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The present study aims to estimate the basement depth and contact locations, deduced from the available aeromagnetic data. The total intensity aeromagnetic (TMI) map was fi rst corrected by the application of the reduction to equator technique. Different edge detection processes, for example, tilt angle derivative (TDR) and its total horizontal derivative (HD_TDR) as well as 3D-Euler deconvolution can determine the edges of these sources. These techniques were carried out on the aeromagnetic data of Minta region (the study area). A correlation was noticed between these techniques indicating that both of them can be attributed in delineating the general structural framework of the area. The aeromagnetic data analysis enables to highlight many deeply-seated structural features trending in the E-W, ENE-WSW and NE-SW directions in this region. The E-W trend is more strongly developed than the other identified trends. Moreover that, two depth methods were applied: analytic signal (AS) and source parameter imaging (SPI). They r efl ected similar results for estimating the basement depths. From both of them the depth ranges from 150 to 2800 m. Five methods (TDR, HD_TDR, 3D-Euler deconvolution, AS and SPI) for locating magnetic sources indicated that the depth of the basement rocks range d between 150 and 3000 m as the average range. Also, the comparative study among the 2D magnetic modeling was established by one profile constructing.

The magnetic method is one of the most commonly used geophysical tools. This stems from the fact that magnetic observations are obtained relatively easily and cheaply and few corrections must be applied to the observations. The aim of a magnetic survey is to investigate subsurface geology based on anomalies in the Earth’s magnetic field resulting from the magnetic properties of the underlying rocks. The magnetization of rocks and associated remanence is affected by deformation, tectonism, magmatism and metamorphism hence they reﬂet geological processes [

The area that is the subject of our study is east of Yaoundé (Central Cameroon). It covers the portions of the departments of Haute Sanaga (capital city Nanga Eboko) in the central region, Nyong and Mfoumou (capital Akonolinga) in the Central region, and Upper Nyong (capital city Abong-Mbang) in the Eastern Region. The area under study has a relatively monotonous relief, with an altitude which is between 600 m and 700 m. Our survey area is crossed on the north by the Sanaga River flows in a sinisteral ductile fault oriented N70E and corresponds to a westward extension of the Bozoum fault-N’délé located in the Central African Republic [

1) The Northern Cameroon Supergroup (NCSG) consists of metase-dimentary rocks known as the Poli Group which is associated with subordinate 830 Ma-old volcanics of fault and alkaline affinities (

2) The Southern Cameroon Supergroup (SCSG) is subdivided in two domains by the Sanaga Fault (

The study area situated at the east of Yaounde (

formations, ancient syntectonic granite, is represented in the north of the region, in Ngobadé. It is a heterogeneous granite, both in structure and texture, and in its mineralogical composition: the dominant type is a calc-alkaline granite. The granodiorite massifs in the south of Nkoambang and north-east of Ovong are well individualized in the middle of metamorphic rocks: the rock is granular and contains, among others, andesine, very ferriferous biotite and hornblende. The metamorphic series of Nanga-Eboko constitutes the substratum of the study area: the series is strongly folded and the dips are very variable, which does not allow to easily reconstruct the stratigraphy and the tectonics of these formations [

The tectonic evolution of the area was affected by the Pan-African tectonothermal event which is characterized by a polyphase deformation with the stages D_{1} - D_{4} as reported by [_{1} predated emplacement of calc-alkaline dioritic bodies and caused the formation of nappes that resulted in high-pressure granulite metamorphism of soft sediments. A strong overprinting of these nappes during D_{2} symmetric extension, probably associated with large-scale foliation socking and (or) gneissic doming and intense magmatic underplating, gave rise to regional flat-lying fabrics. The latter were further buckled by D_{3} and D_{4} folding phases defining a vertical constriction occurring with a major east-west to NW-SE shortening direction. The corresponding F_{3} and F_{4} folds trend north-south to NE-SW and east-west to NW-SE, respectively, and represent the main regional strain patterns. Based on the east-west to NW-SE maximum shortening orientation indicated by F_{3} folds, it is proposed that the nappe-stacking phase D_{1} occurred in the same direction.

The key component of this study involved image enhancement of existing aeromagnetic data sets acquired by the company SURVAIR (contractor) for the CIDA (client) in 1970. The survey was carried out in a nominal field clearance of 235 m which was monitored by a radar altimeter with an accuracy of ±20 m. The line spacing of the flight was 750 m but the real distance rarely went above 1 km and the flight direction was N-S. After correction of the measurements for the temporal variations of the magnetic field, the total magnetic intensity map of the study area is obtained with the inclination and declination angles of the ambient −15.92˚ and −5.73˚ respectively, in January 1970 according to IGRF.

In geomagnetic methods the shape of magnetic anomalies due to vertical bodies depends on the inclination and declination angles of the geomagnetic field. In the north and south magnetic poles the main field plunges vertically and magnetic abnormalities have a symmetric shape, with the maximum or minimum located directly over the causative magnetic body. At low magnetic latitude (between 15˚S an 15˚N), it is not very easy to correlate the observed abnormal maxima and the positions of sources since magnetic signature of magnetized bodies at low latitudes always have two extreme values because of their bipolar nature. To remove this effect, as the name suggests, the reduction to the pole (RTP) transforms the data to the signal that would be measured at the magnetic poles [

TDR and THDR_TDR are used for mapping shallow basement structures and mineral exploration targets [

TDR = tan − 1 VDR THDR (1)

where VDR is the vertical derivative and THDR is the total horizontal derivative.

i.e.:

TDR = tan − 1 ( ∂ f ∂ z ( ∂ f ∂ x ) 2 + ( ∂ f ∂ y ) 2 ) (2)

The Tilt derivative (TDR) is similar to the local phase but uses the absolute value of the horizontal derivative in the denominator. Due to the nature of the arctan trigonometric function, all amplitudes are restricted to values between +π/2 and π/2 (+90˚ and -90˚) regardless of the amplitudes of VDR or THDR [

[

THDR_TDR = ( ∂ TDR ∂ X ) 2 + ( ∂ TDR ∂ Y ) 2 (3)

The total horizontal derivative of the tilt derivative (THDR_TDR) is independent of geomagnetic inclination like to the analytic signal (AS). The difference between these derivatives is that the former is sharper and generates better-defined maxima centered over the body edges. Another advantage of this independence, that it will generate useful magnetic responses for bodies having induced or remnant magnetization, or a mixture of both [

Some authors [

A ( x , y , z ) = ∂ f ∂ x i → + ∂ f ∂ y j → + ∂ f ∂ z k → (4)

where i ⇀ , j → and k → are unit vectors in the x , y and z directions, respectively, ∂ f ∂ y is the vertical derivative of the magnetic anomaly field intensity, ∂ f ∂ x and ∂ f ∂ y are the horizontal derivatives of the magnetic anomaly field intensity. The amplitude of the analytic signal in 3D is given by:

| AS | = ( ∂ f ∂ x ) 2 + ( ∂ f ∂ y ) 2 + ( ∂ f ∂ z ) 2 (5)

AS simplifies the magnetic signal of anomalies by centering anomalies over the magnetic body as well as, having peaks over the edges of wide bodies. Thus, a simple relationship between the geometry of the magnetic bodies and the transformed data are observed. The magnetic sources depths using the magnetic method are estimated from the ratio of the total magnetic AS to the vertical derivative analytic signal (AS1) of the total magnetic field.

AS1 = ( ∂ f v ∂ x ) 2 + ( ∂ f v ∂ y ) 2 + ( ∂ f v ∂ z ) 2 (6)

On the maximum amplitude:

D = AS AS 1 × N (7)

where f v is the first vertical derivative of the total magnetic ﬁeld, and D is the depth to the magnetic body, N is known as a structural index and is related to the geometry of the magnetic source. For example, N = 4 for sphere, N = 3 for pipe, N = 2 for thin dike and N = 1 for magnetic contact [

Euler deconvolution’s technique is an equivalent method based on the Euler’s homogeneity equation as developed by [

∂ f ∂ x ( x − x 0 ) + ∂ f ∂ y ( y − y 0 ) + ∂ f ∂ z ( z − z 0 ) = SI ( B − f ) (8)

where f is the observed field at location (x, y, and z) and f is the base level of the field [regional value at the point (x, y, z)] and SI is the structural index or degree of homogeneity. Therefore, we have assigned a value of 1.0 as a structural index to locate the possible magnetic contacts because it is particularly good at delineating the sub-surface contacts. We used an overlapping moving window of 10 km by 10 km, a tolerance of 15% and a proportioned symbol base of 235.

This method developed by [

k ( x , y ) = ∂ 2 f ∂ x ∂ y ∂ f ∂ x + ∂ 2 f ∂ y ∂ z ∂ f ∂ y + ∂ 2 f ∂ 2 z ∂ f ∂ z ( ∂ f ∂ x ) 2 + ( ∂ f ∂ y ) 2 + ( ∂ f ∂ z ) 2 (9)

For the dipping contact, the maxima of k are located direct over the isolated contact edges and are independent of the magnetic inclination, declination, dip, strike and any remnant magnetization. The depth is estimated at the source edge from the reciprocity of the local wavenumber, as follows:

Depth ( x = 0 ) = 1 k max (10)

where k max is the peak value of the local of number k over the step source.

The present total intensity aeromagnetic (

530,000 m and 520,000 m latitudes. These circular trends with large magnitudes suggest the presence of highly magnetized cylindrical intrusive bodies within the basement. The map illustrates a large positive magnetic zone located to central part. Another positive magnetic anomaly is located at the western part of the map (at Bana), which attains amplitude of +120 nT and trends along E-W attitude. The correlation of TMI anomalies map and geological contact is weak. It is noted that the positive anomalies are limited to the west by a weak gradient (quasi-horizontal gradient) showing the intensity of the geological formations overlaping. The Bana-Okaa region is formed by a bipolar anomaly: a negative pole in Bana with a long wavelength of 44.4 km and negative amplitude of −201.86 nT, and a positive pole in Akaa with a high amplitude of +120 nT and wavelength of 54.6 km. In the Minta zone, there is also a horizontal gradient of oblong and NW-SE direction that seems to correspond to the Nkoambang-Nguelemendouka tectonic line highlighted on the geological map.

The total Intensity Magnetic Map (

minimum values in the TMI-RTE map have reduced to +66.60 nT and increased to −208.73 nT. From Ovong to Bibé, positive TMI anomalies have shifted slightly vertically to the north. On the other hand, from the southwest to the west of the study area, the anomalies preserve generally their forms compared to TMI. The circular magnetics trends in the south of N’Djombe persist. On the TMI-RTE map, the study area can be subdivided into fourth magnetic zones, each having a unique magnetic anomaly pattern (

The first zone occupies the north-eastern (at Nguiwass), south-western (at Bana) and south (Ovong) parts of the area and is underlain by the Precambrian crystalline basement rocks (migmatites, especially embrechites, quartzite in embrechite). It is characterised by very low, Broad and elongate wavelength (low wavenumber) anomalies with magnetic intensity amplitude varying from -208.73 to −78.44 nT (light and dark blue colors). The second zone occupies the west (north of Akaa), south-central (Mbaka-Tombo), north-west (Nkondo) parts of the area. It is underlain by the ectinites of the old metamorphic series of Nanga-Eboko (especially quartzites with minerals in the west part, feldspathics micaschists in the north part and schisto-quartz group of Akonolinga in the south-central). It exhibits high (positive) anomalies: amplitudes of the magnetic intensity in this zone range from +66.60 to +90 nT (magenta and red colors). The third zone occurs within the part of the area underlain by gneiss with two micas at Angossa II. It displays relatively low (negative) to moderate (positive) magnetic anomalies. Amplitudes of the magnetic intensity in this zone range from −54.32 to + 4.80 nT (green ligth and yellow ligth) (

The TDR_TMI-RTE analysis of [

A total horizontal derivative filter was applied to the tilt derivative of the TMI-RTE grid data to generate the THD_TDR anomaly map (

source [

The amplitude of the analytic signal depends very little on the direction of magnetization [

Minta north of the study area, they are found in the south of the area in Bana and Mbaka. The map of the first vertical derivative for the TMI-RTE (

Euler’s deconvolution is one of the most reliable methods for obtaining depths under cover. In this investigation, ED solutions were calculated for IS = 1 for

thin-layer boundary (sill, oblique intrusive vein, banded iron formation, etc.) or faults [

and 2273.68 m. The non-uniformity of the depths of said contacts in the area suggests that all the outlines of the box do not have the same origin. These solutions are trending in E-W, ENE-WSW and NE-SW directions.

On Euler’s solutions map, the limits of the faults intrusive bodies are perfectly distinguished. To the north, at Ngobadé in the granites; in the center, between Nkoambang and Nguélémendouka; in the south, at Angossas II, the shape of the Euler solution groupings would characterize the limits of the intrusive bodies in the basement, whereas the straight and continuous alignment of the Bibé, Minta, Efoulan and Mbaka solutions would, on the other hand, characterize the normal faults hidden in the covers.

An interpretative structural map has been drawn from maps of

The analysis of the interpretative structural map of study area shows four predominant structural trends having variable intensities and lengths. These are the E-W, ENE-WSW and NE-SW trends, representing the most predominant

tectonic trends affecting the investigated area as deduced from the magnetic point of view. The relationships among these trends suggest that, the area was subjected to more than a single tectonic event. Vertical accidents characterized by nearly rectilinear solutions have NE-SW directions at Okaa, E-W at Nkondon, Ovong. The deepest accidents are of E-W main directions with depths of over 2300 m and are in Efoulan, Lembé and Tombo. The folding system-oriented E-W to NE-SW, are in accordance with the directions highlighted in geological investigations focused the Awaé-Ayos strike-slip shear zones (southern Cameroon): Geometry, kinematics and significance in the late Pan-African tectonics by [_{2}, characterized by folds (S_{2}), foliation (F_{2}). At the regional scale, the near surface NE-SW contacts who represent the regional deformation events D_{2} (compression) and D3 (wrenching) may correlate with the development of the Centre Cameroon Shear Zone witness by the Foumban Shear Zone.

The tectonic features put in evidence have linkages with faults and folds lines-oriented E-W, ENE-WSW and NE-SW, as identified by geophysical surveys carried out in gravity [

The Source Parameter Imaging (SPI) module of the Oasis Montaj software was applied to the TMI data of the study area. The SPI (Source Parameter Image) method is a technique for calculating source depths from magnetic data. It is a tool based on the extension of the complex analytic signal to estimate magnetic depths [

The SPI depth map (

Theory and application modeling the source body of this study was performed

by the Oasis Montaj’s GM-SYS module 8.3 that permits forward modeling of magnetic data to obtain the optimal fit of the generated source model to the observed data. GM-SYS is based on the algorithms described by [

Using the available geologic information and the results of qualitative and quantitative interpretation of magnetic maps; basement structural cross-section is constructed along this profile to initiate modeling. The profile AB were chosen and drawn on the TMI-RTE map (

This study is based on the analysis and interpretation of aeromagnetic data to define the subsurface basement depth and contacts location’s inference of the study area. First, the Total Magnetic Intensity Map reduced to the equator (TMI_RTE) is used to locate the magnetic anomalies directly above their causative sources. This map reveals various causative sources, as well as varying

depths and compositions, with different anomalies of varying frequencies and amplitudes. The tilt angle derivative (TDR) was used to locate the edges of this TMI-RTE. Positive values should be located above the magnetic sources while negative values are located away from them. The half distance between ±π/4 (±0.785) Radian was used to calculate the depth to these edges. By applying [

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was carried out at the University of Yaoundé I, Cameroon, as part of first author’s Ph.D. studies. The authors are thankful to the anonymous reviewers for their thorough comments which enabled to improve the initial version of this paper.

Mono, J.A., Ndougsa-Mbarga, T., Bi-Alou, M.B., Ngoh, J.D. and Owono, O.U. (2018) Inferring the Subsurface Basement Depth and the Contact Locations from Aeromagnetic Data over Loum-Minta Area (Centre-East Cameroon). International Journal of Geosciences, 9, 435-459. https://doi.org/10.4236ijg.2018.97028