Detection and characterization of lineaments using gravity data in the south-west Cameroon zone: Hydrogeological implications

4.1 Stable downward continuation method

The downward continuation is an operator that acts as a filter. It is a filter that amplifies the noise contained in the signal, thus revealing areas of anomaly discontinuities related to shallow structures. To overcome this instability problem, we used the stable downward continuation algorithm proposed by Ma [31] and applied by Li et al. [32] for the detection of discontinuity zones.

We present a computational approach using the NSTD. We started with the stable downward continuation algorithm that uses the upward continuation and the total horizontal derivative to perform the downward continuation, with the following equation:

where, g m ( x , y , z ) is the anomaly at depth z .

Equation (1) is obtained by following steps. A Taylor series expansion is used to obtain the initial gravity anomaly of g ( x , y , z ) at depth z by the following formula:

where g (x, y,−z) is the anomaly at depth −z.

The Laplace equation [33] given by the following equation has been used to reduce the instability of the calculations and the effect of noise:

The horizontal derivative is computed in the spatial domain, which improves the computation and antinoise ability of the downward continuation algorithm. The anomaly g 1 ( x , y , 0 ) has been obtained via the upward continuation of the anomaly g ( x , y , z ) at the zero observation level. g ( x , y , 0 ) should be equal to g 1 ( x , y , 0 ) but g ( x , y , z ) is only an approximate value, so they differ. The following iteration process is used to minimize the difference:

By applying equation (2) to Δ g 1 ( x , y , 0 ) , we obtain the following formula:

where Δ g 1 ( x , y , z ) is the anomaly after the downward continuation of the anomaly Δ g ( x , y , 0 ) to z and Δ g 1 ( x , y , − z ) is the anomaly after the upward continuation of the anomaly Δ g 1 ( x , y , 0 ) to −z. Δ g 1 ( x , y , z ) represents the correction of the anomaly at depth z; therefore, the anomaly is given as follows:

We repeat the calculations in equations (4)–(6) until the root mean square deviation of Δ g ( x , y , 0 ) is less than a given value; therefore, the final expression for the anomaly at depth z is given by formula (1).

4.2 NSTD method

The NSTD technique highlights areas of discontinuity and the contours of geological structures. It is used to enhance subtle details in potential field data. The standard deviation norm calculation window of an image or gravity map is a simple measure of local variability [34]. Discontinuities can be observed from equation (7):

The standard deviation ( σ ) in equation (7) is determined using a 5 × 5 square data point computation window, which features all observed data locations [34]. This processing of the gravity maps clearly gives excellent contour resolution for structure models. The NSTD method allows the identification of discontinuity zones and contours of subsurface structures with greater accuracy than methods such as the total horizontal derivative, tilt angle, and theta map [34].

4.3 Euler’s deconvolution method

Euler deconvolution is currently used as method of the automatic calculation of depths of gravity or magnetic sources. However, this method can be applied in order to distinct geological scenarios and does not require a specific geological model hypothesis [35]. The estimation of the depths of gravity or magnetic field sources is derived from the Euler homogeneity equation given by Relation (8). This equation relates the gravity field and its gradient components to the location of the source, with the degree of homogeneity, expressed as the structural index N [36]. The resolution of the Euler homogeneity equation by the least-squares method is made simultaneously for each grid position in a moving window:

where ( x 0 , y 0 , z 0 ) are the coordinates of the gravity source; g is the field strength measured at position ( x , y , z ) ; and δ g δ x , δ g δ y , and δ g δ z are its gradients with respect to variables x , y , and z , respectively. T is the total field strength determined at position ( x , y , z ) , which is the sum of the regional field B and the anomaly Δ g due to the causal source given by the following formula:

The importance of the choice of the structural index N, which depends on the nature of the structure, has been pointed out [35,36,37]. This structural index is defined as a measure of the rate of change of a field with the extent of the source. It is shown that the structural index N, for gravity, can take a value between 0 and 2 corresponding to a number of structures. It is believed that a structural index varying in the interval [ 0 ; 1 ] is best suited for faults, and N = 2 for a sphere [36,37]. Euler deconvolution is a suitable and more interesting method as it allows the true depths of existing structures to be determined and estimated at any location.

5.1 Map of the NSTD corresponding to a stable downward continuation

The map shown in Figure 4a is the NSTD map corresponding to a downward continuation at a height of 10 m. To obtain this map, formula (7) was applied to calculate the NSTD using the data obtained from the stable downward continuation. It highlights the boundaries of the structures present in the study area for the corresponding depths. It is observed that the effects of the structures are quite distinct, giving a good appreciation of the discontinuities at this continuation height. Figure 4a shows the arrangement of the association between yellow and red ripples. A linear arrangement of these ripples corresponds to a lineament, and their curvilinear arrangement corresponds to an intrusive body but we are only interested in the lineaments (Figure 4b).

Figure 4

(a) The NSTD map and (b) the superposition of lineaments with the NSTD map.

5.2 Lineaments from the NSTD map

The lineament map was plotted in ArcGIS software (Figure 5). The NSTD map allowed us to identify 71 of the superficial lineaments present in this area. The directions of these lineaments are N-S, W-E, NW-SE, SW-NE, WNW- ESE, NNW-SSE, SSW-NNE, and WSW-ENE. The number of lineaments per direction and the related percentage are mentioned in Table 1. The predominant direction of near-surface gravity lineaments, shown by the Rose diagram of the lineament orientations (Figure 6) is W-E; it plays a key role in the control of the geodynamic evolution of the region.

Figure 5

Lineament map.

Figure 6

Rose diagram of the lineaments orientations in the study area.

5.3 Euler’s solutions superimposed on the lineament map

The Euler method was applied to the Bouguer anomaly data using a 3 km × 3 km moving window with a structural index N = 0. The superposition of the lineaments with the Euler solutions allowed us to obtain Figure 7. On this map, we evaluate the interval in which lies the depth (of the roof, on the one hand, and of the base, on the other) of each lineament hosting Euler solutions. To obtain these different depths, we proceeded as follows: for a lineament that overlaps several intervals of Euler solutions, the interval with smaller depths corresponds to the depth of the roof and the interval with larger depths corresponds to the depth of the base of the lineament. Table 2 shows the depths of these lineaments.

Figure 7

Lineament map superimposed on Euler solutions from 0 to 5,000 m, index N = 0.

6.1 Structural aspect

The lineaments in the structural map of our study area highlighted by NSTD (Figure 5) are mostly new lineaments. However, we can mention lineaments L18 and L33 that are probably the same as lineaments ( 1 ) and ( 2 ) highlighted by Koumetio et al. [8]. Also, lineament L18 is probably the same as lineament ( 11 ) highlighted by Koumetio [38]. We can add that lineaments L20, L33, and L34 are probably the same as lineaments (28), (2), and (21) highlighted by Clotilde et al. [39]. We can also add that lineaments L41 and L46 are probably faults f13 and f9 seen, respectively, on the geological map (Figure 1). By finding, in this study, the traces of certain lineaments highlighted in previous work, we can say that this increases the credibility of our results. These lineaments are those whose roofs are close to the surface among all the lineaments detected by previous studies.

We have seen that the Bouguer anomaly map (Figure 3) presents elongated anomalies along dominant directions SSW-NNE to N-S, which are probably privileged directions for deep structures given that the gravitational effects of these predominate over those of surface structures. On the other hand, our results show that the lineaments close to the surface are mainly oriented E-W. This result is in agreement with the known tectonic and structural directions in the regional scale of South Cameroon. Indeed, the framework of regional structures is particularly characterized by the dextral shear corridor, which is the Ngoro-Belabo Shear passing just after the northern edge of our study area in directions E-W and SW-NE thereafter [40]. We can therefore say that in our study area, the deep structures have mainly undergone meridian and submeridian tectonic movements, while the near surface has been much more influenced by E-W tectonic movements. However, it is important to note that the second direction in terms of predominance is SW-NE, which is that of the largest lineament that crosses the study area, namely, the Sanaga Fault (it is the southern and most continuous tectonic lineament of Central Africa stretching from the Gulf of Guinea to the Central African Republic). All this shows that our study area has experienced several tectonic sequences.

Nsangou et al. [41] make a study to identify possible active tectonics crossing the passive margin and its effects on landscape evolution in the area from Edea to Eseka. It appears that Tectonics across the Cameroon Volcanic Line (CVL) and the Sanaga Fault that cross the passive margin are still active and are the main factor controlling the morphology of the Edea-Eseka region in south-west Cameroon. The passive margin of south-west Cameroon seems to be a good natural laboratory for active tectonics. This may justify the large number of lineaments obtained by this study.

6.2 Hydrogeological aspect

The occurrence of groundwater in hard rock environments is related to the secondary porosity and permeability, which are geological discontinuities caused by tectonic movements or weathering process [42]. These discontinuities are fractures faults, joints, dykes, and geological contacts. Then, the density of lineament is a characteristic feature of the permeability and porosity of a region. Since lineaments are considered as the potential conduits for groundwater flow, their mapping is essential for groundwater monitoring in any area [43].

Figure 8 is a superposition of the lineament map and the hydrographic map of the study area. It can be seen in Figure 8 that there are the rivers that are superposed on some lineaments, while others cut the lineaments in their transverse direction. The lineaments that stretch longitudinally to rivers (examples of lineaments L1, L3, L6, L20, L24, L35–L37, L66, and L71) may be the places of surface water circulation. The lineaments that cut across watercourses (examples of lineaments L2, L8–L10, L18, L25–L29, L31–L34, L37, L39, L42, L44, L45, L51, L53–L56, L58–L62, L67, L68, and L70) can be the sites of groundwater circulation. This is much safer for very shallow lineaments whose roofs are very close to the surface. Using Euler’s solutions, lineaments with roofs between zero and 250 meters deep (Figure 7 and Table 2) are favorable for hydrogeological prospection (these lineaments are L2, L3, L7, L8, L23, L24, L28, L30, L31, L36, L64, and L65).

Figure 8

Overlay of the hydrographic map on the lineaments map.

6.3 Validation of results regarding the distribution of data points

The measurement points of the gravity data used in this study follow lines that properly grid the area in which the results are considered. Following these lines, the inter-station distances are approximately 3 km [29]. These data have already been tested in the area through some previous work. Indeed, Koumetio et al. [9] obtained, from these data, a residual map from which they established a 3D structure model of an intrusive body detected in Bipindi area by multi-scale analysis of the maxima of the horizontal gradient of the gravity field upward continued at different altitudes. The results are in agreement with those obtained by Owona et al. [14] from magnetotelluric data taken in this area. Also, a study carried out by Koumetio et al. [44] on regional and residual anomalies maps of various orders produced from these gravity data made it possible to obtain results, which are in agreement with those obtained by Tokam et al. [45] based on seismological data. These two examples show that the filters and transformations applied to the gravity data used in this study produced credible results for both deep and superficial structures. In the case of the present study, given that we have, in addition, found certain lineaments (having a roof close to the surface) already highlighted in old works, we can conclude that the methods of stable downward continuation and NSTD applied on the data used led to credible results.