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Geophysical surveying is crucial in the investigation of mineral resources in poorly exposed areas such as SE-Cameroon, a region known for its gold mineral potential. In this paper, gravity survey is carried out in the Batouri area, SE-Cameroon based on land gravity data from the Centre-south Cameroon.
Therefore, an analytical polynomial separation program, based on least-square fi
tting of a third-degree polynomial surface to the Bouguer anomaly map, was used to separate the regional/residual components in gravity data. This technique permitted to better understand the disposition of the deep and near surface structures responsible of the observed anomalies in the Batouri area. Spectral analysis and 2.5D modelling of two profiles P
_{1}
(SW-NE) and P
_{2}
(N-S) selected from the residual anomaly map provided depths to basement. These depths constrain the gravity models along the profiles, indicating a variable thickness of the sedimentary infill with an approximate anomaly of -
33 mGal. The 2.5D model of the basement shows a gravity body, with a signature suggesting two close and similar masses, which characterize the quartz-bearing formations associated here to granite and gneiss. Our work highlights a main heavy gravity: Gwé-Batouri anomaly, containing the major part of auriferous deposits located along the NE-SW direction. Further, three tectonic sub-basins bounded by normal faults have been highlighted at Guedal, Gwé, and Bélimban, in the south of Guedal-Bélimban depression. They are associated with the extension tectonics, more or less vertical tangential cuts and accidents that have affected the region. A correlation with previous results from tectonic, lithological and gold mineralization activities proves the relevance of the study and the need to intensify geophysical surveying in the area.

The Batouri area (

A crucial step in gravity investigations is that consisting in removing the effects of deep or shallow structures from the Bouguer anomaly [_{1} and P_{2} on the residual map in the Batouri region, Eastern Cameroon. For this purpose, a regional-residual gravity separation of anomalies based on the least squares is initially made, and the results are discussed, taking into consideration the geological knowledge of the region and the modelled mean densities. The intense gold mining in the area will enable to link gravity signatures to gold bearing targets.

Geological mapping of the study area has been done and modified by [

belongs indeed to the NEFB or Central Africa Orogen with a major link to the Trans-Saharan belt of western African and to the Braziliano Orogen of north eastern Brazil [_{1}-D_{2} deformation associated with amphibolite facies metamorphism.

The rocks of the area (

From the geological point of view (

The superficial formations are composed of 1) the eluvium observed in the granitic and gneissic zones south of Batouri; 2) recent alluvium observed in the Kadei valley; and 3) abundant iron or argillite-rich laterites. The Precambrian basement rocks in the region have undergone granitization and migmatization. The granitization yielded syn and post-tectonic granites [

Tectonics shows that the basement was intensively reworked during a polyphase Pan-African D_{1}-D_{2} deformation associated with an amphibolite facies metamorphism. The deep folds of the basement are Huronian, in a broad sense. Previous geological investigations have recognized orthogneiss, rejuvenated granite and migmatite intruded by granitoids during epizonal metamorphism [

The Batouri area has been one of the main sites for artisanal gold mining in Cameroon for more than 50 years. [^{−1} Au). The Granitic rocks of Batouri (around Djongo) host U-Pb and Ar-Ar mineralizations including monzogranite-granodiorites formed by differentiation of I-type tonalitic magma under oxidizing conditions in a continental volcanic arc setting [

The current study uses historical data from 54 gravity stations that are part of the dataset collected by ORSTROM in 1995 and [^{TM}. These points are separated by a non-regular average distance of 56.3 km longitude, covering an area of 394.4 km × 307.04 km.

into regional and residual anomaly using a polynomial method. This filtering approach widely used by several authors [

The Bouguer anomaly values (690 values) obtained by interpolation of existing data (

The study applies the analytic polynomial regional-residual separation to the interpolated gravity anomalies grid. In addition, application of the 2D Fast Fourier Transform transforms gravity data from space to frequency so as to consider the depths average of the sources of anomalies. This approach is referred to as the qualitative and a preliminary quantitative interpretation of gravimetric anomalies [

The method allows the estimation of regional anomaly by considering, on one hand that, it is regular with a slope that slightly varies; on the other hand, it is modelled using an analytical regional surface (2-D modelling).

Let B(Pi), the value of Bouguer anomaly at the point P(x, y); The objective is to calculate regional values (Reg(x, y)) in (Pi) and residual values (Res(x, y)) in (Pi) by a suitably chosen polynomial F(x, y) of N order, which generates an analytical surface Reg(x, y) as close as possible to the experimental surface B(x, y). The polynomial expression of the regional can be written as seen below [

F ( x , y ) = C 1 + ∑ J = 1 N ∑ l = 0 J C m A m ( x , y ) (1)

or F ( x , y ) = ∑ m = 1 M C m A m ( x , y ) (2)

with N: order of the polynomial

A m ( x , y ) = x l y j − l

m = j ( j + 3 ) / 2 − l + 1

C_{m}: coefficient to be determined.

with 1 ≤ m ≤ M where M = [ ( N + 1 ) ( N + 2 ) ] / 2 .

Defining ε i = B ( x , y ) − F ( x , y ) , the difference between corresponding points of the experimental and analytical surfaces respectively, N_{0} the number of points or Pi stations where observed Bouguer anomaly B(Pi) is known. To adjust the surfaces, we must reduce to the minimum the square deviation:

E = ∑ i = 1 N 0 ε i 2 making ∂ E ∂ C K = 0 (avec K = 1 , 2 , ⋯ , M )

This amounts to:

∑ i = 1 N 0 ε i A k ( x , y ) = ∑ i = 1 N 0 [ B ( x , y ) − F ( x , y ) ] A K ( x , y ) = 0 (3)

Taking into account the above equations yields:

∑ m = 1 M C m ∑ i = 1 N 0 A K ( x , y ) A m ( x , y ) = ∑ i = 1 N 0 B ( x , y ) A K ( x , y ) (4)

C_{m} coefficients are obtained by solving the M ×M system above with a MATLAB code following the polynomial degree. With C_{m} coefficients, we deduce the regional analytical by the formula

R e g ( x , y ) = F ( x , y ) .

The residual Res(x, y) is calculated by the formula:

R e s ( x , y ) = B ( x , y ) − R e g ( x , y ) with x and y in km. (5)

The residual and regional maps derived are useful in a qualitative study of the area.

Generally, inverse distance-weighted gridding of gravity data enables to investigate the shape of the anomaly and then large geologic features are [

B j * = ∑ i = 1 n 1 h i j β B i ∑ i = 1 n 1 h i j β with h i j = d i j 2 + δ 2 ; (6)

h_{ij} represents the separation distance between the node j on the grid and each of its neighboursi brought back from the field.

B j * is the interpolated value of the anomaly at node j of the grid.

δ represents the smoothing parameter of anomalous iso-contours,β is the power parameter.

The choice of the order of the polynomial representing the regional is not arbitrary; it depends on the nature of the residual anomaly to interpret. Generally, the more a regional is smoothed, the more it helps to eliminate only deep lines of the bark. If, again the regional analytical is a polynomial of high order, the lines closer to the surface will be the most accountable, which means that these lines will be of benefit shown in the residual. We must also consider assumptions suggested by the data set available that stick to the best geological and tectonic environment of the study. Data from the separation yielded regional and residual anomaly maps of different levels. The residual map of degree 3 (

The intensity of gravity measured at a point translated simultaneously, the effects of all the masses of the earth, the topography, and all the contrasts of densities inside the globe. The gravity anomaly maps express the density anomalies situated both in the superficial terrains and in the basement. The anomalies put in evidence on the regional anomaly map have large amplitude whose variations are greater than the one of the moho discontinuity [

The gravity anomalies have been grouped in fourth classes [

1) The closed circular isogales anomalies correspond to domes, grabens or basins, or to the mass of ore.

2) The closed ellipsoid shaped isogales anomalies with the long axis λ and the short axis β linked by λ ≥ 3β correspond to synclines, the anticlines, lodes or to galleries.

3) The horizontal gradients correspond to the anomalies related to the change between two gravity levels. These gradients are provoked by folds or faults, down bending, fault steps affecting one or many formations;

4) The positive anomalies are associated with dense sedimentary rocks very dense intrusions in the crust, or to the uplift of substratum.

The negative anomalies are associated with the thickening of the sedimentary layers, slight intrusive rocks in the crust or to thickening of the crust.

The application of spectral analysis (SA) acknowledged many significant advances since its introduction in geophysics, as interpretation tool quantitative for potential field data by several authors [

In this study, the spectral analysis estimates the average depths of the magnetic or gravimetric source bodies. SA does not require prior knowledge of the geometry, the density contrast or magnetic susceptibility of the causative bodies; it simply studies the power or energy spectrum as a function of wavelength or frequency. The power or energy spectrum of the anomaly will have dominant high frequency components when the anomaly is continued to the proximity of the source [

h = Δ ( log E ) / 4 π Δ ( n ) (7)

where E represents the energy spectrum; Δ(logE) is the variation of logarithm of energy spectrum in the interval of frequency Δ(n). Depths obtained by spectral analysis are then used as constraints in the modeling so as to limit the non-uniqueness of the solutions for inverse problems to a unique solution. To propose a unique and acceptable geophysical model, information arising from spectral analysis or Euler deconvolution [

The data processing and interpretation was conducted through the following steps:

- The generation of a new dataset obtained by interpolating data from (

- The Regional-residual filtering based on the regional-residual analytical polynomial separation method [

- The spectral analysis determines depth of the sources of observed anomaly(ies). In this step, curves are generated in Matlab based on the Fourier equation cited above. The depth value is deducted based on the linear regression approach;

- The 2.5D modelling is done, by using spectral analysis results and geological facts as constrains. The density contrast of rocks is obtained by making the difference between the earth’s crust (d_{0} = 2.67 g·cm^{–3} and the various rock density (d_{i}). The strike length is fixed to 100 km, because of the extent of the study area. The maximum depth window for the modelling of residual anomaly is not exceeding 10 km. For this modelling, the different rock types seemingly belong to the PAB [

In the area, the Bouguer anomaly features have a general ESE-WNW, NNE-SSW, N-S gravity gradient (

The map displays three main types of gravity anomalies over the area which are respectively high, intermediate and low values anomalies.

High gravity anomalies (values ranging from −35 to more than −33 mGal) broadly correspond to a circular region covering 2/3 of the study area, from east to west and south to north. This high gravity anomalous portion exhibits one oval peak centered at Ndélélé with a SE-NW major axis along in the Ndélélé-Gwé direction; and encompassing Ngoura, Mindourou and Bélimban, the peak may geologically correspond to either dense or basic deep intrusions within the main formations broadly characterized by the high intensity anomaly values; or probably to the uprising of some mantellic bodies. The anomaly field signal herein, most likely indicates the Neoproterozoic realm that occurs in the study area. The high gravity anomaly values domain is flanked to the north between Guedal-CAR by an intermediate anomaly portion (between −37 mGal to −35 mGal) whose iso-lines present an approximately E-W direction.

The intermediate Bouguer’s anomaly portion forms a transition zone that separates the previous described domain from the low anomalies domain (

1) Regional Gravity anomalies

The regional gravity anomaly map (^{rd} order polynomial. This map shows an overall set of negative isogales presenting a general NW-SE gradient. There is a group of isogales almost horizontal, identical and separated by a nearly circular area containing the iso-lines amplitude −37 mGals. These two groups may correspond respectively to a very dense bedrock south of Gwé and a relatively dense in the region north of CAR separated by a flaw or discontinuity. The map exhibits a regional maximum assimilable to a thinning of the upper crust due to mantle materials uplift. The gravity gradient and the architecture of the contour lines on this map probably reflect the homogeneity of the basement of the region.

2) Residual Gravity anomalies

Residual anomalies are mainly variations of densities at the upper crust, including the variation of thicknesses and densities of the sedimentary rocks overlaying the basement; or either the density contrast induced by intrusive bodies.

The residual map (

The residual map does not keep the same form of contours as Bouguer field map (

Mineral indices such as gold [

Units | Direction/shape | Location | Significance |
---|---|---|---|

Unit I | NW-SE to N-S (linear) | Banyo-Bélimban | Contact Precambrian rock of basement metamorphic series |

Unit II | N-S (ellipsoïd) | Guedal-CAR | Granodiorites, Calc-alkaline and Alkaline granites (Precambrian basement rock) Panafricain Post-tectonic and late syn-tectonic granites (Granitoïds) |

Unit III | W-E | SE-Bimba | Anastexites and embrechites gneisses (metamorphic series) |

Unit IV | NE-SW to NW-SE (Circular) | Batouri-Gwé and Ngoura | Intrusion of anastexites (metamorphic series) |

smoky quartz, characterized by drusy textures with abundant vugs [

The spectral analysis (

Profile | Direction | Hres1 | Hres2 |
---|---|---|---|

Batouri-Gwé (P1) | N-S | 1.66 ± 0.22 | 0.30 ± 0. 04 |

Guedal-Mborguéné (P2) | SW-NE | 2.54 ± 0.18 | 0.50 ± 0.30 |

Profile P2 | |||||
---|---|---|---|---|---|

Density contrast (CGS unit) | Depth (km) | Width (km) | Transversal extension (km) | Vertical extension (km) | |

Body 1 | −0.07 | 0.3 | 5.2 | 50 | 3 |

Body 2 | −0.037 | 0.4 | 6.4 | 10 | 3.2 |

Body 3 | −0.026 | 0.3 | 6.7 | 10 | 3.2 |

Body 4 | 0.084 | 0.7 | 8.4 | 10 | 2.9 |

Profile P1 | |||||
---|---|---|---|---|---|

Density contrast (CGS unit) | Depth (km) | Width (km) | Transversal extension (km) | Vertical extension (km) | |

Body 1 | 0.08 | 0.4 | 6.9 | 20 | 2.9 |

Body 2 | −0.07 | 0.4 | 7.2 | 50 | 2.6 |

Body 3 | 0.03 | 0.3 | 6.1 | 50 | 2.5 |

The 2.5D modelling of surface formations from study area was conducted with the Grav2DC 2.10^{®} [

For this quantitative study, we plotted two gravity profiles P1 and P2 of respective directions N-S and NE-SW (

For profile P2, we obtained a model (^{th} order polynomial curve with two relative maxima and a minimum, characterising a fault. This curve allows −5.72 mgals for minimum and maximum 3.81 mgals north; a

relative maximum variable 9.54 mgals south. The terrain model which follows from the gravity profile is a four lithologic units model.

Body 1

Its 2.75 g/cm^{3} density is characteristic of gneiss outcrops in southwestern Baugogo. Further, the same area flushes with ancient syntectonic granites formations in the south.

Body 2

With 2.6 g/cm^{3} density, it can be associated to late syntectonic granite met in the heart of Baugogo. The E-trending fault in the W region, as prortrayed in the gradient observed above 3˚N parallel, can also correspond to a discontinuity or lithological contact between the gneiss and late granite.

Body 3

It has 2.7 g/cm^{3} density and it is associated with anatexic granites met mostly in the heart of Batouri. The overlap between the late syntectonic granites of Baugogo anatexites and granites south of Batouri would be a flaw. Additionally, an anomaly gradient observed around SN parallel 4˚N may clearly highlight a fault between Southern and Northern Batouri-Baugogo.

Body 4

Whit 2.65 g/cm^{3} density, it can be associated with shale encountered at northern Gwé. The discontinuity observed in this model is probably the lithological contact between the granites and Batouri schists observed in the Moundia area, as shown by the gradient observed around the parallels 4˚50'N. The flaw characterized by the gradient observed between E-W direction and Baugogo-Batouri has a depth of nearly 2800 m and the upper roof of the fault would be deeper than 800 m.

In profile P1, we obtained a model which is defined by a 4^{th} order polynomial, more spread that the curve displayed in profile P2. This curve allows

for minimum-4.47 magls and maximum 7.42 mgals on the south. The terrain modelled from the profile 1 exhibits three lithologic units (

Body 1

Density 2.75 g/cm^{3}, it is characteristic formations of gneiss with an average density of 2.8 g/cm^{3}. This seems to be gneiss unconformably laying on late syntectonic granites of the area. Note here that the linearly increasing gravity gradient in the E-W direction is observed above the 3˚N parallel. This model may correspond to a discontinuity or contact between the gneisses and granites.

Body 2

This body has 2.6 g/cm^{3} density and it can be associated to syn to late-tectonic granites met Bandongoue.

Body 3

With a 2.7 g/cm^{3} density, it can be associated to old syntectonic granites which outcrop mainly in Mbangou above the parallel of 4˚N. The discontinuity observed in this model is probably a contact between the granites of different ages. Note also that the N-S linear gradient identified around 4˚N parallel, precisely between north and south Guedal-Mbaorguéné identifies this fault E-W direction. Observed between the fault and Batouri-Gwé have a 2300 m depth.

In this study, we used the method of interpolation by the inverse square of the distance, a method that requires the introduction of a quantity called strictly positive smoothing parameter (smoothing factor), depending on data. As part of this study, it is δ = 45. Spectral analysis of data along the profiles P1 and P2 we were localized at 2.54 km and 1.66 km deep above the roof of the body and at 0.50 km, and 0.30 km respectively, the lower limit of structures responsible for major anomalies. The maximum depth of the sources detected in the P1 profile realized on the map of Bouguer is 8 km. Processing and modelling of gravity data from Batouri permitted us to get third order residual maps on which two profiles have been drawn to highlight subsurface structure models. These models are characterized by the thickness, density contrast, depth to the top, the geologic shape, the width and major tectonic unevennesses. Gravity profiles studied were interpreted into three or four terrain models. Structural analysis of models shows that the basement presents many intrusions responsible of the anomalies observed. High wavelength anomalies in the northeast Batouri are mainly due to schist or light granite intrusions. Light anomalies in the south of Baugogo can be related to a collapse of a terrain or the basement. The over thrust line between late syntectonic granites in the north Baugogo and anatexic granites in the south of Batouri, may be an E-W fault as suggested by S-N gravity gradient. The throw of this fault is 2800 m. Spectral analysis of data along profiles has permit to locate anomalies at 8 km, 2.5 km and 1.7 km depth.

Comments and suggestions by two anonymous reviewers greatly helped to improve the paper.

The authors declare no conflicts of interest regarding the publication of this paper.

Claude, N.P., Patrick, A.S., Igor, O.A.O.U., Arsene, M., Justine, Y., Daniel, N.J. and Didier, P.M.-M.A. (2021) 2.5D Crustal Models Derived from Analytical Polynomial Separation Technique and Spectral Analysis of Gravity Data with Their Probable Gold Mineralization Migrations (Batouri, SE-Cameroon). Advances in Remote Sensing, 10, 1-24. https://doi.org/10.4236/ars.2021.101001