Choice of Suitable Regional and Residual Gravity Maps, the Case of the South-West Cameroon Zone

Earth and Planetary Physics RESEARCH ARTICLE 3: 26–32, 2019 SOLID EARTH: GEODESY AND GRAVITY doi: 10.26464/epp2019004 Choice of suitable regional and residual gravity maps, the case of the South-West Cameroon zone Fidèle Koumetio1*, Donatien Njomo2, Constant Tatchum Noutchogwe3, Eric Ndoh Ndikum4, Sévérin Nguiya5, and Alain-Pierre Kamga Tokam2 1Department of Physics, Faculty of Science, University of Dschang, PO Box 67 Dschang, Cameroon; 2Department of Physics, Faculty of Science, University of Yaounde I, Cameroon; 3Department of Physics, ENS Bambili, University of Bamenda, Cameroon; 4Department of Fundamental Sciences, H.T.T.T.C. Bambili-Bamenda, University of Bamenda, Cameroon; 5Department of Physics, Faculty of Genial Engineering, University of Douala, Cameroon Abstract: The quantitative interpretation of gravity anomalies due to shallow structures needs separation between long wavelength anomalies (regional anomalies) and short wavelength anomalies (residual anomalies). The regional-residual field separation can be carried out using the polynomial method. In this case, the so-called regional field of order n is treated as a polynomial of degree n. The present study shows that the degree n must vary between a smallest value nmin and a maximum value nmax. This article presents a method to process gravity data that allows determination of nmin and nmax for a given study area. We apply the method to gravity data of the South-West Cameroon zone. In this chosen study area, we find that regional anomaly maps of orders ranging from 1 to 9 and residual anomaly maps of orders ranging from 1 to 8 can be used for suitable interpretation. The analyses show that one may need residual anomaly maps of several orders to perform satisfactory quantitative interpretation of the different intrusive bodies found in a given area. Keywords: gravity; regional anomaly; residual anomaly; upward continuation; correlation factors; intrusive body Citation: Koumetio, F., Njomo, D., Noutchogwe, C. T., Ndikum, E. N., Nguiya, S., and Tokam, A. P. K. (2019). Choice of suitable regional and residual gravity maps, the case of the South-West Cameroon zone. Earth Planet. Phys., 3(1), 26–32. http://doi.org/10.26464/epp2019004 1. Introduction is evident that the best anomaly map for quantitative interpreta- On a Bouguer gravity anomaly map, gravity effects of shallow in- tion of a given geological structure is that which amplifies its grav- trusive bodies are often masked by the influence of structures that ity effects to their maximum. Thus, one may need residual anom- are located deeper in the crust and generally of larger size. In such aly maps of several orders to perform comprehensive quantitat- cases, it is possible to separate the gravity effects of the deep ive interpretation of the different intrusive bodies found in a giv- structures contained in regional anomaly maps and the gravity ef- en area. At the same time, for a given study area, a maximum fects of superficial structures contained in residual anomaly maps. value nmax has to be assigned to the order n of regional field; this This regional-residual field separation can be carried out using the means that any residual field of order n ≥ nmax is unusable be- polynomial method (Agocs, 1951; Abdelrahman et al., 1985; cause of high noise level. In consequence, only residual and re- Radhakrishna and Krishnamacharyulu, 1990) in which the so- gional fields of orders ranging from nmin to nmax can be exploited called regional field of order n is treated as a polynomial of de- in a credible way. Having said this, the following question arises: how can nmin and nmax be determined for a given study area? gree n. We can determine the smallest value nmin of the order of the residual field for which all the gravity effects of deep struc- In this article, we describe a method to process gravity data which tures are eliminated leaving only those of all intrusive bodies and we suggest will allow determination of nmin and nmax for a given other superficial structures. However, it is generally observed that study area. the residual of order nmin does not amplify, to its maximum, the gravity effects of all the intrusive bodies. For a given area, the 2. Regional-Residual Separation gravity effect of an intrusive body, c1, can be amplified to its max- Regional-residual separation of gravity anomalies was performed imum by the residual of order n1 while that of another intrusive using the polynomial method. The idea was to build a polynomial body, c2, is amplified to its maximum by the residual of order n2. It of suitable degree that generates an analytical area that fits the experimental surface by the least squares method (Agocs, 1951; Correspondence to: F. Koumetio, [email protected] [email protected] Abdelrahman et al., 1985). This analytical surface represents the Received 07 AUG 2018; Accepted 04 DEC 2018. regional field. In practice, the so-called regional field of order n is Accepted article online 28 DEC 2018. treated as a polynomial of degree n. At a point (x, y) on the sur- ©2019 by Earth and Planetary Physics. face, the regional field of order n can be written as (Radhakrishna Earth and Planetary Physics doi: 10.26464/epp2019004 27 and Krishnamacharyulu, 1990) and the Canadian Scintrex (n° 305G) gravimeters. The measure- Xn Xp ments were connected to the gravitational bases of the ORSTOM Fn (x;y) = CmAm (x;y); (1) base network in Africa, known as the Martin network (Duclaux et p=0 q=0 al., 1954). The gravity values were measured with an average pre- cision of 0.2 mGal. The error on the coordinates of most stations where C is a real coefficient, A (x;y) = xqyp−q and for every pair m m was around 0.1 minute, and varied from 0.1 to 1 minute for some of points (p, q), m = ½ [p (p + 3)] – q + 1; with the maximum value hard-to-reach stations, i.e., approximately 200 to 2000 m. This er- of m being ½ (n+1) (n+2). ror was less than 200 m for coordinates measured by GPS. A Let G (x, y) be the value of the anomaly at a chosen point with co- Bouguer reduction density was 2.67 g/cm3. The reference system ordinates (x, y) on the surface; then the least square method gives: chosen was the IGSN71 (International Gravity Standardization Xn 1=2(nX+1)(n+2) Xn Network 1971). The data acquired by ORSTOM were attached to G (xi;yi):Ak (xi;yi) = Cm Ak (xi;yi):Am (xi;yi); the reference system of Postdam 1930. In order to maintain ho- i=1 m=1 i=1 mogeneity, all the compiled data were converted into the IGSN71 (2) system. The distribution of points of measurement of gravity is shown in Figure 1. where k = 1, …, ½(n+1)(n+2). By developing equation (2), ½ (n + 1) (n + 2) equations are ob- 10°E 11°E tained which allow for the determination of ½(n + 1)(n + 2) coeffi- 4°N LOG BADJEK cients Cm. Fn(x, y) can then be calculated using equation (1) and NGOG MAPUBI the residual of order n deduced by POUMA MATOMB R (x;y) = G(x;y) − F (x;y): (3) EDEA n n ESEKA The calculations were done using the Fortran 77 program "POLY- N DEHANE FIT" (Radhakrishna and Krishnamacharyulu, 1990) that generates NGOMEDZAP the n-degree polynomial, and establishes and solves the system of LOLODORF linear equations to determine the coefficients Cm of the polynomi- BIPINDI al. It then gives the values of the regional and residual anomalies at each point where a Bouguer anomaly is defined. When n is 3°N KRIBI small, the regional anomaly has values with a relatively large devi- AKOM II EBOLOWA ation from those of the Bouguer gravity anomaly. Gradually, as NYETE the order of the polynomial increases, the regional anomaly gets closer to the Bouguer gravity anomaly, favouring the identifica- AMBAM tion, with the corresponding residual anomalies, of the structures MA′AN 0 20 100 km that are increasingly close to the surface Figure 1. Distribution of gravity measurement points. 3. Choice of Regional and Residual Anomaly Maps In this section, we select regional and residual anomaly maps that 3.1 Determination of nmin can serve as the basis for a credible analysis of the geological structures of a particular basement. We then describe a method to The smallest value nmin must correspond to the order of the residual field that fully captures the gravity effects of all the intrusive process these gravity data that allows the determination of nmin bodies of the study area. The upward continued field at optimum and nmax, and we apply our method to gravity data of the South- West Cameroon zone, which lies between latitudes 2°24′N–4°08′N height (Zeng HL et al., 2007) gives the regional field in which the and longitudes 9°55′E–11°30′E. These gravity data were first col- gravity effects of all intrusive bodies are eliminated. To determine lected during gravity surveys of Central Africa by ORSTOM (Col- nmin, we use the analytical method based on the minimum square lignon, 1968). They were later completed by surveys of Princeton deviation between the regional field and the upward continued University in 1968, University of Leeds in 1982, IRGM and Uni- field at the optimum height ho. We explain this method below, versity of Leeds between 1984 and 1988 (Poudjom-Djomani et al., after briefly discussing the upward continued field at different 1996). The data acquisition campaigns were carried out using cars, heights and describing our procedure for determining ho (Figure 2).

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