Gravity studies have been carried out in the Douala sub-basin which is a sedimentary basin located both onshore and offshore on the South coast of Cameroon between latitudes 3 ° 03'N and 4 ° 06'N and longitudes 9 ° 00' and 10 ° 00'E, covering a total surface area of 12,805 km2. On its onshore portion, the Douala sub-basin has a trapezoic shape and covers a total surface area of about 6955 km2 while the offshore part covers an area of about 5850 km2. Gravity data used in this study are constituted of 912 gravity data points located between longitudes 8 ° 10.2' to 10 ° 59.4'E and latitudes 2 ° 30.6' to 4 ° 59.4'N and the study area is located to the NW section of the onshore portion of the Douala sub-basin. This study area is characterised by considerably high positive anomalies attaining peak values of about 104.1 mGals at longitude 9 ° 9.9' and latitude 4 ° 1.1' with contour lines which are mostly oriented in the NNE direction. Residual anomalies were extracted by upward continuation of the Bouguer anomaly field at an optimum height of 30 km. This residual field and those obtained by the separation of polynomial of order 4 had a very high correlation coefficient factor of 0.979. The multi-scale horizontal derivative of the vertical derivative (MSHDVD) method was applied on the extracted residual anomalies for the delimitation of possible contacts in the source while the amplitude spectrum was used to estimate the depth to the top of the potential field source. The MSHDVD method did not delimite any clear cut contacts in the source but the amplitude spectrum estimated the potential field source at a depth of about 4.8 km. The ideal body theory was used to determine the density contrast along a 65 km NW-SE profile yielding a value of 0.266 g/cm3. 2.5D modelling aimed at bringing out the underlying structural layout of this study area presents a source body which is very probably an intrusive igneous block surrounded by sedimentary formations and having a density of 2.77 g/cm3 at a depth of about 5.88 km below the surface and an average thickness of about 26.95 km.
Two major basins make up the Cameroon Atlantic basin localized in the Gulf of Guinea which is one of the West African coastal basins, they are: the Douala/Kribi-Campo basin and the Rio Del Rey basin [
The Douala sub-basin is located between the Cameroon Volcanic Line (CVL) [
The gradual North-South opening of the South Atlantic is linked to the formation of the Douala sub-basin, which resulted in the diachronism of deposits from South to North and a temporal and spatial variation of sedimentary environments along the West African coast [
It is worth noting that the structural dynamics that led to the formation of the sedimentary basin of Douala/ Kribi-Campo like other basins of the West African coast has resulted in the sequence variability of deposits by sector considered. Moreover, many of the works carried out in this sub-basin are unpublished because of the known confidentiality characterizing the oil research domain [
In this study, gravity data has been processed for 2.5D models to bring out the underlying structural layout of the NW onshore portion of the Douala sub-basin characterized by strong positive Bouguer anomalies (
The Douala sub-basin is a sedimentary basin which lies both onshore and offshore on the South coast of Cameroon between latitudes 3˚03'N and 4˚06'N and longitudes 9˚00'E and 10˚00'E, covering a total surface area of 12,805 km2 (
The Douala sub-basin has a basic stratigraphy which is interpreted to comprise of pre-rift, rift, transition and drift megasequences related to the tectonic evolution over African cratonic basement and associated Atlantic margin. The regional stratigraphy and tectonics can be summarized in four main phases of evolution related to pre, syn and post-rift separation of Africa from South America [
The Douala sub-basin has a lithostratigraphy which consists of seven major Formations related to its geodynamic and sedimentary evolution [
Syn-rift rocks are known to exist in the Rio Muni, Douala, and Kribi-Campo Basins of Equatorial Guinea and Cameroon (
The oldest post-rift rocks in the Douala sub-basin (as well as in the Kribi-Campo, and Rio Muni Basins), are represented by mid-Aptian organic-rich shales, marls, and sandstones [
The evaporites and interbedded lacustrine shales thin northward and have not been penetrated by drilling in the northernmost part of the Douala sub-basin. However, diapiric evaporites were penetrated in the Kribi Marine-1 well in offshore Cameroon [
Middle Albian to Cenomanian cyclic, shallowing-upward units of oolitic limestone and calcarenite from 5 to 15 m thick make up the shelf-carbonate rocks in the Rio Muni Basin [
Progradational marine sedimentation that included the development of several Tertiary deltas, especially those of the Niger and Congo Rivers in the Niger Delta Province and West-Central Coastal Province, respectively, dominated the Cenozoic sedimentation. Resulting from this progradational phase was the deposition of regressive sandstones and siltstones, turbidites, and deep-marine shale units during the Paleocene and Eocene. In the Douala sub-basin, calcareous mudstones and marls were deposited in the Paleocene and Eocene [
The Douala sub-basin is larger than the Rio del Rey basin, and contains a more continuous stratigraphic section. Continental basal Cretaceous sands are overlain by shallow marine limestones, sandstones and shales of Late Cretaceous, Palaeogene and Neogene ages. At the western margin of the basin these formations are overlain by basaltic lavas from the Cameroon volcanic centre. When traced offshore the sedimentary formations thicken markedly, with evidence for over 7 km of subsidence since the middle of the Cretaceous Period. There are more sands and fewer shales than in the Rio del Rey basin, and growth faulting and diapirism due to overpressured shales are largely absent [
Products of volcanism (Miocene) are known to cover sediments in some area (e.g. Volcanic products of Mount Cameroon) [
The Cretaceous break-up of Gondwana and the separation of Africa from South America gave rise to the development of the Douala sub-basin. The initial rifting phase may have started during very Early Cretaceous time (Berriasian-Hauterivian) but the principal rifting episode in these areas occurred from late Barremian-Aptian time. During the late Aptian-late Albian interval, it is believed that the initial formation of oceanic crust began as the continents separated. The rifting would appear to have been asymmetrical, as many of the syn-rift features that would normally be expected are not apparent at depth in this area, whereas they are abundant in the corresponding South American segment. Several additional tectonic events occurred during the passive “drift” phase of the continental margin evolution at 84 Ma (Santonian), 65 Ma (Cretaceous/Tertiary boundary) and 37 Ma (late Eocene). These events, resulting in uplift, deformation and erosion at the basin margins, are generally attributed to changes in plate motion and intraplate stress fields due to convergent and collision events between Africa and Europe. The Santonian uplift and possibly the late Eocene events also appear to have resulted in significant mass wasting of the continental margin by gravity sliding, contributing towards reservoir formation. The final uplift event relates to the growth of the Cameroon Volcanic Line (CVL) and effectively lasts from 37 Ma through to present day on the northwest margin of the basin [
The gravity data set used in this study is constituted of 912 gravity data points located between longitudes 8˚10.2' to 10˚59.4'E and latitudes 2˚30.6' to 4˚59.4'N. The study area is the onshore portion of the Douala sub-basin which lies between longitudes 9˚ and 10˚ and latitudes 3.05˚ and 4.1˚; it contains about 116 gravity data points (
The Kriging method was applied on the gravity data for interpolation to obtain a 100 by 100 square grid having spacings of 0.0285 in longitude axis and 0.0250 in latitude axis. The Bouguer anomaly map (
The different sources beneath the study area which characterize the Bouguer anomaly map can be identified by generating the residual field from the observed gravity field. This residual field is the result of estimating and extracting the more uniform regional field caused by sources situated at very great depths due to long wavelength anomalies of a regional scale across the entire area from the Bouguer anomaly field. The residual field is produced from more localised sources with short wavelengths which usually are found at shallow depths. The regional and residual fields were separated from the observed field by using the upward continuation method and also the analytical method by least squares, which generates the closest possible mathematical surface to the experimental surface [
Since the gravity field obeys Lapace’s equation, it is therefore possible to apply continuation to it which is a process that permits the determination of a field over an arbitrary surface if the field is known completely over another surface and no masses are located between the two surface [
Upward continuation is an operation that shifts the data by a constant height level above the surface of the earth (or the plane of measurement). It is used to estimate the large scale or regional (low frequency or long wave length) trends of the data [
Upward continuation can be formulated thus:
where
The empirical method of [
· Obtaining the upward continuation of Bouguer anomalies at heights from 5 to 120 km, by 5 km intervals.
· The calculation of correlation factors
where
· Plotting the correlation factor as a function of increasing continuation height by making each correlation factor correspond to the lower of the two successive heights (
In the analytical method by least squares, the regional field of order
A maximum correlation factor of 0.978581453 was obtained for an order of
The obtained residual field has been interpolated using the Kriging method to yield a 100 × 100 square grid with longitude and latitude spacings of 0.0285 and 0.0250. A residual field plot with a contour interval of 5 mGal was drawn from the grid (
This map presents our study area with the same characteristics as the Bouguer anomaly map but with picks of maximum value 90.02 mGals at longitude 9˚9.9' and latitude 4˚1' in the NW portion of the study area. This value is 14.09 mGal less than the peak value on the Bouguer anomaly map. The high gravity supposes a high density intrusive body in this zone which was studied along one profile (
sive body was determined by the ideal body solution.
The residual field obtained here (using the upward continuation method which has been shown to be equivalent to the residual field from the analytical method of order 4) will be studied using the multi-scale horizontal derivative of the vertical derivative (MSHDVD) method (employed for the analysis of the multi-scale vertical derivative), the ideal body solution method, the spectral analysis method and the 2.5D modelling method in order to bring out the nature of the intrusive body.
The vertical and/or horizontal derivatives of gravity fields have been used to obtain source parameters when interpreting gravity data [
The MSHDVD method entails the following three steps:
1) Calculating the first-order vertical derivative for upward continued gravity field at different heights, called here the MSVD (multi-scale vertical derivative);
2) Determining the maxima of the horizontal gradient of the MSVD;
3) Superposing the maps obtained for different continuation heights.
In this study, the method of finite differences proposed by [
The vertical derivative
where
The first-order vertical derivative of the gravity field was therefore obtained at heights of 5, 10, 15, 20, 25 and 30 km.
The (local) maxima of the horizontal gradient of the vertical derivative
The Blakely and Simpson [
These maxima of horizontal gradient determined from the vertical derivative of the Bouguer anomalies were superimposed to give the plot on the map in
This plot does not contain any emphasis of quasi-linear contacts, which can describe faults and quasi-circular contacts corresponding to horizontal limits of intrusive bodies. It can therefore be considered that no fault lines cut across this zone; but the presence of local maxima spread across the region can suggest the presence of a body with horizontal variation in surface height but whose boundaries extend beyond this zone of study or which lies on a broader body of similar density.
The program Fourpot version 1.3 [
along rings with radius
transform of the potential field in the frequency domain.
The amplitude spectrum was used to estimate the depth
Results of spectral analysis carried on the residual at upward continued height of 30 km suggest that the depth of the potential field source is about 4.8 km. This can be seen on
The theory of ideal bodies was originally developed by Parker [
solution with the smallest possible maximum density which greatly helps in the fundamental problem of non-uniqueness encountered in the interpretation of gravity anomaly data even when the solution set is bounded by physical or geologic constraints.
The basic philosophy behind this theory is that when a data set admits an infinite solution set, as the case is with potential fields like the gravity field, properties common to all solutions are sought and as such definite information about the unknown true solution is derived.
For gravity data specifically, bounds on the uniform norm or maximum absolute value of the density contrast of the source were treated by Parker. When a data set and a region in which a source is confined are considered, there exists a unique solution with the smallest possible uniform bound. This source is attributed the term “ideal body” for all possible sources in that region of confinement and its norm is the greatest bound on the maximum absolute value of all sources fitting the data. Consequently, any solution (as well as true one) must somewhere reach or exceed this bound.
The theory of ideal problems has been applied to different disciplines like to gravity data [
Gravity ideal-body analysis is an excellent reconnaissance exploration tool because it is especially well suited for handling sparse data contaminated with noise, for finding useful, rigorous bounds on the infinite solution set, and for predicting accurately what data need to be collected in order to tighten those bounds [
Analytical solutions for ideal bodies can only be constructed for two data [
In this study, the program, IDB2 developed by Huestis and Ander [
The program IDB2 was used in an initial run such that the ideal body touches the bottom of the volume (this is the point at which any further increase in depth does not change the ideal body and the value of the density contrast).
This indicates the greatest lower bound on the density contrast of the source which is equal to 0.266 g/cm3 (see
From this point, the maximum allowable thickness of the body is confined such that it reduces systematically. The values of increasing density contrasts are plotted for corresponding decreasing values of thickness on the first tradeoff curve (
The top of the confining region is then pushed down below the surface while not bounding the bottom of the ideal body from below. The top is pushed down until the density far exceeds any geologically reasonable density contrast. The values of density contrasts obtained are plotted against values of depth to top of body to give the second tradeoff curve (
2.5D modelling was carried out on the residual field obtained in this region along the NW-SE profile (PP’) aimed at bringing out the structure of the intrusive body contained below this study area.
The program GRAV2DC [
To the left of this major block is a very thin elongated block of density contrast 0.266 g/cm3 at a depth of 6.8 km overlying another thin block of density 0.106 g/cm3. Similarly, to the right of the major block is another very thin elongated block of density contrast 0.266 g/cm3 at a depth of 5.3 km overlying another thin block of density 0.0617 g/cm3.
The high gravity values noticed in the NW portion of the area studied in this work on both the Bouguer anomaly and the residual anomaly maps (
In this study, gravity data have been processed for Bouguer anomaly and residual fields in the NW portion of the Douala sub-basin along a 65 km NW-SE profile (PP') using the method of upward continuation with correlated results from the polynomial analytical method. 2.5 D modelling on data along this profile was carried out by considering the results obtained from spectral analysis, the multi-scale analysis of the maxima of gradients, and the inverse method of the ideal body solution as constraints; this 2.5 D modelling presents a source body which is very probably an intrusive igneous block in a sedimentary background having a density contrast of 0.266 g/cm3 and consequently a density of 2.77 g/cm3 when the average density of the surrounding sedimentary rocks is taken to be 2.5 g/cm3. The inclusion of more data points in the data used in this work which will lead to a reduced spacing between data points and the application of other methods of survey like the seismic method will surely bring in more details and information concerning the structure of the underlying intrusive igneous body in this region.
The very useful technical assistance of Ngatchou Evariste and the insightful contributions of Alain-Pierre K. Tokam which have led to the considerable amelioration of this work and the eventual realisation of this paper cannot be over emphasized. They are deeply acknowledged.