High precision structural mapping using advanced gravity processing methods: a case study from the North region of Cameroon

doi:10.21203/rs.3.rs-2719904/v1

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Research Article

High precision structural mapping using advanced gravity processing methods: a case study from the North region of Cameroon

https://doi.org/10.21203/rs.3.rs-2719904/v1

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published 08 Nov, 2023

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The main purpose of this work is to perform a high-precision mapping of geological features (lineaments and faults) likely to develop underground aquifers in the crystalline and metamorphic rocks of northern Cameroon. The main techniques used for gravity data processing included the tilt angle of horizontal gradient (TAHG), the improved logistic filter (ILF), the fast sigmoid edge detector filter (FSF), and an edge detection filter based on the arcsine function (ASF). Before applying these edge detection filters to major geological units of North Cameroon, their effectiveness and performance have been assessed through synthetic gravity data with and without gravity perturbation. In addition, the Euler deconvolution formula has been used to estimate the position and the apparent depth of anomalous gravity sources in the study region. It appears that the main structural features are trending along the N-S, NNE-SSW and NE-SW directions. The deepest density anomalies in the region are identified in the NW-SE direction, which coincides well with the extension of the West and Central African rift system in the study area. The advanced edge detection techniques and the Euler deconvolution method have both identified a network of superficial lineaments around longitude 13^oN and latitude 8^oN, and located between 0 and 4 km depth. The NW-SE trending crustal features outlined in the northeast of the region, indicate that the area would have been the target of a uniform tectonic activity. This work is a contribution to a better knowledge of the configuration of fractures network, and to a better exploitation of groundwater resources available in the region.

Geological fractures

Gravity processing

Edge detection filter

Groundwater resources

North Cameroon

The study area covers one of the ten regions of Cameroon located in the north of the country. It extends from 7° to 10° North latitude and from 12° and 15°30’ East longitude (Fig. 1). This region is located between the Mandara Mountains of the Far North region, the Adamawa plateau, Chad and Central African Republic to the East and Nigeria to the West. The North Cameroon region is an area of interest for researchers given the large number of geophysical and geodynamic studies already carried out in this part of Cameroon (Kamguia et al. 2005; Tokam et al. 2010; Mouzong et al. 2014; Ghomsi et al. 2022). In addition, the vulnerability of this region leads researchers to improve their investigations for a better exploitation of natural resources. A precise and detailed mapping of the geological structures (lineaments and faults) of this region would be a great contribution for mining or water resources research. Also, the realization of major projects in the region require a detailed knowledge of the main and deep faults affecting the area.

Gravity data are widely used for earth sciences research. The majority of these studies are carried out with either ground-based (terrestrial) gravity data (Borghi 2022; Ardestani and Mousavi 2023), or satellite gravity data (Chouhan et al. 2019; Sahoo and Pal 2021; Kumar et al. 2022). Terrestrial gravity data, unlike satellite gravity models, have a great advantage in terms of accuracy on short wavelength information. However, their lateral distribution can be irregular and sparse, especially in risky and inaccessible areas. Besides, satellite gravity models generally show a good coverage of the global gravity variations but have some limitations to accurately represent shallow and localized information. This limitation is called the omission error (Gruber 2009; Torge 2001). A suitable combination of ground-based and satellite gravity data would be very useful to improve the consistency and accuracy of the database.

In geophysics, the delineation of gravity sources boundaries is the most used technique to determine the position of geological structures such as faults and fractures. Since years, edge detection filters have been increasingly developed and improved to display better precision in the delineation of the boundaries of geological sources (Kumar et al. 2018; Eldosouky et al. 2022). Edge detection filters are generally developed using horizontal or vertical gradients of gravity anomalies (Cordell and Grauch 1985; Roest et al. 1992; Marson and Klingele 1993; Fedi and Florio 2001; Zhang et al. 2005; Cella et al. 2009; Oksum et al. 2019; Chouhan et al. 2020). However, edge detection techniques only based on gradient amplitude have shown some limitations in outlining both shallow and deep anomalous discontinuities. Then, several researchers proposed phase-based filters to determine lateral boundaries of gravity sources (Miller and Singh 1994; Wijns et al. 2005; Alamdar et al. 2012; Fereira et al. 2013; Li et al. 2013). Despite the advantage of phase-based filters in balancing signals from deep and shallow anomalous sources, these filters tend to draw false edges. Ferreira et al. (2013) proposed a phase-based filter entitled the tilt angle of horizontal gradient. This filter would have the advantage of highlighting the edges of geological features and balancing the signals of both deep and superficial sources. Pham et al. (2020) conducted a study to evaluate the performance of commonly used filters in highlighting the geological boundaries of gravity and magnetic anomalous bodies. They introduced the improved logistic filter which appeared to have a good performance in detecting the contours of geological structures. In order to improve the limitations of some edge detection methods, Pham et al. (2022) proposed a new filter using the arcsine function and the derivatives of the horizontal gradient amplitude. Also, Oksum (2021) recently developed an approach using the fast sigmoid function to estimate the boundary of positive and negative sources with the same accuracy.

In this work, we combine ground-based gravity data available in the North-Cameroon region with a high-resolution global gravity model for high-precision mapping of major structures. The main techniques used for gravity data processing are the following: the tilt angle of horizontal gradient (TAHG), the improved logistic filter (ILF), the fast sigmoid edge detector filter (FSF), and an edge detection filter based on the arcsine function (ASF). Before applying these edge detection filters to major geological units of North Cameroon, their effectiveness and performance are first assessed through synthetic gravity data with and without noise. In addition, the Euler deconvolution theory is used to estimate the position and the apparent depth of anomalous gravity sources in the study region.

The geology of the North Cameroon region is essentially marked by sedimentary and metamorphic formation (Fig. 2). In the south, there are syn- to post-tectonic granitoids intrusions and covered by tertiary volcanic deposits. This north region of Cameroon is also characterized by the presence of faults evolving from the Adamawa plateau and trending towards a NE direction in the region. These faults extend up to the south of the Benue Trough, thus separating the region into two main geological domains: the southern part made up of metamorphic rocks such as gneiss and schists, and the northern part made up mainly of sedimentary rocks. The Tcholliré-Banyo shear zone (TBF) is a major tectonic structure passing through the region. It separates Meso to Neoproterozoic units in the west of the region from Paleoproterozoic formations located in the eastern part (Toteu et al. 2001, 2004; Houketchang et al. 2009).

One of the major geological structures in the study region is the Benue Trough. It is a huge sedimentary basin coming from Nigeria and which a part sinks into northern Cameroon in a NE-SW direction (this is the Yola-Garoua rift). The Benue Trough is part of the Central and West African rift system (WCARS), formed at the beginning of the Cretaceous (Adighije 1979). According to Wright et al. (1985), there are intrusions of volcanic and plutonic rocks in this trough. Two main groups of lithological formations are covering the region: a group made up of amphibolites and gneiss; and another also made up of amphibolites, metagabbros, orthogneisses, and granites (Nzenti 1998). According to Kamguia et al. (2005), the sediments of the Benue basin would have an average thickness of 4 km and the underlying continental crust would be thinner than neighboring areas (about 24 km). Structurally, the Garoua area in northern Cameroon would have been the target of tectonic movements during the occurence of the Benue Trough at the Cretaceous period. Major NW-SE trending structural features have been identified in the area by Mouzong et al. (2014).

3.1 Ground based gravity data

Ground-based gravity data are exploited in this study to provide a good precision in the delineation of crustal structures. This gravity database is provided by the Bureau Gravimétrique International (BGI). These data have been collected during the gravimetric campaigns carried out by Institut de Recherche pour le Développement (IRD, France) previously called Office de la Recherche Scientifique et Technique d’Outre-Mer (ORSTOM). Further technical details on the survey and the database are provided by Collignon (1968). The ground gravity data have been measured using Lacoste and Romberg gravimeters (version G, n° 471 and 823). The average accuracy of the ground gravity data is about 0.05 mGal (Djomani et al. 1995). The uncertainty on geographic coordinates of these gravity data is estimated to 100 m. Figure 3 presents the lateral distribution of 2223 gravity stations available in the study area. A good densification of the data can be observed in the northern part. The distribution of data in the southern part is limited by the presence of voids. This scarcity is due to the difficulty of access in wild fauna and flora during data collection. Free-air gravity disturbances have been obtained after correction of effects caused by the instrumental drift and lunar-solar tides.

3.2 Satellite gravity data

In order to fill gaps contained in the terrestrial gravity data, we used a high-resolution satellite gravity model. The satellite gravity data processed in this paper are extracted from the global gravity field model XGM2019e. It is a combined model with spherical harmonic coefficients developed up to degree and order (d/o) 5399 (this corresponds approximately to a resolution of 2' or 4 km). This gravity model has been designed by combining data from the GOCO06s satellite model, terrestrial gravity data, and a gravity model computed using Earth2014 global topography data (Hirt and Rexer 2015). Above sea, gravity data from the DTU13 satellite altimetry-derived gravity model (with a grid spacing of 1') are also used in the modeling of XGM2019e data. By carrying out a comparison with some classical models widely used in geophysics (EGM2008, EIGEN6c4 and XGM2016), Xingerle et al. (2020) showed the good performance of the XGM2019e model at high frequencies (above d/o 719), despite the use of topographic modeling to fill very high frequencies of the gravity field. Since, gravity data from the high-resolution model XGM2019e have been used by geophysicist researchers both for structural studies of the crust (Novais and Sampaio, 2020; Sampietro and Capponi 2021) and to model Moho undulations and its density contrast (Abrehdary and Sjöberg 2021a, b; Tchoukeu et al. 2021). The free-air gravity data of the XGM2019e model is freely available on the ICGEM website. These data have been downloaded with a spatial resolution of 0.03 degree and at a distance of 50 km above the ellipsoid to avoid deteriorating the original precision and resolution of the model.

3.3 Method

3.3.1 Least-squares collocation

To take advantage of each gravimetric database (ground-based and satellite) in order to improve delineation of crustal features, we used the least-square collocation (LSC) technique (Moritz 1978). This statistical estimation technique is based on the joint use of least-square adjustment with least-square prediction in a linear regression model. Some studies have recently and successfully applied this technique to combine heterogeneous data of different kinds (Zaki et al. 2018; Kamto et al. 2021). In the case of this work, the procedure employed by this technique starts with the calculation of the residual values between the ground-based gravity data and the satellite gravity model. Then, these residual values, which actually represent the omission error, are suitably interpolated at the satellite model resolution. Finally, a residual grid is obtained and combined with the satellite model to correct its limitations at short wavelengths. The GEOGRID program of the GRAVSOFT software (developed by Forsberg and Tscherning 2008) is used to implement this technique. The second-order Markov covariance is the model used for LSC:

$$c\left(s\right)={c}_{0}(1+\alpha s){e}^{-\alpha s}$$

Where ${c}_{0}$ is an initial parameter calculated from the database; $\alpha$ is obtained from a correlation length parameter; and $s$symbolizes the step between two points. The correlation length and white noise parameters have been introduced in the model with optimal values of 25 km and 1 mGal respectively. These optimal parameters values are chosen following a preliminary test on a value scale of 10–50 km and 1–5 mGal.

3.3.2 Advanced edge detection methods

To delineate structural features within the crust, several edge detection techniques exist in the literature. In this work, we used some advanced methods of gravity data processing. In order to produce a technique to highlight simultaneously boundaries of deep and shallow bodies, Fereira et al. (2013) proposed the tilt angle of horizontal gradient filter. This filter is defined as:

$$TAHG=\text{a}\text{t}\text{a}\text{n}\left(\frac{{HG}_{z}}{\sqrt{{{HG}_{x}}^{2}+{{HG}_{y}}^{2}}}\right)$$

Where $HG$ represents the horizontal gradient of the gravity disturbance $F$,

$$HG=\sqrt{{{F}_{x}}^{2}+{{F}_{y}}^{2}}$$

${F}_{x}$ and ${F}_{y}$ symbolizes the gradients of the gravity disturbance $F$ in the $x$ and $y$ axis respectively; ${G}_{x}$, ${G}_{y}$ and ${G}_{z}$ represents derivatives of the horizontal gradient amplitude $HG$ in the $x$, $y$ and $z$ axis respectively.

Still with the aim of refining the enhancement of the crustal lineaments and boundaries of gravimetric sources, Pham et al. (2020) recently suggested the improved logistic filter defined by the following formula:

$$ILF=\frac{1}{1+\text{e}\text{x}\text{p}[-c\left(R-1\right)+1]}$$

With $R$ obtained by dividing the z-axis derivative of $HG$ by the total horizontal gradient of$HG$,

$$R=\frac{{HG}_{z}}{\sqrt{{{HG}_{x}}^{2}+{{HG}_{y}}^{2}}}$$

$c$ is a constant and positive parameter selected by the used. Pham et al. (2020) studied the best resolution of edge detection results applying different $c$ values in the ILF formula. Values of $c$ranging from 2 to 5 yields to best results. So, we choose $c=2$ for this study.

Pham et al. (2022) proposed a new high-resolution filter to highlight the edges of geological anomalous sources. This is an edge detection filter using the arcsine function and given by:

$$ASF=\mathcal{R}\left(\text{asin}\left(p\left(\frac{{HG}_{z}}{\sqrt{{{HG}_{x}}^{2}+{{HG}_{y}}^{2}+{{HG}_{z}}^{2}}}-1\right)+1\right)\right)$$

Where $p$ is a positive and constant parameter use to improve the quality of edge detection. For this filter, Pham et al. (2022) also studied the values of $p$ in the ASF formula. They found that optimal values were obtained at $p\ge 2$.

We also exploited the fast sigmoid edge detection filter proposed by Oksum et al. (2021) to improve the resolution and accuracy in the estimation of geological structures compared to classical and commonly used edge detection techniques. This filter is defined by:

$$FSED=\frac{R-1}{1+\left|R\right|}$$

3.3.3 Euler deconvolution method

The Euler deconvolution theory is a method broadly utilized in structural geophysics to assess the location of gravity or magnetic anomalous structures (Thompson 1982; Reid et al. 1990). This method is also used in structural geology to delimit transition zones in crustal formations or to estimate lithological discontinuities. Up to now, the Euler deconvolution method shows its effectiveness and is currently applied in structural studies (Singh and Singh 2017; Baxter 2022; Chen et al. 2022). This implementation of this method is perform by linking components of the potential field and location of anomalous structures by integrating a parameter of homogeneity called structural index. The Euler deconvolution formula can be defined as follows (Thompson 1982):

$$\left(x-{x}_{0}\right)\frac{\partial F}{\partial x}+\left(x-{x}_{0}\right)\frac{\partial F}{\partial x}+\left(x-{x}_{0}\right)\frac{\partial F}{\partial x}=-N(B-F)$$

Where $({x}_{0}, {y}_{0}, {z}_{0})$ represent the position of the potential field anomalous source, $F$ is the gravity anomaly at $(x, y, z)$, $SI$ represents the structural index which represents the geometric configuration of anomalous sources, and $B$ is the regional gravity anomaly.

In this section, we evaluate the effectiveness of the edge detection techniques presented above. We choose a relatively complex gravimetric model composed of six prismatic sources (A, B, C, D, E and F) as shown in Fig. 4. The prismatic bodies contain alternately negative and positive density contrasts, superimposed and positioned at different levels. The geometric characteristics of these prismatic sources are presented in Table 1. The synthetic gravity model generated by the six density sources has been calculated on a grid of 201 x 201 points, with a spatial resolution of 0.5 km (Fig. 5a). Figures 6a-d depicts the results obtained following the application of the TAHG, ILF, ASF, and FSF techniques respectively, on the synthetic gravity model in Fig. 5a. The four filters highlight well the edges of prisms A, B, C and F. However, these filters struggle to identify accurately the boundaries of prisms D and E, probably because of the complexity of their geometric arrangement and successively positive density contrasts. However, the ILF, FSF and ASF techniques stand out for their ability to reduce spurious signatures around delineated edges. To further assess the performance of the above techniques, the synthetic gravity anomalies in Fig. 5a have been perturbed with additive parasitic noise of 3% of the synthetic anomaly grid. Figure 5b presents the noise-corrupted synthetic gravity anomalies. Also, Figs. 6e-h show the results obtained by applying the TAHG, ILF, ASF, and FSF, respectively, to the noisy synthetic gravity model in Fig. 5b. Despite an amplification of the parasitic noises by the four filters, an identification of the edges of the anomalous sources remains possible. The boundaries of the prismatic model C are clearly highlighted by the ILF, ASF, and FSF which minimize any surrounding noise as much as possible. The injection of a parasitic noise in the synthetic gravity model has a bad influence on the enhancement of the superimposed prismatic sources. To have a better reading of the boundaries of the prismatic sources in a noisy environment, an upward extension filter of 1 km was applied to the noisy synthetic gravity anomalies. Figure 5c presents the noise-corrupted synthetic gravity model upward continued to 1 km. Figures 6i-l show the results obtained by applying the TAHG, ILF, ASF, and FSF, respectively, to the noisy synthetic gravity model after applying an upward continuation filter of 1 km. Better results are obtained with a considerable reduction in surrounding noises. However, the edges of the prismatic body C are difficult to identify, probably because of the attenuation of high frequencies following the application of the upward continuation and the influence of the underlying positive density sources. Excepting the edges of density bodies D and E which tend to merge, the edges of density prismatic bodies A, B and C are enhanced. However, the best resolution goes to the ILF technique which minimizes the surrounding intrusive signatures as much as possible.

Table 1

Geometric and density settings of the six prismatic bodies
Settings/Prismatic bodies	A	B	C	D	E	F
x-coordinates of center (km)	25	25	75	50	50	50
y-coordinate of center (km)	75	75	75	25	25	25
Length (km)	10	30	10	50	40	30
Width (km)	30	10	10	30	20	10
Depth to the top (km)	4	6	5	7	4	2
Thickness (km)	2	2	3	3	3	2
Density contrast (g/cm³)	0.2	-0.2	0.3	0.2	0.1	-0.1

5.1 Combined Bouguer anomalies

The combination of ground-based gravity data with the global gravity field model XGM2019e was carried out using the least squares collocation technique. A more realistic gravity model is therefore obtained over the study area. The free-air anomaly grid has been corrected from the gravimetric effects of topography. A constant average density of $\rho = 2.67 g/{cm}^{3}$ was considered when computing Bouguer reductions. As our study area at a local scale, we neglect errors due to the earth’s curvature. Figure 7 displays the combined Bouguer anomalies, with a grid spacing of 0.033 degree (~ 4 km). The signatures vary from − 190 to 12 mGal, with a mean of -57.5 mGal. Overall, the North Cameroon region shows negative anomalies. The highest anomalies are depicted in the northern part of the study area. The evolution of Bouguer anomalies observed on the map (Fig. 7) have a great correlation with the Moho geometry estimated over Cameroon by Ghomsi et al. (2019). The Moho undulations in the study area undergo a strong gradient around latitude 8^oN, with a sudden lowering towards the Adamawa plateau. Bouguer anomalies are the representation of a superposition of deep and shallow density sources. Since our main objective is to study the structural features within the crust, regional gravity anomalies caused by deep structures (Moho undulations, variations in density contrast at the crust-mantle interface, density anomalies in the upper mantle...etc) must be appropriately subtracted from Bouguer anomalies. So, the application of a regional/residual separation is necessary.

5.2 Regional/residual separation

To apply a regional/residual separation on the Bouguer anomaly grid, we used the radial average power spectrum (Spector and Grant 1970). The power spectrum is a technique widely used in geophysics to estimate the average depths of major density contrasts in a well-defined area. The application of this technique consists in converting Bouguer anomalies into the frequency domain to bring out the range of wavelengths over the area. Figure 8 presents the graph of the power spectrum as a function of wavelengths. The power spectrum values can be separate into blocks of linear segments, so the slope represents the average depth of the underlying discontinuities or major density sources (Spector and Grant 1970). In this case, three average depths at density discontinuities have been estimated. The average depth of the first density discontinuity, corresponding to deep anomalous structures, is estimated at 18.4 km. The second discontinuity is attributed to intermediate density sources, with a mean depth of 7.4 km. The last linear segment is attributed to the average depth of shallow features within the uppermost crust. The Conrad discontinuity, which is a crustal boundary generally located between 15 and 20 km depth within the continental lithosphere, could correspond to the first density contrast. To ensure the removal of density sources beneath this crustal discontinuity, a low-pass filter was applied on Bouguer anomalies to amplify signatures caused by Moho undulations and other underlying density variations.

Figure 9a shows regional Bouguer anomalies in the North Cameroon region. A grid of negative anomalies is observed, with values ranging from − 112 to -20 mGal. The regional anomaly map presents a great gradient with values decreasing gradually from North to South. The correlation is directly made with the thinning of the lithospheric crust towards the North in the study area (Tokam 2010; Ghomsi 2019). According to Kamguia et al. (2005), this crustal thinning in the North would be linked to an uplift of the upper mantle following the lithospheric extension. Another correlation made with the topography of the study area (Fig. 1), confirms the isostatic compensation in the region. The high elevations of the South would be compensated at depth by a subsidence of the Moho (Tokam 2010). Figure 9b displays residual gravity anomalies with values ranging from − 83 to 53 mGal. Localized areas marked by positive and negative anomalies are well highlighted. A close correlation is made with some shallow geological units (Fig. 2). The two positive anomaly picks exposed in the north coincide with Tertiary volcanic rocks. Also, the Benue Trough shows negative signatures ranging from − 20 to 0 mGal in a NW-SE direction on the residual anomaly map. The positive anomalies observed on either side of the Benue Trough have recently been identified by Fotze et al. (2021). These positive anomalies have been attributed to intrusions of granitic and volcano-sedimentary rocks. Beyond the anomalous formations identified within the crust, advanced edge detection techniques can be applied on the residual Bouguer anomalies to bring out structural features of the North-Cameroon region.

5.3 Application of the advanced gravity processing filters

The results of the application of advanced edge detection techniques are presented in this subsection. The structural features outlined by these edge detection techniques could be fracture zones, lithological contacts or even boundaries of intrusive density sources. Figure 10a presents the results of the application of the TAHG technique on the residual Bouguer anomalies. As shown in Eq. (2), this technique is based on the ratio of the derivatives of the horizontal gradient of gravity data. As the enhanced edges in the synthetic example, the TAHG seems to be effective in balancing both deep and shallow structural lineaments in the North Cameroon region. Figure 10a displays a wide variety of geological features in the study area. The analysis of the features highlighted in the South-East shows approximately a N70°E direction which coincides with the orientation of fractures affecting the basement in the south of the region (Noutchogwe et al. 2006). The lineaments trending NE-SW in the South-West are probably related to the evolution of the Tcholliré-Banyo shear zone in the North Cameroon region. Along the extension of the Benue Trough in Cameroon, major NW–SE and NE–SW trending geological structures have been delineated. In addition, we also note the presence of several curved geological features. These features could correspond to boundaries of intrusive bodies or geological contacts/discontinuities. According to the synthetic results presented in section 4, the TAHG filter could demonstrate some limitations in terms of resolution. Also, Eldosouky (2020), Pham et al. (2022) and Prasad et al. (2022) revealed that this technique might draw geological edges larger than reality.

Figure 10b shows results of edge detection obtained following the application of the ILF technique to the residual Bouguer anomalies. According to Pham et al. (2020), this technique based on an association of the logistic function to the horizontal gradient of gravity data, shows a good performance with its high-resolution results. The performance of this filter is further validated through its application to synthetic data (section 4). Unlike the TAHG map (Fig. 10a), the ILF map (Fig. 10b) appears to enhance the geological lineaments of the study area with better resolution. The signatures of the geological features are well highlighted, reducing any surrounding signal. The ILF would therefore be effective in avoiding the appearance of spurious geological discontinuities in the output results. The lineaments trending in the same direction as the Adamaoua and Tchollité-Banyo faults are well defined. The features identified in the Garoua area (center of the northern part) by Fofie (2019) coincide well with the lineaments outlined on the ILF map. Despite its ability to produce high-resolution results, the ILF remains sensitive to the delineation of close and similar geological features, as we stated in the synthetic example.

The geological structures (lineaments and faults) detected by the ASF method in the study area are displayed in Fig. 10c. The ASF filter is established using the arcsine function of the ratio of the vertical derivative of the total gradient amplitude and the total gradient of the horizontal gradient amplitude. This filter seems to highlight both deep and shallow geological discontinuities in the North region of Cameroon. Also, the reading of the lineaments on the ASF map is easily done compared to the TAHG map. The lineaments identified by the ASF confirm those outlined by the ILF. We note a good resolution of the output results as those depicted by the ILF. As the application made to synthetic data in section 4, the ASF reduces to zero signals other than edge signatures. However, the highlighted edges are bordered by signals which tend to thicken the actual geological features. The synthetic example further confirms this drawback of the ASF compared to the ILF. In addition, the enhanced edges of the geological structures appear weakened compared to those produced by the ILF.

The FSF has been also applied to the residual Bouguer gravity grid to produce the results displayed in Fig. 10d. Established by Oksum (2021), the FSF is an application of the fast sigmoid function to the ratio of the vertical derivative and the horizontal gradient of the horizontal gradient amplitude. This technique has the advantage of being fast in the implementation of results. Like the cards presented previously (TAHG, ILF and ASF), the FSF map displays well deep and shallow geological discontinuities. Unlike the results of the TAHG map, the lineaments highlighted by the FSF have a better resolution, with a considerable reduction of spurious edges. The outlined geological features are continuous and well defined compared to those presented on the ILF map. However, the lineaments produced by the ILF (Fig. 10b) appear with better resolution than the results of the FSF. The results obtained following the application of edge detection techniques to synthetic data confirm the performance of the ILF compared to the other three filters. The lineaments highlighted by the FSF in the study area are confirmed by the results displayed on the TAHG, ILF and ASF maps. Given the minority of NE-SW trending lineaments and faults, the fractured bedrock in the North region of Cameroon would be less affected by the extension of the Adamawa and Tcholliré-Banyo faults.

Considering the results displayed by the TAHG, ILF, EHGA and FSEG maps, the North Cameroon region shows a variety of lineaments (faults, fractures and geological contacts) with various shapes and directions. The similarities of geological features enhanced by each method demonstrate their performance in highlighting both deep and shallow discontinuities. The analysis of Figs. 10a-d validates the ILF method as the technique that highlights at best the structural features of the basement in the study area. Figure 11 presents the structural features extracted from the ILF map and the rose diagram. The rose diagram indicates that the majority of the outlined lineaments trend in the N-S, NE-SW and NW-SE directions. The orientations of the tectonic features highlighted near Bafouni are in agreement with the work of Ndjeng (1992). The latter showed that the area was subject to two intense tectonic episodes with fractures mainly oriented N-S, NNE-SSW and NE-SW. According to Fairhead and Okereke (1987), the Benue and Yola faults have been the target of extensional and shearing tectonics during the Cretaceous and early Tertiary. These tectonic episodes would be the primary cause of the major NW-SE lineaments outlined along the Benue basin. The trend of the lineaments observed in the southern part are varied. Except structural features evolving near the Banyo-Tcholliré and Adamawa faults, the other lineaments seem less influenced by the shear zone coming from the Adamawa region in the South. The geological features outlined in the North Cameroon region could be the results of various tectonic activities. However, the joint use of ground-based and satellite gravity data enable to improve the precision of structural mapping in the study area.

The Euler deconvolution technique is also applied to the residual Bouguer anomalies to estimate the depths of crustal density sources. The quality of Euler's solutions depends of certain parameters, especially the window size (W), the maximum depth tolerance (T) and predominately the structural index (SI). According to Reid et al. (2014), the Euler deconvolution technique offers better linear solutions for a minimum window size of 3x3. However, the choice of the optimal parameter W depends on the dimensions and resolution of the anomaly grid, and on the parameters of the residual Bouguer anomalies (Marson and Klingele, 1993). In this work, the best clustering model of Euler’s solutions is obtained for W = 8, SI = 0.1 and T = 10. Figure 12 displays the structural results following the application of the Euler deconvolution technique. The faults outlined on the Euler map (Fig. 12) are constrained by the ILF lineaments shown in Fig. 13. The other solutions, attributed to anomalous intrusion boundaries or geologic contacts, are displayed with the information on their average depth. The faults/fractures appear with different depths and trends, as summarized in Table 2. The Euler’s solutions show that the deepest geological discontinuities are mainly trending along the NW-SE axis, with a depth of more than 16 km. These deep anomalous sources would have a link with the tectonic activities of shearing and extension undergone by the region during the Cretaceous in a NW-SE direction (Fairhead and Okereke 1987). Also, most major density sources would be absent at less than 4 km depth. Nevertheless, Fig. 12 shows slight intrusions located between 0 and 4 km depth and whose position correlates well with a series of short lineaments highlighted on the previous maps (TAHG, ILF, ASF and FSF). As the results obtained by the ILF edge detection technique, the Euler deconvolution method displays fewer linear solutions near the Adamawa and Tcholliré-Banyo shear zones. The bedrock fracture networks in the South would be less influenced by the extension of these shear zones in the study region. The Northeast is strongly marked by the presence of four features (F23 to F26) trending generally in the NW-SE direction, with their depths averaging between 8 and 12 km. This strongly demonstrates that the faults and fractures of this northeastern area would appear as a result of a uniform tectonic activity.

Table 2

Trends and depth of features delineated Euler deconvolution solutions
Feature	Trends	Depth (km)	Feature	Trends	Depth (km)
F1	NW-SE	> 16	F15	N-S	[8,12]
F2	ENW-WSE	[8,12]	F16	WNW-ESE	[4,8]
F3	NE-SW	> 16	F17	NW-SE	> 16
F4	NE-SW	[12,16]	F18	WNW-ESE	[4,8]
F5	WNW-ESE	[12,16]	F19	NW-SE	> 16
F6	NE-SW	[4,8]	F20	NNE-SSW	[8,12]
F7	WNW-ESE	[4,8]	F21	WNW-ESE	> 16
F8	NNW-SSE	[4,12]	F22	N-S	[4,8]
F9	WNW-ESE	[12,16]	F23	NW-SE	[4,8]
F10	NE-SW	[4,8]	F24	NW-SE	[8,12]
F11	NW-SE	[8,12]	F25	WNW-ESE	[8,12]
F12	WNW-ESE	[8,12]	F26	NW-SE	[8,12]
F13	NE-SW	[4,8]	F27	N-S	[12,16]
F14	NE-SW	[4,8]	F28	NNE-SSW	[12,16]

Improving research that can lead to better exploration of groundwater in the North Cameroon region is a major challenge. So, advanced detection techniques of geological lineaments have been used for structural mapping in the region. The TAHG, ILF, ASF and FSF high-resolution filters were applied to a residual Bouguer anomaly grid erected from terrestrial and satellite gravity data. Then, a precise mapping of geological contacts and faults in the region has been established. It appears that the majority of the geological features are trending along the N-S, NNE-SSW and NE-SW directions. The orientation of the lineaments in the south of the region denoted that the extension of the Adamawa and Tcholliré-Banyo shear zones would have had a weak impact on the fracturing of the basement. The linear solutions (identified as fractures or faults) produced by the Euler deconvolution method match well with several features resulting from edge detection techniques. The deepest density discontinuities in the study area are identified along the NW-SE axis, corresponding to the extension of the Benue Trough in the study area. The accuracy and resolution of the residual Bouguer anomaly grid enable the identification of a network of shallow lineaments located between 0 and 4 km depth. Also, the NW-SE orientation of the crustal features located in the northeast of the region indicates that the area would have been the target of a uniform tectonic activity. The results obtained in this work could be a great contribution for a better understanding of the tectonic events undergone by North Cameroon region. Beyond the precision provided by the combination of ground-based and satellite gravity data, edge detection techniques must be further refined to improve structural studies.

Author contributions

PGK: Conceptualization, Data curation, Methodology, Formal analysis, Writing. LY: Methodology, Resources, Software, Validation, Visualization; LHK and JK: Supervision, Validation, Visualization, Review, Editing.

Declaration of competing interest

The authors declare that there are no competing interests that are directly or indirectly related to this scientific work.

Acknowledgments

The National Institute of Cartography (NIC) is appreciated for supporting and encouraging this work. We are also grateful to members of the Geodesy Research Laboratory for their comments and criticisms which enable to improve this paper. The first author is grateful to Professor René Forsberg who kindly shared us the GRAVSOFT package, used to perform the interpolation of the combined gravity grid. We also thank the editor and anonymous reviewers for their relevant suggestions on this paper.

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High precision structural mapping using advanced gravity processing methods: a case study from the North region of Cameroon

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Abstract

Figures

1. Introduction

2. Geological and structural settings

3. Data and Method

3.1 Ground based gravity data

3.2 Satellite gravity data

3.3 Method

3.3.1 Least-squares collocation

3.3.2 Advanced edge detection methods

3.3.3 Euler deconvolution method

4. Application to synthetic data

5. Results and discussion

5.1 Combined Bouguer anomalies

5.2 Regional/residual separation

5.3 Application of the advanced gravity processing filters

6. Conclusions

Declarations

References

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