Quantitative Interpretation of Gravity Anomalies in the Kribi-Campo Sedimentary Basin (South Cameroon) Based on Spectral Analysis and 2.5D Modelling: Structural Implications

Ground gravity survey was recently carried out in the Lolabe-Campo area, which constitutes the southern onshore portion of the Kribi-Campo sub-basin in South Cameroon. The obtained gravity data were processed and interpreted in order to elucidate the subsurface geology of the area in which preliminary studies highlighted the presence of an intrusive igneous body. In order to determine the nature and the characteristics of this body, spectral analysis, ideal body solution and 2.5D modelling methods were applied to the gravity data. The results suggest that the emplacement, breaking up and separation of the intrusive igneous body were the outcome of two tectonic events corresponding to an upward vertical the rocks and their location around the Atlantic Ocean led to the conclusion that the two intrusive bodies are composed principally of gabbro. The disposition and shape of the open zone resulting from the separation of the blocks are suggestive of a trap for the accumulation of hydrocarbons and mineral resources.


Introduction
The area under study is situated in the southern part of Cameroon (Central Africa), and constitutes part of the onshore domain of the Kribi-Campo sub-basin located between latitudes 2˚20'N and 3˚20'N and longitudes 9˚15'E -10˚00'E. It is situated at the junction between three main structures: 1) the sedimentary Kribi-Campo sub-basin; 2) the southern edge of the Kribi-Campo fault and 3) the metamorphic cratonic Ntem Complex. This area was affected by a series of tectonic activities due to the collision between the Pan-African belt and the Congo craton that formed the structural features of Southern Cameroon [1] [2]. The collision resulted in the over thrusting of the Pan-African units over the craton to depths of about 50 to 150 km [3] [4] [5] [6]. The Precambrian basement is deeply buried beneath the Pan-African formations across most of the study area. The regional structure and distribution of fault zones within the deeply buried Precambrian basement in southeastern Cameroon have been the subject of many investigations. [7] on delineating lineaments in the region, highlighted a series of deep and shallow faults traversing the area with a SW-NE dominating orientation. [8] [9] suggested the presence of high density intrusions in the subsurface of this study area from the analysis and interpretation of the maxima of horizontal gradient of the Bouguer anomalies. In presenting the interpreted structural map of the Kribi-Campo basin, [10] highlighted circular contacts indicating boundaries of intrusions in the Lolabe-Campo zone. In order to provide more detailed information on the nature and the characteristics of this intrusion, after a brief analysis and interpretation of the gravity anomaly map for the study area, this work consists of combining the indirect method (spectral analysis), the inverse method (ideal body solution) and the direct method (2.5D modelling) to analyze and interpret the new gravity data collected in this region. The main aim is to present the extensional and longitudinal dimensions of the Lolabe-Campo subsurface structure in general and to locate the gravity intrusion identified in the area. structural zones [11]- [15]: 1) the stable Congo Craton in the Southern and Central areas and the 2) Mobile Zone of Central Africa (MZCA) known as the Pan-African belt of Central Africa to the northern area [16]. These structural zones were formed during the Pan-African tectonic events that are related to the Pan-African orogeny (550 ± 100 Ma).
The Congo Craton, which is known as the Ntem Complex in Cameroon [17] constitutes the greater portion of the study area. It consists predominantly of Archean rocks with some reworked and re-sedimented material formed in the Paleoproterozoic era [18] [19]. The Archean period is dominated here by Liberian orogeny (2700 -2600 Ma), which began with the intrusion of magmatic rocks from which the greenstone belts were derived. Diapiric intrusion of Tonalite-Trondhemite-Granodiorite (TTG) followed the Greenstone belt formations between 2900 and 2800 Ma during the major tectonometamorphic phase [5] [18] [20]. Other intrusions were revealed in the region by [21] [23]. The northern portion of the region of study belongs to the geological unit called "Nyong Unit" composed mainly of gneisses, metagranidiorites and green rock belts.
In general, the region (see Figure 1) has a complex and uneven tectonic structure.

Origin of the Data Used
The ground gravity data used in this study were collected during a geophysical field campaign organized by the geophysics team of the  s) receiver of Garmin International Inc. For each station, the Global Positioning System receiver is first used to determine the angular coordinates and the altitude. Then the gravity-meter is used to measure the value of the variation of the gravitational attraction.
Our area of study is located in the dense equatorial forest making access very difficult. A great portion of the area is covered by the Campo-Ma'an national park and the Ntem river flood plains which are very swampy, woody and extremely inaccessible by foot. Data were only collected on open fields and roads.

Processing of the Data Used
The gravity data were reduced in order to obtain the value of the Bouguer anomaly in each station. Gravity measurements were made with a Lacoste and Romberg Gravimeter having its temperature calibration constant at 50˚C. Observations were made with respect to the base station located in Kribi town. Free air and Bouguer reductions based on mean density of 2.67 g•cm −3 were applied to the measured data. The free-air anomaly is calculated by subtracting the latitude correction (theoretical gravity) from the absolute gravity and adding a correction for the station elevation. The latitude correction requires the theoretical gravity at the station location on the earth's spheroid. The formula of free air Open Journal of Earthquake Research anomaly as defined by [29] is given by the formula where ∆ AL is the Free air anomaly in milliGals (mGal); ga absolute gravity; γ latitude correction in degrees; h s station elevation in metres (m) and φ the latitude of the station in degrees. The formula accounts for the non-linearity of the free-air anomaly as function of both latitude and height above the geoids.
The Bouguer anomaly corrects the free air anomaly for the mass of rock that exists between the station elevation and the spheroid. For ground survey (including lake surface survey) the Bouguer anomaly formula is: where, ∆ B is the simple Bouguer anomaly in milligals; ∆ AL free air anomaly; ρ Bouguer density of the earth in g•cm −3 , ρ w Bouguer density of water in g•cm −3 ; ρ i Bouguer density of ice in g•cm −3 ; h s station elevation in metres; hw water depth in metres (including ice); ice thickness in metres; δ c curvature correction. Terrain correction was also applied on the data and complete Bouguer anomaly derived using the formula: where ∆ CB is the complete Bouguer Anomaly; ∆ B simple Bouguer anomaly and δ T terrain correction. This equation was used to determine the Bouguer anomaly at each survey station in the area. The resulting Bouguer anomaly data were used to obtain the Bouguer gravity anomaly map of the area (Figure 3). We present in Figure 2 a distribution of the field data points.

Spectral Analysis Method
Spectral analysis as described by [30] is an interpretation technique based on the study of power spectrum properties. The gradient of the linear segments of the Fourier power spectrum is related to the depth of the density below the surface of the earth. From the study of logarithmic power spectrum as a function of the spatial frequency, the mean depth to bodies responsible for the observed gravity anomalies can be estimated. The power spectrum is the magnitude of the discrete Fourier transform of the gravity data. It has been used extensively by many authors namely (1975) [31] [32]. The finite discrete Fourier transform is given by the equation: where b(x) represents the discrete N data array of gravity data obtained by sampling a continuous profile at evenly spaced intervals Δx. i is the complex operator, ω = 2πk is the spatial frequency and k = λ −1 is the wavenumber in the x direction.
The expression of the Bouguer Slab Effect is given by the equation: where B(k) z = 0 is the Fourier transform of the Bouguer anomaly profile b(x) z = 0 Δρ is the density contrast between two layers; F(k) is the Fourier transform of f(x), the derivation of the interface from the mean depth z; G is the gravitational constant. The mean depth can then be calculated using the following equation: where E is the power spectrum of B(k).
The square of the Fourier amplitude spectrum is plotted versus the radial frequency. The slope of the relationship between the wave number of the gravity field and the logarithmic power spectrum provides information about the depths of the source bodies.

Ideal Body Determination
As pointed out by [33], ideal body theory is used to delineate bounds on the spatial extent of the anomaly source with an approximate model. It is important to have an idea of the suspected anomaly source in order to give a good approximation of it. The inverse method developed by Parker allows us, when the anomalies are well individualized, to choose amongst all possible solutions, those that best fit the data. The linear programming technique is used to carry out the calculations. This technique consists of considering a model where the density value ρ is known at certain given positions (X 0 , Z 0 ). The domain under the profile is subdivided into quadrangular cells with dimensions d x and d z (d x is the dimension of a cell following the profile direction and d z is the dimension following the vertical axis) centered in (X 0 , Z 0 ) and for which the value of ρ is assumed to be constant (Figure 3). The gravity field at each point denoted i is the sum of the effects of all the cells. It is given by the following formula: where N is the number of cells in the profile direction, K the number of cells in the vertical direction. G ijk is the Green's function associated with the gravimetric effect of the elementary prism (j, k) observed at the point i, ρ jk is the density of prism centered in (x j , z k ) and ε i is the error on the value of field observed at the point i.

Direct Modelling
3D modelling has proven to be the most descriptive in terms of characterizing bodies, given that it allows the observation on the lateral, longitudinal and angular extends. While 2D modelling is applied to structures with infinite extensions, 2.5D modelling allows a good control of the lateral extension of geological structures [34]. In Figure 4, we see that the body causing the anomaly observed on the map could have a southward extension beyond Campo zone. This way, the data do not permit us to carry out 3D modelling. We have therefore chosen to apply the 2.5D modelling.

Bouguer Anomaly Map
The Bouguer anomaly map was elaborated by an automatic computer drawing from the Geosoft Package software v.8. from the established grids using a contour interval of 3 mGal (Figure 4). The area of interest is dominated by a relatively broad gravity high extending southwestward from Lolabe to Campo. The entire western part of the map is dominated by high gravity anomalies with the broader part in the north while the eastern part shows relatively low values. This indicates a strong gradient of anomalies between the east and the west which is  (Figure 1). According to [9], the northwestern and southwestern high circular-shaped anomalies are caused by intrusive dense bodies in the subsurface of the region. The gravity modelling will situate these intrusions into the subsurface.

Ideal Body Solution
In order to determine the ideal body for the investigated anomaly, we used the IDB2 Fortran Program [35] which calculates Parker's ideal body using the simplex algorithm for the linear programming. The solution of the ideal body is calculated along the 40 km profile P (Figure 4) and the characteristics of the initial model for data inversion are as follow: • horizontal length of prisms: ∆x = 1 km; • vertical length of prisms ∆z = 0.5 km; • number of prisms following the horizontal nx = 20; • number of prisms following the vertical nz = 10; • error on the value of anomaly: 1 mGal. Figure 6 presents the solution of the ideal body in which are represented the two bodies responsible for the observed anomaly. The ideal body gives an idea on the distribution of these responsible masses and their apparent geometry. On the right, we have the larger block located between at 0.5 km and 3 km, and a smaller block on the left situated between 0.5 km and 1.5 km. These two masses, with a predominant density contrast of 0.13 g•cm −3 compared to the surrounding rocks, are relatively located in the northern side of our selected profile.

2.5D Model
The model presented in Figure 7 consists of various bodies which are responsible for the observed anomalies along the profile. We used the computer program Grav2dc [36] to carry out this modelling. This interactive software allows one to design a geological model in the form of the polygon, whose gravity signature is in accordance with the observed anomalies. It takes as initial values the density contrast and the lateral extension of any given body. Three main parameters

Discussion
The to its structural disposition coupled with the already known tectonic activities in the region [8] show that the tectonic events responsible for the emplacement, breaking up and separation of the intrusive igneous body into two bodies could first of all have been as a result of an upward vertical translational tectonic movement followed by an anticlockwise rotational faulting tectonic movement. This is in agreement with the results of [37], which indicate that the relief of the study area generally conserves the imprints of the phenomena of faulting tectonics. [38] also mentioned the occurrence in the region of a strong extensional tectonic event that dates back to the Cretaceous. [8] on delineating the lineaments in south Cameroon obtained a structural map which shows that major tectonic events are responsible for the structural layout of this study zone. Furthermore, [9] presented a 3D model of another intrusive body located at about 40 km to the north of these two bodies. Compared to his model, the present study presents a density contrast which indicates the difference in types and densities of rock bodies in the region as one moves from the north towards the south. Considering that the average density of the metamorphic formations in the study area is equal to 2.67 g•cm −3 and given that the density contrast of the intrusive igneous body is 0.13 g•cm −3 , the density of this body can be estimated at about 2.80 g•cm −3 . Table 1 below presents the density ranges of the various intrusive rocks in the region [21], from which it can be deduced that the intrusive body obtained in this study by the 2.5D gravity modelling could be composed principally of gabbro rocks.
Micro-gabbro and gabbro are intrusive igneous rocks that occur as dikes and sills and contain minerals such as olivine, plagioclase and feldspar. This assurance about dolerite is based on the fact that the study area forms the onshore portion of the Kribi-Campo sedimentary sub-basin found around the Atlantic Ocean.
The open zone (Z) between the two bodies ( Figure 8) obtained from this  modelling, which is apparently triangular in shape could be favorable for the accumulation of hydrocarbons or minerals and should constitute a topic for more detailed studies to be carried out in the area using microgravity survey or other geophysical prospecting methods.

Conclusion
The purpose of this study was to provide more information on the nature and the characteristics of the intrusive body in the Lolabe-Campo Area as proposed by [10]. The analysis of the gravity map, the interpretation of the gravity anomalies by spectral analysis, ideal body solution and by 2.5D modelling reveal high gravity discontinuities between rocks of different densities and the presence of two high density bodies of rocks in the subsurface of Lolabe-Campo. The emplacement, breaking up and separation of the intrusive igneous body resulting in these two blocks have been interpreted as deriving from two tectonic events corresponding first of all to an upward vertical translational tectonic movement followed by an anticlockwise rotational faulting tectonic movement. The isolated intrusive igneous blocks whose density has been estimated at 2.80 g•cm −3 based on an average density of 2.67 g•cm −3 for the local rocks and a density contrast of 0.13 g•cm −3 , are completely surrounded by both sedimentary and metamorphic formations. A comparison of this high density value with that of other intrusive rocks in the study area and also the location of this area around the Atlantic Ocean has led to the conclusion that the two intrusive bodies may be composed principally of gabbro. The disposition and shape of the open zone (Z) highlighted by the resulting separation of the intrusive blocks is suggestive of a very good trap for the accumulation of hydrocarbons and mineral resources. This conclusion however paves the way for more detailed studies to be carried out in the area using either microgravity survey or other geophysical prospecting methods.