to complete data visualization. The Total horizontal derivative of the magnetic tensors technique (Fig. 7a) defines the boundary of magnetic causative source in an informative way than any single term by accentuating linear magnetic trends, faults, and Cratons’ boundaries. In Fig. 7a, areas corresponding to surface discontinuities have maximum amplitude, with high magnetic gradients occurring along the zones of intrusive structures. The Analytic signal map (Fig. 7b) shows an arrangement of magnetized bodies with a different resolution. Despite differences in magnetic intensities between the Analytical signal and the Total horizontal derivative maps, both maps identify the alignment of maxima that encircle the east and western boundaries of the Kaapvaal and the edges of the Zimbabwe Cratons. In Fig. 7(a & b), the central part of the Zimbabwe Craton has extremely weak amplitudes of magnetic signals. In Fig. 7c, the zero contour line provides a quick estimation of the boundary of geological sources. The Tilt angle technique restored the information at the southwest of the Zimbabwe Craton, which was not properly visible on the Analytic signal and the Total horizontal derivative maps. Fig. 7 (a, b & c) shows the N–S trending magnetic structure at the boundary of the Kaapvaal Craton and Kheis Belt. The general interpretation of the pattern observed in magnetic anomalies would be due mainly to intrusions of magmatic bodies along the fractured boundaries or the trend of geological rocks.

Despite the strength of the Analytical signal (Fig. 7b) in mapping the ∼180 Ma Zimbabwe intrusion (the southwest of the Zimbabwe Craton), the Total horizontal derivative of the magnetic tensors technique (Fig. 7a) provides a clear resolution of the linear structures making it a suitable tool to study faults and lineaments. In a study of the structural anatomy of the Limpopo Belt by Refs. [19,33], concludes that the Limpopo Belt consists of three separated lobes, and the observed magnetic anomaly pattern of linear structures with the northeast-southwest trend in the Total horizontal derivative map conforms to the geometry of the Belt. There is an existing relationship between features observed in the Total horizontal derivative of the Tilt angle map (Fig. 7d) and the Tilt angle map (Fig. 7c). Inside the zero contour of the Tilt angle map, the magnetic signal map reaches the maximum peak with linear elongated magnetic structures. However, the Total horizontal derivative of the Tilt angle map cannot be used independently to study lineaments since the technique eliminates the information about geological contact, and the map is generally noisy and complicated to interpret. The Theta map (Fig. 7e) emphasizes and accurately outlines the shape and geometry of the major uplifted structures in the region. The Cape Fold Belt exhibits a strong amplitude of magnetic anomaly over the Belt with main magnetic trends elongated in the East-West direction.

The Horizontal tilt angle map (Fig. 7f) shows a high-intensity magnetic anomaly demarcating the boundary of the Zimbabwe Craton. The general orientation of the magnetic structures inside the Zimbabwe Craton is orientated in a NNE direction. The general arrangement of the magnetic structures inside the Zimbabwe Craton has the NNE orientation. In the Limpopo Belt, magnetic structures are elongated and oriented parallel to the southern boundary of the Zimbabwe Craton. The orientation of magnetic structures inside the Kaapvaal Craton is arranged roughly east-west along the eastern section and NNE parallel to the Kheis Belt in the west section. The Namaqua-Natal Metamorphic Belt is demarcated and presented with high magnetic anomaly structures. The results on the Enhanced Tilt filter map (Fig. 7g) are similar to the Tilt angle map with a strong emphasis on what constitutes a maxima on the Tilt angle map. The correlation between the two maps plays a crucial role in the depth estimation of the field source body and lateral extent of the magnetic bodies. The Enhanced total horizontal derivative of the tilt angle (Fig. 7h) emphasizes the fabric of shallow magnetic structures with detailed resolutions and delineates the edges of shallow magnetic bodies for structural interpretation.

The results on Theta map (Fig. 7e) are comparable with the observations on the Enhanced tilt filter map (Fig. 7h). For both maps (Fig. 7e and h), the magnetic structures at the boundary of the Namaqua-Natal metamorphic Belt and Cape Fold Belt are better delineated. There is a direct correlation between the magnetic anomalies observed on the Horizontal tilt angle map (Fig. 7f) and the Enhanced tilt filter map (Fig. 7g). In Fig. 7 (e, f & g), the shape and geometry of the Cape Fold Belt are delineated. The magnetic anomaly in the Limpopo Belt is influenced by uplifted structures and exhumed high-grade metamorphic rocks [33,41]. The East and West parts of the Namaqua-Natal Belt are distinct on magnetic signature. The high magnetic signal in the structure adjacent to the southwest part of the Kaapvaal Craton corresponds with low-pressure granulite facies in the metamorphic zone [48,49]. The differences in the magnetic anomaly signature observed between the Zimbabwe and Kaapvaal Cratons are influenced by lithological differences. In the Zimbabwe Craton, the irregular patches in a magnetic signature are influenced by the East-West trending Greenstone Belt [37]. In the Kaapvaal Craton, the magnetic signature is mainly influenced by granitoid gneisses, the rocks of Ventersdorp Super Group, and Dominion Groups [43].

7.3 Lineaments and structural maps

Fig. 6, Fig. 8 represents the lineaments derived from the gravity and magnetic data respectively. The general pattern of the lineaments in the region are random, but follow a particular trend around certain geological structures and causative features. In the Cape Fold Belt and Limpopo Belt, lineaments are parallel to the direction of the geological Belt (see Fig. 6, Fig. 8). In Fig. 6, the east and the west edges of the Cape Fold Belt has long lineaments interpreted as the continental fault. Inside the Kaapvaal Craton, magnetic lineaments are randomly oriented. The distribution of gravitational lineaments inside the Kaapvaal Craton are randomly oriented with curved lineaments located closer to the position of the Bushveld complex. In the Zimbabwe Craton, the gravitational lineaments are concentrated in the center, trending NNE and NNW (see Fig. 6). The study identified three zones of highly dense regional gravity and magnetic lineaments, namely the S1, S2, and S3. The S1 magnetic lineaments are concentrated along the Limpopo Belt, and aligned parallel to the direction of the Belt.Fig. 8 The magnetic lineament map of southern Africa. The CFB = Cape Fold Belt, NNB = Namaqua Natal Orogenic Belt, LB = Limpopo Belt, KC = Kaapvaal Craton, ZC = Zimbabwe Craton, OB= Okwa Belt, MB = Magondi Belt, and KB= Kheis Belt.

Fig. 8

The S2 are short scale magnetic lineaments concentrated at the boundary of the Kaapvaal Craton and Kheis Belt. The S3 magnetic and gravity lineament are the short-length multi-directional lineaments concetrated along the boundary of Cratons, parallel to the edges of both the Zimbabwe and Kaapvaal Cratons. The S1, and S3 lineaments occur around a ∼180 million years Karoo Cape Fold Belt lava and intrusion (see Fig. 1 by Ref. [21]). Looking at the two maps, the magnetic lineaments inside the Zimbabwe Craton are generally sparse (Fig. 8), as opposed to the gravitation lineaments observed in Fig. 6. The gravity lineaments in the Limpopo Belt are poorly distributed, and generally weak in the Natal metamorphic Belt on Fig. 6 compared to Fig. 8 magnetic lineaments. The circular lineament in the South edge of the Kaapvaal Craton may result from the cooling of a localized intrusion. Inside the Limpopo Belt, the lineaments may be the result of craton-craton collision. The long-scale lineament around the cratons may be associated with the deformation during Craton rotation in polymetamorphic deformation. The gravitational and magnetic lineament map results settle and specify the regional layout of brittle zones recognized by previous geological studies, but also identify the new lineament pattern.

8 Conclusions

The gravity and magnetic data of the southern African region is processed, analyzed, and interpreted to extract the tectonic boundaries and subsurface structures, demarcating the edges of Cratons, and determine the trend of regional gravity and magnetic lineaments. This paper adopts different filter methods without a scale value to enhance the subsurface geologic structures and delineate the boundaries of major tectonic features. Various authors (e.g. Refs. [20,25,26] constructed subsurface structure maps utilizing potential data and seismic interpretation. The shear zone's lineaments and the correlation of density lineament with boreholes are understood by Refs. [27,28], respectively. However, the current study is different since it is conducted at the regional scale and focuses on delineating regional shallow causative basement structures, lineaments, and in-depth interpretation of causative structures. The filters in the gravity section enhanced shallow features and provided a clear-resolution visual image of the subsurface features and geology. Despite the success of filters used in the gravity data section, the filters did not extract details about the orientation and geometry of geological Belts in the region.

The magnetic filters reflect different attributes of features, structural discontinuities, contacts of causative bodies, and the geometry of Belts. The individual filter on gravity and magnetic sections provide exclusive details of the causative source, which helps to visualize the full image of structural features and eventually decreases the uncertainty in the interpretation. The analyses provide insight into the demarcation of structural boundaries and the general pattern of regional trends in the region. The study emphasizes the role of joint filter methods in the potential field data processing to understand the subsurface structural features, especially when dealing with complex geological settings. In the early stage of geophysical exploration, using both data sets instead of only one data set can reveal important geological features, promoting increased confidence in geological mapping exercises.

CRediT authorship contribution statement

Zenzele Osborne kubeka: Writing – original draft, Supervision, Software, Resources, Project administration, Methodology, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix Figure Tzz is the second order of vertical derivative of gravity anomaly gradient. The gradient tensor component Tzz (second order of vertical gravity anomaly gradient) reveals more information related to subsurface geology.

Figure

Acknowledgements

The author declares no conflict of interest.
==== Refs
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