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Journal ofAfrican Earth Sciences, Vol. 15, NO. 1, pp. 81-90,1992. 0899-536U92$5.00 + 0.00 Printed in Great Britain @ 1992 Pergamon Press Ltd

Mechanical behaviour of the beneath the Adamawa Uplift (, West ) based on gravity data

Y.H. POUDJOMDJOMANI, M. DIAMENT" and Y. bow""

Universid de Paris Sud, Lab. de Géophysique (URA 1369 du CNRS), Bat. 509.91405 Orsay CBdex France *IPG Paris, DBppartement des Observatoires, 4 place Jussieu, B89.75252 Paris Cedex 05, France **ORSTOM. Lab. de Géophysique, 72 route d'Aulnay, 93140 Bondy, France

(First received 25th September, 199l;,revised form received 27th April, 1992)

Abstract - The Adamawa massif in Central Cameroon is one of the African domal uplifts of volcanic origin. It is an elongated feature, 200 km wide. The gravity anomalies over the Adamawa uplift were studied to determine the mechanical behaviour of the lithosphere. Two approaches were used to analyse six gravity profiles that are 600 km long and that run perpendicular to the Adamawa trend. Firstly. the coherence function between topography and gravity was interpreted; secondly, source depth estimations by spectral analysis of the gravity data was performed. To get significant information for the interpretation of the experimental coherence function, the length of the profiles was varied from 320 km to 600 km. This treatment allows one to obtain numerical estimates of the coherence function. The coherence function analysis points out that the lithosphere is deflected and thin beneath the Adamawa uplift, and the Effective Elastic Thickness is of about 20 km.To fit the coherence, a load from below needs to be taken into account. This result on the Adamawamassif is of the same order of magnitude as those obtained on other African uplifts such as Hoggar, Darfur and Kenya domes. For the depth estimation, three major density contrasts were found the shallowest depth (4-15 km) can be correlated to shear zone structures and the associated sedimentary basins beneath the uplift; the second density contrast (18-38 km)corresponds to the Moho; and finally, the last depth (70-90 km)would be the top of the and denotes the low density zone beneath the Adamawa uplift.

INTRODUCTION Cornacchia et Dars, 1983; Reyre, 1984;Almeida The Adamawa uplift in Central Cameroon is a et Black, 1967;Louis, 1970, 1978).The active vol- volcanic dome which was formed during Tertiary cano on the Cameroon line is times together with other African uplifts: Darfur, where the last eruption occurred in 1982. Hoggar. Tibesti, Air (Fig. 1). The A Bouguer anomaly map of Cameroon, com- is located at the northeastern limit of the puted from ORSTOM data shows that the "Cameroonvolcanicline" which comprises a series Adamawa massif is characterized by a long wave- of Tertiary to Recent volcanoes from the Atlantic length negative Bouguer anomaly of about -120 island of Annobon to the Bambouto and Oku mgals (Collignon. 1968).Seismological studies (C. mountains in Cameroon. This volcanic line splits and L. Dorbath. 1984)revealed the presence of an into two branches at the north of Oku: one branch abnormal upper mantle beneath the Adamawa crossing the into eastem uplift. (Biu plateau), and the other branch running In this study, we interpret the gravity data: in eastward to the Adamawa plateau (Fig. 2). The order first to determine the mechanical behaviour Adamawa uplitt is an elongated feature of 200 km of the lithosphere by estimating the flexural rigi- wide. The origin of the volcanism on the Cameroon dity and thus the Effective Elastic Thickness of line is still a matter of discussion; for the conti- the lithosphere beneath the Adamawa uplift. The nental part of the line, 1) it has been proposed that approach used in this flrst part is the analysis of this volcanism was associated with intraconti- the coherence functionbetween the gravity and the nental hotspots (Fitton, 1980, 1983; Tchoua. topography. The results are compared to those 1974; Duncan, 1981);2) the volcanism could be obtained on the other African domes and some related to a rejuvenation of major faults that either continental areas using the same approach. exist before the opening of the South Atlantic Finally, we perform source depth estimations by a Ocean or are related to an early stage of the seafloor spectral analysis of the gravity data to flnd the spreading (Vincent, 1970: Mascle, 1976; depth of the major density contrasts.

81 QRSTOM Fonds Documentaire 82 Y. H. POUDJOMDJOMAM, M. DIAMENTand Y. how

Fig. 1. Location of volcanic domes in Northem and Central Afìica (redrawn from Brome and Fairhead, 1983). !o" -- __ __ - 9.L ADAMAW& GEODYNAMICAL CONTEXT IL---.-- n

Central Cameroon in Central Africa has been, affected by the Pan-African cycle (600 +lo0 Ma) which produced deformation, metamorphism and intrusion of abundant granitoids. During the stages of the Pan-African, important tectonic movements occurred by megashear zones orientated ENE- WSW from to Cameroon (Comacchia and Dars, 1983). During the initial phases of the opening of the south ()a series of sub- siding grabens and troughs filled in by sediments were formed: Benue in Nigeria-Cameroon, Doba, Fernando POO Bousso in Chad, Mbere-Dierem in south Adamawa. Some were also initiated (Ngaoundere, Abu Gabra and others). principe 9 A reactivation of the Ngaoundere rift occurred during Tertiary times, and so was the formation of o some Africanvolcanic domes asAdamawa, Darfur. Hoggar...( Brome and Fairhead, 1983) (see O 30kn Air, .AC::lY6 k-' ' ' ' Fig. 1). The Adamawa massif represents a post-

--L--.-.'------'-- - J------Cretaceous uplifted area at the north-eastem mt 1 of the Cameroon volcanic line. Flg. 2. Position of the Cameroon1 volcanic hein Africa. Some geophysical studies have been carried out Bouguer anomaly, of about -120 mgals and 200 on this domal uplift: b wide (Fig. 3).Following Brome and Fairhead's - Collignon (1968) showed that Adamawa is interpretation (1983).this anomaly is due to a low characterized by a long wavelength negative -density body in the upper mantle. Mechanical behaviour of the lithosphere beneath the Adamawa Uplift ... 83 8 9 10 11 12 13 14 15 16 17 14

13 13l4 tN

I? 12

11 11

10 10

9 9

8 8

7 7

6 6

5 5

4 4

3 3

2 2

1 1 8 9 10 11 12 13 14 15 16 17 O 500 km

Fig. 3. Bouguer anomaly map of Cameroon (Collignon. 1968) and location of the six profiles used in this study. Note the long wavelength Bouguer anomaly on the Adamawa massif. 84 Y. H. POUDJOMDJOMANI, M. DIAMENTand Y. how - Using seismic refraction data and teleseismic loads. Therefore, topography and gravi@ are not delay times, Dorbath and Dorbath (1984) studied correlated and thus the coherence is close to O. the structure of the and upper mantle - Finally, if the plate has a non zero rigidity beneath the Adamawa uplift. They found an ab- (Te > O), loads are compensated at long wave- normally thin crust (23 km)underlain by an upper lengths (coherence close to 1)and uncompensated mantle with anomalously low P-wave velocity at short wavelengths (coherence close to O). The (7.8 km.s-l) for the northem margin of the uplift. wavelength of the transition from compensated to The southern part is characterized by a crust with uncompensated topography provides a direct esti- a normal thickness (33 km) and a normal upper mation of the flexural rigidity and thus of the mantle P-wave velocity (8.0 km.s-l).According to effective elastic thickness, since the flexural rigi- these results, the lithosphere is revealed as thin in dity and the EET (Te) are related by: the northern part of Adamawa where the rocks are essentially volcanic. E Te3 D= ( 1) COHERENCE FUNCTION ANALYSIS 12 (142)

The method where E is the Young's modulus = 10" Nm-l, Our aim is to study the mechanical behaviour of u denotes the Poisson's ratio = 0.25 the lithosphere beneath the Adamawa uplift by determining its effective elastic thickness (EET). To compute the coherence, it is possible to use Model interpretations of the coherence function in either a 2d or a 3d approach according to the terms of the flexural rigidity of the lithosphere structure to be studied. In our case, since the commonly assume that the lithosphere is deform- Adamawa is an elongated feature, we used a 2d ed by the application of surface loads (McKenzie approach. and Bowin, 1976; Banks et al., 1977; McNutt and An estimation of the coherence is given by the Parker, 1978;Loudenand Forsyth. 1982; McNutt, following formula (e. g. Bendat et Piersol, 1986): 1983). Forsyth (1985)studied the importance of surface and subsurface loading on the determination of the flexural rigidity of the lithosphere for conti- nental regions. He showed that the coherence function is, as compared to the admittance func- where B(k) and G(k) are the Fourier transform for tion (Lewis and Dorman, 1970; McNutt and topography and gravity respectively. Parker, 1978).the best way to quantlfythe flexural * is the complex conjugate sign and the angle rigidity of the lithosphere in continental areas, brackets denote the averaging in the spectral since the interpretation of the admittance function domain over a series of profiles. leads to underestimates of the effective elastic Munk and Cartwright (1966) showed that this thickness of the lithosphere (see Forsyth, 1985; estimation of the coherence could be affected by Cochran, 1980). in the presence of sub-surface noise in the data sets. So they suggested to com- loads. This approach has been later on widely used pute the coherence using the formula: in continental areas and proved to be efficient. Moreover, several results were obtained in Africa: , Banks and Swain (1978);Bechtel et a¿.(1987) for (3) the Kenya dome: Lesquer et aL (1988) for the Hoggar massif; Jallouli (1989)for the Air massif; Bonvalot (1990) for Fouta-Djalon (see Fig. 1 for where n is the number of profiles and Co(M is the location of these features). coherence defined by equation (2) The coherence function quantifies the relation- We also estimated the error on each value of ship of the topography and the Bouguer anomaly coherence using the following equation (Bendat in a given area as a function of wave number. Its and Pierso1,1986): shape is controlled by the rigidity of the plate: - If the plate is weak (Te --> O),a load from below produces a topographic dome and a surface load creates a compensation root, The coherence is thus close to 1. This feature corresponds to the classical Airy model. The data - If the plate is rigid (Te -> =), there is no The data used in this study were acquired by compensation of the surface and (or) subsurface several surveys carried out by ORSTOM (France) Mechanical behaviour of the lithosphere beneath the Adamawa Uplift ... 85 in Cameroon between 1960 and 1967.From these Figure 4 shows the six resulting profiles. This data, we computed six proflles oriented N-S and figure reveals that there is generally a good nega- running perpendicular to the Adamawa trend tive correlation between gravity and topography. (Fig. 3). The locations of the proflles were chosen This correlation was also pointed out by Okereke such that they are as close as possible to the (1984).For example, the mean Bouguer gravity is original data. For each point of a profile, Bouguer close to -100 mgals (200 km wide) over the anomaly and topography values were obtained by Adamawa plateau where the average topography interpolation applying a least square method of all is nearly loo0 metres above mean sea level. the original points contained in a given radius of We computed the Fourier transform of the data 20 lan around the computed point. Each proflle is using an algorithm which does not require a 600 km long and the sampling interval is equal to number of points as a power of two. "lho treat- 6 Inn. ments were checked to minimize the edge effect:

Profl: Bouguer and Topography Prof4: Bouguer and Topography B -1

30- O F -300 o -680

7 \- -900 v - 1200 100 260 3dB 4bß 500 600 Distance (Km) Distance (Km)

Prof2: Bouguer and Topography Prof5 Bouguer and Topography S 1588 1

O

c v - 1200 Distance (Km) Distance (Km)

Prof3: Bouguer and Topography - Prof6: Bouguer and Topography

Topography Bouguer

I-._'

\-- -\- --* i! vi! 600 I ,.. - --)

Distance (Km) Distance (Km) Fig. 4. Plot of the six profiles with the topography and the Bouguer anomaly. ,

86 Y. H. POUDJOMDJOMANI, M. DIAMENTand Y. ALBOW mirror imaging and derivative (Diament, 1985). The observed coherence was fitted to some pre- Due to the finite length of the data in the spatial dicted coherence curves with dffEerent elastic thick- domain, the coherence function that is computed nesses and load ratio values (subsurface versus in the frequency domain has a sampling interval surface load) to find the elastic thickness of the given by 1/ 1and is theoretically defined up to the lithosphere for Adamawa region. The best fit is Nyquist frequency (N/2 1) with 1is the length of the obtained for an Effective Elastic Thickness of 20 profile and N the number of points. The transition km and a load ratio f = 0.8. The flexural rigidity is from one to zero for the coherence function lies at thus of about O.7*1Oz3 Nm (Fig. 61. 100 to 200 km. Therefore, it is controlled by very It is known that the Effective Elastic Thickness of few points especially since the estimation of the a lithosphere increases with increasing plate age. coherence function at short wavelength is biased Since continents are on average very old, the by noise. Thus, to get significant information of the thermal effect is not so apparent as that of oceanic experimental coherence function, we varied the plates (e. g. Watts et al, 1980),and the elastic plate length of the profiles from 320 to 600 km taking thickness is caused by massive failure in the lower care that the Adamawa massif was well centered. continental crust. Nevertheless, the values of the This treatment allows us to get better results than Effective Elastic Thickness in continental areas the usual approach does. Figure 5 shows the generally vary from 25 to more than 100 km (see computed coherence for the six profiles and for McNutt et al., 1988). But for domal uplifts and several lengths. continental rift areas, the Effective Elastic Thick- ness is lower and close to 30 km. The Effective RESULTS AND INTERPRETATION Elastic Thickness obtained in this study for the Adamawa region lies in the range of values found Both treatments of the edge effect give similar for thermal domes (seeTable 1).On the other hand, results. As predicted, three main wavebands can some preliminary studies were carried out on this be distinguished: uplifted area. Indeed, Girod ( 1984) analysed some - the long wavelength domain ( 1 > 300 km); the mantle rocks from volcanic pipes in south coherence is very close to 1.0 Adamawa. He found that the rocks were essential- - the short wavelength. band (1 < 100 km) where ly made of peridotite and plagioclase developed in the coherence approaches 0.0 temperature and pressure conditions that corres- - the wavelength of the transition from coherent pond to less than 25 km depth. We can recall that to incoherent topography and gravity Occurs in the Le Marechal (1970) studied some thermal pheno- same range as the transition from compensated to mena beneath the Adamawa uplift. uncompensated topography (100 < 1 < 300 km). The value of the load ratio (f = 0.8) means that the This wavelength of the transition is well controlled subsurface load, produced by abnormal mantle due to the numerous estimations of the coherence beneath the Adamawa region, is slightly less than obtained by varying the length of the profiles. the topographic load. This is probably due to volcanism. To better constrain the depth of the low Wavelength < km) density zone, inferred from interpretation of the 1.2r 600 300 200 WO 120 100 long wavelength Bouguer gravity anomaly by J

.O1 .O2 .O? .O1 .r15 .O6

Waver iiinibe r (Kin - ' !

Fig. 5. Observe coherence for the Adamawa region versus the Fig. 6. Fit of the observed coherence (the symbols) with some wavenumber. The empty symbols indicate the points obtained predicted coherence curves (Forsyth, 1985). The numbers with a large error band. The edge effects here were avoided by denote different values of Effective Elastic Thickness. The best a mirror imaging treatment (coherence: eat 600 km length, fit is obtained for an EET equal to 20 km and thus a flexural + at 480 km, at 430 km, A at 360 km, and I at 320 km). rigidity of about 0.7*lom Nm. Mechanical behaviour of the lithosphere beneath the Adamawa Uplift ... 87 Table 1. EffectiveElasticThicknesses for some rifts and domes. al to the depth to the top of the body. Name of the Effective elastic Reference To estimate the source depth from this power region thickness (km) spectrum, we used the approach proposed by K. I I I I Dimitriadis et al. (1987).After the logarithm of the power spectrum is plotted versus the wave num- ber, the depth is estimated using a linear regres- sion method. For each window, we selected the proper linear segments: the depth to the source for the specific window and the corresponding rms error is evaluated. This error is estimated accord- ing to the points which define the segments chosen. We used the same slx profiles as for the cohe- rence function analysis. To solve the leakage pro- blem, we applied three windows on the profiles: Hanning, Blackman-Harris and the Kaiser-Bessel windows and we also used a mirror imaging treat- Browne and Fairhead (1983). we performed a ment. We chose these windows because they are spectral analysis of our profiles. characterized by a highly concentrated central lobe and a very low sidelobe structure (Harris, SPECTRAL ANALYSIS AND 1978). SOURCE-DEPTH ESTIMATION Fig. 7 shows, for one of the six profiles, the plot of the logarithm of the power spectrum versus the To estimate the depth to the major density con- wave number, using the fourtreatments. Each plot trasts within the lithosphere of the Adamawa can be approximated by three main straight line plateau, we applied spectral analyses to Bouguer segments. And we can estimate the source depth gravity data. This method has been widely used by using the slopes of those segments. Table 2 lists, several authors (e. g. Spector and Grant, 1970;Pal, for each window and for each profile, the depth to Khuruna and Unnikrishvan. 1979). the source and the corresponding rms error. It Spector and Grant (1970)showed that ifS(t)is a should be noted that for some treatments (e.g., series of N sampleswith a constant step intervalat. mirror imaging),the second segment and the cor- the discrete Fourier transform of this series is responding source depth are not resolved. given by: Table 2 shows that the source depth estimations N using the four treatments are within a few lan. To select the most reliable values, we checked the S(k) = 1/N c S (t).exp(-2flkt/N) (6) t=O windows with synthetic data by constructing a gravity model with a body at a given depth. We thus k = O, ....N-1 computed the corresponding gravity anomaly produced by this body, and, using this anomaly, The power spectrum is thus: we computed the source depths for the four treat- ments. The method which provided the best result, identical to the synthetic model, was the Kaiser- Bessel window. Therefore, we selected the source The fft algorithm is normally used for infinite depths obtained with this window, as shown on record processing. For finite length series as it is Fig. 8 for profiles 3 and 4. the case here, the periodic extension of the signal - The first line on the figures dominates the low exhibits discontinuities at the boundaries of the wave numbers (k e 0.02 km-’)and the calculated observation. These discontinuities are responsible depth (hl)is of about 70 to 90 km. for spectral leakage as it was the case for the - The second segment dominates the mid-wave coherence function analysis. To suppress the leak- numbers (0.02 e k e 0.06) with a depth (h2) in the age problem, it is common practice, to window the range of 18 to 38 km. data, and soreduce the order of the discontinuities - Finally, the third straight line occupies the high on the edge of the records to be analyzed. For this wave numbers (k > 0.06) and the corresponding purpose, several windows are proposed by Harris depth (h3) is between 4 and 15 km. (1978). The power spectrum shows frequency These values of the depth source are of the same intervals where the logarithms of the amplitudes order as those obtained by Fairhead and Okereke may be represented by a linear function of fre- (1988)using a grid of gravity data on the Adamawa quency. The slope of the straight line is proportion- region. The calculated depths are in good agree- 88 Y. H. POUDJOMDJOMAM, M. DIAMENTand Y. how

Profile 4 mirror "h Profile 3 Kaiser-Bessel I

L o L W

-151 I *--r---I I I I I 0.00 0.02 , 0.b4 9.06 0.08 0.10 0.12 -15 1 0.00 0.02 0.04 0.06 0.08 0.10 15j Wavenumber (1 /km) 151 Wavenumber (1 /km) 12 Profile 4 Black-Harris 9 "i Profile 4 Kaiser-Bessel I 6 I

Q0 ol o -3 -I -6

-9

-12

-151 L I I I I 0.00 0.02 0.04 @.'si, 0.h @.Il0 0.\2 Wavenumber (1 /km) 151 Profile 4 Hanning Fig. 8. Depth estimations for pmffles 3 and 4 with the Kaiser- Bessel treatment; hl for the deepest density contrast, h2 the hl transitional density contrast and finally h3 the lower depth. O L ment with some seismological studies that have ;3 been carried out on the region. a0 The shallowest depth (4-15 lun) agrees with the ol depth of inferred shear zone structures beneath o -3 -1 the Adamawa uplift and the associated sedi- -6 mentary basins (Mbéré-Djerem) by Cornacchia -9 and Dars (1983).Furthermore, Stuart et al. (1985) -12 pointed out that the limit between the upper and the lower crust is located at about 10 to 14 km -15 0 2 depth. i 15 The depth between 18 and 38 km corresponds to 12 the crust-mantle interface which. as proposed by Profile 4 Kaiser-Bessel 9 Dorbath and Dorbath (1984).varies from 23 to 33 km for the northern and the southern parts of the 6 I Adamawa massif respectively. And finally, we interpret the deepest density $3 a0 contrast (70to 90 km) as the low density zone of ol thermal origin which gives the low value of o -3 -I Effective Elastic Thickness forthe Adamawa massif.

CONCLUSION

-12 \* Our results reveal that the mechanical litho- ' @.Ile ' ,.\,sphere is thinbeneath the Adamaw amassif. The -15 ' 0.~2 i @.la4 @.bb ' Wavenumber (1 /km) computed Effective Elastic Thickness is about 20 Fig. 7. Plot of the power spectrum versus the km.This value of the EET is of the same order of wavenumber for profde 4 and different treatments. magnitude as those obtained for the other h\frican Mechanical behaviour of the lithosphere beneath the Adamawa Uplift ... 89 Table 2. Source depth estimations (km)for the six proaes and for different treatments

hl=64f0.8 I hl=66f1.8 i hl=56f1.6 I hl=85f6.4 Proa 1 h2 = undet. I h2 = 17 It 0.5 h2 = undet. I h2 = 38 It 1.0 h3 = 7f 0.6 h3 = 5 f 0.2 I h3 = 6.550.3 h3 = 4f 0.1 ------~'-----~------~------hl = 87 f 4.5 hl = 68 f 2.0 hl = 71 f 3.0 hl = 74 f 6.0 h2 = undet. h2 = 17 f 0.8 h2 = undet. h2 = 34.8 f 0.6 h3 = 12 f 0.2 ------h3 = 10f 0.3 ------h3 = 9 f 1.6 ------h3 = 6 f 0.3 hl = 90f 2.6 hl = 66 f 2.5 hl = 82 f 1.7 hl = 78 f 6.5 h2 = undet. h2 = 32 f 0.3 h2 = 43 f 0.7 h2 = 33 f 0.8 h3 = 6 f 0.5 h3=5f0.1 h3 = 4 f 0.6 h3 = 4 f 0.6 I I I I hl=82f7.1 I hl=62f1.8 I hl=71f3.1 hl = 70 f 2.7 proa 4 h2 = 36 f 5.2 I h2 = 31 f 0.3 I h2 = 43 f 0.7 h2 = 27 f 0.6 -----~-----~-----t------I h3 = 7 f 0.1 h3 = 8 f 0.6 h3 = 9 f 0.6 ------h3 = 7 f 0.6 I hl=50f1.4 I hl=50f3.8 I hl=77f1.3 I hl=79f1.3 Profd5 I h2=undet. I h2=30f 1.3 I h2=undet. I h2=undet. ----- Lh3-----= 7 f 0.1 I, -----h3 = 10 f 0.1 L ------h3 = 4.5 f 0.3 I h3 = 15 f 0.6 I hl =44f6 I hl=78f2.4 I hl =71f1.3 I hl=76f1.8 Profil 6 I h2=20*0.4 I h2=26f0.5 I h2=45f1.0 I h2=25f0.4 I h3=4fO.1 I h3=8f0.2 I h3=4f0.6 I h3=9f0.2 I I I I uplifts (Air, Hoggar, Darfur, Fouta-Djalon) and versus regional mechanisms. Ceophgs. J. R. Astron some continental rift areas (Kenya, Baikal). Thus, Soc. 51. 431-452. this favours the idea that the African uplifts were Banks, J. and Swain, C. 1978. The isostatic compensa- formed by similar processes. tion of East Africa. Proc. R. Astron. Soc. Ser. A 364. The spectral analysis allows us to locate three 331-352. Bechtel, T. D. D., Forsyth, D. W. and Swain, C. 1987. major density contrasts. These depth estimations Mechanism of isostatic compensation in the vicinity of are in good agreement with seismological studies. the EastAfrican rift, Kenya. Ceophys.J. R.Astron. Soc. The shallowest depth (4-15 Inn) agrees with the 90, 445-465. seismic limit of the upper and lower crust (10-14 Bendat. S.. Piersol. A. G. 1986. Random data: analysis km)as proposed by Stuart et al. (1985).The second and measurement procedures, second edition, Wiley density contrast (18-36 lan) corresponds to the ed., 566 p. Moho (Dorbathand Dorbath, 1984).Finally, the 70 Bonvalot. S., 1990. Mesures gravimétriques en Guinée to 90 km depth is interpreted asthe depth of a zone et Sierra-Leone. Modélisation structurale et étude du of partial melting producing the volcanic activity comportement mécanique de la lithosphère: étude beneath the Adamawa massif. This depth cor- d'une chaîne péricratonique. dun bombement intra- responds to the top of the upper mantle that was plaque et de marges transformantes. Thése Universite proposed by and L. Dorbath (1984) to be ab- Paris W. C. Browne. S. E. and Fairhead. J. D. 1983. 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