The ground gravity data used in this study were collected during a geophysical field campaign organized by the geophysics team of the University of Yaoundé 1 in March 2015. Before then, no ground geophysical gravity survey had been carried out in the region. Using a Lacoste & Romberg G-823 gravimeter, 223 gravity data were measured for points. The data consists of irregularly spaced gravitational acceleration values and corresponding geographical coordinates (longitude, latitude and altitude) with a station-spacing varying from 0.5 km to 2.0 km. The coordinates were obtained from a Global Positioning System (GPSMAP 64

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.

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 anomaly as defined by [29] is given by the formula

Δ A L = g a − γ + ( 0.308767763 − 0.000439834 ( sin ϕ ) 2               − 0.000000072124602 ⋅ h s ) ⋅ h s (1)

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:

Δ B = Δ A L − 0.0419088 [ ρ h s + h w ( ρ w − ρ ) + h i ( ρ i − ρ w ) ] − δ c (2)

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:

Δ C B = Δ B + δ T (3)

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 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:

B ( ω ) = ∑ 0 N − 1 b ( x ) exp ( − i ω x ) ⋅ Δ x (4)

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:

B ( k ) z = 0 = 2 π Δ ρ G ⋅ exp ( − 2 π k t ) ⋅ F ( k ) z = 0 (5)

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:

h = Δ log E 4 π Δ k (6)

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.

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 (X₀, Z₀). 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 (X₀, Z₀) 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:

g i = ∑ j = 1 N ∑ k = 1 K G i j k ρ j k + ε i (7)

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.

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.

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

probably linked to the Kribi-Campo fault oriented NE-SW and noted f₂ on our geological map (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.

Figure 5 shows a representation of the gravity power spectrum with respect to the wave number for the profile P. Three different lines can be observed on this graph, that has been used to determine the average depths h₁ = 3.1 km, h₂ = 1.2

km and h₃ = 0.6 km corresponding to the interfaces of low, average and high frequencies respectively. These results show that the depth of the form of the intrusion is not uniform. h₁ represents the depth to the base of the body and h₃ the depth to the top, while h₂ is the depth to a particular section of the intrusive body.

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.

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

were used to constrain this model, namely: the value of the density contrast (0.13 g∙cm⁻³) obtained from the ideal body solution (Figure 6); the depths of the intrusions obtained from the spectral analysis calculations (depth to the top 0.6 km and depth to the base of 3.1 km for the main body to the right and 1.2 km for the small block to the left) and the known geological information in the region (region mainly covered by sedimentary and metamorphic formations and other intrusions). The obtained model (Figure 7) shows a structure of two bodies which seem to have resulted from the dislocation of a single body interpreted to be a dense intrusive rock surrounded by metamorphic and sedimentary formations. The first body, which is the smaller one is confined at depths of 0.6 km and 2 km approximately, and it is located in the northern edge of the profile. The geometrical observation and the structural disposition of this body, suggests that it initially formed a single body with the larger one situated on its right. The larger body on to the right, with a wider extend than the first is confined at depths of 0.6 km and 3.2 km approximately and occupies mainly the middle portion of the profile. The dislocation of the two body could be as a result of the geo-tectonic activities observed in the region which gave rise to various faulting systems [8] [9] [10] [37].