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Dynamic interactions between the Gulf of Guinea
passive margin and the Congo River drainage. Part II :
Isostasy and uplift
F. Lucazeau, F. Brigaud, Pascale Leturmy
To cite this version:
F. Lucazeau, F. Brigaud, Pascale Leturmy. Dynamic interactions between the Gulf of Guinea passive margin and the Congo River drainage. Part II : Isostasy and uplift. Journal of Geophysical Research, American Geophysical Union, 2003, 108 (B8), 2384, pp.1-19. �10.1029/2002JB001928�. �hal-00067787�
Dynamic interactions between the Gulf of Guinea passive margin
and the Congo River drainage basin:
2. Isostasy and uplift
Francis Lucazeau
Laboratoire Ge´osciences Marines, UMR 7097, Institut de Physique du Globe de Paris, Paris, France
Fre´de´ric Brigaud
Total E&P Norge AS, Stavanger, Norway
Pascale Leturmy
De´partement des Sciences de la Terre, Universite´ de Cergy-Pontoise, Cergy-Pontoise, France Received 15 April 2002; revised 14 April 2003; accepted 18 April 2003; published 16 August 2003.
[1] The Gulf of Guinea continental margin is paralleled by a coastal relief that isolates
the Congo drainage basin and can play a subsequent role in interactions between margin deposits and continental denudation: Migration of depocenters from the Ogooe and Kwanza Rivers to the Congo fan in the Oligocene, low present-day sediment delivery, or Pleistocene submarine channels instabilities are possible evidences for this interaction. In order to test this hypothesis, we examine successively margin isostasy, regional uplift, erosional unloading and flexural bulge created by sediment loads. Satellite free air gravity and two-dimensional thermomechanical modeling, including depth of necking, are used to determine the structure of continental margin and strength conditions for two selected sections across South Gabon and Congo fan. Both verify similar conditions for extension geometry, depth of necking (10 – 20 km) and strength (equivalent elastic thickness of 20– 30 km); differences in observed gravity are explained mainly by differences in sediment volumes. Regional uplift during Miocene of at least 450 m is attributed for both continent and margin, as evidenced by the elevated base level of the Congo drainage basin and the uplift of shelf break and coastal plains. Topography corrected for regional uplift, valley erosion below relics surfaces, and corresponding erosion unloading has been determined as a proxy of Oligocene topography; it shows a typical rift shoulder topography isolating Congo drainage basin from margin. In such conditions, small-amplitude flexural uplift related to sediment loads can possibly have negative feedbacks for both Oligocene and present time. INDEXTERMS: 1815 Hydrology: Erosion and sedimentation; 1824 Hydrology: Geomorphology (1625); 8105 Tectonophysics: Continental margins and sedimentary basins; 8122 Tectonophysics: Dynamics, gravity and tectonics; KEYWORDS: isostasy, mass balance, thermomechanical modeling, continental margins, Africa
Citation: Lucazeau, F., F. Brigaud, and P. Leturmy, Dynamic interactions between the Gulf of Guinea passive margin and the Congo River drainage basin: 2. Isostasy and uplift, J. Geophys. Res., 108(B8), 2384, doi:10.1029/2002JB001928, 2003.
1. Introduction
[2] Important accumulations of sediments along
conti-nental margins are the expression of surface erosion processes within drainage basins and transport by rivers. Present-day sediment discharge by rivers has been statis-tically correlated to local relief or to tectonic uplift rate [Anhert, 1970; Pinet and Souriau, 1988; Summerfield and Hulton, 1994], but the Congo (Zaire) River discharge seems anomalously low with respect to other large
drain-age basins [Milliman and Syvitski, 1992] and to the sediment volumes Leturmy et al., 2003]. Depocenters have migrated along the Gulf of Guinea passive margin, from the mouths of Ogooe and Kwanza Rivers during upper Cretaceous to that of the Congo during Tertiary [Leturmy et al., 2003], as an evidence for some instability in the drainage system. Furthermore, observations on the turbi-dite system of the Congo deep-sea fan [Babonneau et al., 2002; Savoye et al., 2000] show unusual incision of the present-day channel, and alternation of constructive and erosive episodes for at least ten generations of Pleistocene deep-sea fan channels [Turakiewicz, 2001; M. Lopez, University of Montpellier, personal communication, 2001]; this later unstable behavior is not likely due to
Copyright 2003 by the American Geophysical Union. 0148-0227/03/2002JB001928$09.00
climatic fluctuations because Amazon deep-sea fan chan-nels are conversely all constructive [Lopez, 2001], and because climatic short timescales are probably buffered in large alluvial basins [Me´tivier and Gaudemer, 1999].
[3] On the other hand, Gulf of Guinea is paralleled by a
coastal relief that isolates internal drainage basins (Figure 1): some of them remain endoreic (Chad, Okavongo); others are connected by a narrow valley to the marine domain (Congo River). Origin for this coastal relief is not estab-lished clearly, but might be the principal cause for a present deficit of sediment and observed instabilities of the turbi-dite system, and for migration of Depocenters at geological timescale if recurrent vertical displacements exist. A first possible genetic explanation for that coastal relief corre-sponds to the preservation of an initial rift topography. The nature and architecture of synrift sediment packages along continental margin [Karner et al., 1997] argue for such a significant topography (1.5 – 2.0 km), but present morphol-ogy is not typical rift morpholmorphol-ogy. An alternate hypothesis for this coastal relief origin corresponds to marginal denu-dation of a preexisting plateau [Gilchrist and Summerfield, 1990; Rust and Summerfield, 1990; Van der Beek et al., 1999]: combined effects of differential denudation, escarp-ment retreat, and flexural isostasy can explain important morphologic aspects or fission track chronology. Local base level around 500 m in most of the Congo drainage basin [Leturmy et al., 2003] and stratigraphic observations on the coastal plains of the Gulf of Guinea passive margin [Karner et al., 1997] argue for such a plateau type uplift, but there are many lines of evidence that this uplift is recent: subsidence in central Congo basin was almost continuous from Paleozoic to Tertiary [Lawrence and Makazu, 1988],
Cenomanian marine surfaces are preserved [Sahagian, 1988], truncation of Cretaceous to Paleocene series on the coastal plains of associated passive margin requires about 500 m uplift since early Miocene [Karner et al., 1997], shelf break has been uplifted since early Miocene by the same order of magnitude [Lavier et al., 2001] and plateau topography is not supported isostatically at long wave-lengths [Hartley et al., 1996] but dynamically in the lower mantle [Lithgow-Bertelloni and Silver, 1998]. Regional uplift occurred therefore later than migration of depocenters and cannot be considered as a possible driving mechanism. In this context, interactions between migrating sediment loads in the Gulf of Guinea [Leturmy et al., 2003] and drainage system that provide these loads may be also considered. Such interactions are related to a possible flexural bulge that forms at some distance of the sediment load if the lithosphere has some rigidity. Magnitudes of such uplift is not that important (several tenths of meters), but as it acts in the downstream part of rivers, it can contribute to changes in the drainage pattern. This mechanism has been proposed for the West Indian continental margin [Whiting et al., 1994] and for the Amazon margin [Driscoll and Karner, 1994].
[4] However, possible interactions with this coastal relief
involve flexural isostasy and lithospheric rigidity. If the lithosphere is not rigid enough, this mechanisms is not possible. Conversely, if the lithosphere is too much rigid, it results in too small amplitudes for a significant potential bulge. The transition zone between a demonstrably rigid craton in central Congo [Hartley et al., 1996] and a possibly low rigidity passive margin [Watts and Steward, 1998] is therefore critical for the interaction between drainage and Figure 1. Perspective view of the Congo River drainage basin and the Gulf of Guinea. Color scales
represent topography on shore and total sediment thickness off shore. Limits of the internal drainage (Congo River) and the coastal drainage (Ogooe River and Kwanza River) are also figured. River network extracted from the GTOPO30 digital elevation model is shown in blue.
sediment loads. In this paper, we investigate to what extent coastal relief is genetically related to development of the Gabon-Angola passive margin evolution and/or erosion of continent, and how it can interact with the drainage basin organization. Therefore we first develop an analysis of the mechanisms of isostasy on the margin domain and then identify the different contributions to uplift of the coastal domain.
2. Isostatic Modeling
[5] Because oceanic and continental lithospheres have
finite strengths, loads applied to them lead to departures from isostatic equilibrium at some wavelength that depends on the magnitude of flexural rigidity. Therefore bending response related to finite loads is commonly used to estimate that property of the lithosphere. When loads can be simply related to the variations of topography, correlation between topography and gravity are usually studied as a function of wavelength, and compared to theoretical func-tions. In Africa, different analysis has concluded that there is a very high rigidity associated with Precambrian shields [Hartley et al., 1996]: Equivalent elastic thickness (EET, related to the cubic root of flexural rigidity) has been estimated to be about 80 – 100 km below the Congo shield. In the oceanic domains, EET has been shown to follow a rather simple relationship with age of the lithosphere at the time of loading [Watts, 1978]; EET matches depth of an isotherm ranging between 300C and 600C. This is inter-preted as a consequence of temperature-dependent viscous dissipation at the lower levels of the lithosphere. For an oceanic lithosphere of Aptian age, such as ocean continent transition in the Gulf of Guinea, EET is about 30 km. In the domain between the Congo shield and Atlantic Ocean, and more generally in continental margins, discussions on the importance of lithospheric strength still exist, but it is often admitted that these domains are characterized by persisting low rigidity from rifting to mature stages of evolution [Fowler and McKenzie, 1989; Watts, 1988]. Along a seis-mic profile offshore Gabon, Watts and Steward [1998] have interpreted free air gravity in terms of two isostatic loads, one coming from sediment and the other one from litho-spheric necking during rifting, and they concluded that margin has always been weak (EET < 10 km) since the onset of rifting.
[6] This concept of lithospheric necking is important for
isostasy of rifts and continental margins, as it determines the initial configuration of the extended crust the effect of which persists as long as the lithosphere remains rigid. Braun and Beaumont [1987] have pointed out that during the rifting process, necking occurs around the level of maximum strength of lithosphere (or depth of necking (DON)), normally in uppermost mantle according to the traditional view of continental lithosphere rheology. Be-cause configuration resulting from necking is not equivalent to that for Airy isostasy and is not generally stable, restoring loads can persist as long as the lithosphere remains rigid. This can explain why flank uplifts occur in continental rifts [Braun and Beaumont, 1989; Che´ry et al., 1992; Kooi et al., 1992; Weissel and Karner, 1989] when restoring load is directed upward which can happen for DON deeper than 6 – 8 km (given parameters values). For shallower values
of DON, restoring loads are directed downward and model predicts no flank topography. Other important consequences of DON are the respective magnitudes of subsidence and Moho uplift for a given extension factor: shallow DON results in important Moho uplift but small subsidence, and conversely deep DON in small Moho uplift but large subsi-dence [Braun and Beaumont, 1989; Kooi et al., 1992]. For a specific rift or passive margin, it is therefore possible to determine DON from the knowledge of bathymetry, base of sediment and Moho depth [Keen and Dehler, 1997], but in most cases, Moho geometry is not known and DON can also be inferred from gravity modeling [Keen and Dehler, 1997; Kooi et al., 1992; Watts and Steward, 1998].
[7] Because DON is more or less related to thermal and
rheological conditions during rifting, and response of sed-iment loads to present-day conditions, isostatic analysis can provide good constraints on both stages. Different methods have been used to estimate DON and EET: the more simple is the one used by Watts and Steward [1998] consisting in backstripping the sedimentary load first for a given distri-bution of EET and then computing crustal structure for a given value of DON until a good agreement is obtained for gravity. In this paper, we include DON as a parameter of a more general model that calculates the evolution of temper-ature (including sediment tempertemper-ature), density and subsi-dence in response to a kinematics model of rifting. We chose two 1500 km sections across two characteristic gravity patterns of the Gulf of Guinea (Figure 2): the first one across the South Gabon passive margin (close to that modeled by Watts and Steward [1998]) and the other one across the Congo fan. Patterns of the two anomalies are different in that two high-amplitude negatives in South Gabon flank high-amplitude positive, whereas positive anomaly is larger and flanked by smaller-amplitude neg-atives in Congo. In both cases however, positive anomalies are located above the maximum sediment thickness.
2.1. Method
[8] The method is based on 2-D thermal modeling of a
margin evolution, prediction of flexural rigidity and related response to loads. Thermal modeling includes a 2-D finite element numerical model with a Lagrangian frame in such a way that crustal thinning, sedimentation, compaction, oceanic accretion are all taken into account by modifications of the mesh structure and mesh properties (Figure 3): parts of this model is explained in more detail by Latil-Brun and Lucazeau [1988] and in Appendix A. For the purpose of isostasy, present-day structure, density and temperature dis-tributions only are discussed here. Important aspects are density contrasts across the lithosphere including nature and compaction of sedimentary rocks, as well as overall density dependence on temperature. Additional aspect of the model is the variation of EET with temperature and/or plate curvature, to account for possible strength variations across the margin. An iterative procedure is used until calculated bathymetry matches observations with a maximum RMS of 100 m. We start from a crustal thinning distribution based on Airy type isostasy, and then progressively adapt these values to converge usually in about 10 iterations. DON is a constant parameter value as it describes supposedly the maximum strength of an initially homogeneous lithosphere at the time of rifting. Location of DON basically changes Moho shape
and can be constrained by gravity anomalies [Kooi et al., 1992; Watts and Steward, 1998].
2.2. Model Behavior With a Lithosphere of Constant Rigidity
[9] Conceptual behavior of the necking model has been
described in detail by Braun and Beaumont [1987] and Kooi et al. [1992]. The relevant point is that both DON and present lithospheric strength have a significant impact on Moho geometry for a given present-day basin geometry. This is illustrated in Figure 4, which shows on the South Gabon profile that the shallower the DON or the stronger the present-day lithosphere, the shallower the Moho below basin.
[10] In Figure 4 (left), the resulting present-day Moho
geometry is compared for a shallow DON = 6 km, which generates a downward isostatic restoring force, and a deeper DON = 35 km, which generates an upward isostatic restoring force. Both examples have a same constant
flexural rigidity (EET = 1023 N m). The deep DON
hypothesis results in a smoother Moho than the Airy hypothesis, and conversely the shallow DON hypothesis in a rougher Moho. In Figure 4 (right), the resulting present-day Moho geometry is compared for several strength values
of lithosphere (1021, 1023 and 1025 N m) given a constant value of DON (10 km). Present-day strength has a compa-rable effect on Moho geometry as DON; a high rigidity value increases roughness of Moho while a low rigidity decreases it. For low rigidity, Moho geometry also becomes closer to that obtained under local Airy assumption.
[11] The resulting gravity anomalies are therefore
signif-icantly different according to the different hypothesis for DON and strength. Three values of lithospheric rigidity (1021, 1023and 1025N m) and two values of DON (6 and 35 km) have been considered together with local Airy hypothesis, leading to seven different cases shown in Figure 5. High rigidity hypothesis (D = 1025 N m) results in inappropriate amplitudes and wavelengths in any cases. In the offshore domain, rigidity in the range 1021– 1023N m and DON = 35 km gives the closest match, while a shallower DON = 10 km is better for the onshore domain. However, other aspects such as variations of rigidity along the margin have to be considered for improving fit. 2.3. Variations of Rigidity Across the Margin
[12] Effects of composition (fault zones, preexisting
blocks) and temperature are primary causes for lateral Figure 2. Free air gravity anomalies in the Gulf of Guinea and western border of Africa from the global
satellite database [Sandwell and Smith, 1997]. The two modeled sections are shown as red lines.
Figure 3. Mesh and boundary conditions describing the numerical model of basin. Deformation is obtained by pure shear (columns remain vertical), but thinning of mantle d(x) and crust b(x) can be different. Depth of necking (DON) corresponds to a line of the mesh. Gray area corresponds to thinned continental crust, and black area corresponds to oceanic crust added on the right-hand side of the mesh. Sediments deposited on the top of oceanic and continental crusts correspond to new cells of the mesh. Additional cells are added at the bottom of lithosphere for accommodation of lithosphere thinning. Plate rigidity D(x) can vary along x axis. No heat flux is assumed across the vertical boundaries except when oceanic crust is generated (in that case, T = TLtemperature of asthenosphere). Lower and upper boundary
conditions are isothermal: T = Tsurfaceat the top and T = TLat the bottom of the box which represents the
stable lithosphere thickness.
Figure 4. Morphology of the South Gabon margin in the Gulf of Guinea according to different isostatic hypothesis. (left) Depth of necking (DON = 6 km and DON = 35 km) effect with respect to Airy hypothesis. (right) Effect of plate rigidity (1021, 1023, and 1025N m or corresponding EET 6 km, 28 km, and 130 km) for a given depth of necking (DON = 10 km).
strength variations in the lithosphere. As Atlantic rifting in the Gulf of Guinea has taken place on the Transamazonian and Pan African sutures [Teisserenc and Villemin, 1989], this domain was certainly weaker than the Achaean sur-rounding cratons of Brazil and Congo and probably still remains weaker at the present time, but this is difficult to consider a priori in modeling. On the other hand, effect of temperature variations across the margin as a consequence of variable thermal insulation by sediments and reduced radiogenic heat production in the extended crust can be considered; transient perturbations related to the initial anomaly created by rifting and oceanic accretion are here conversely negligible. Effect of temperature variations along the margin is shown in Figure 6b, which represents the depth of isotherms 400C and 600C for present time and at the end of rifting. At present time, maximum effect of strength reduction is observed at margin hinge (x = 1300 km on the diagram) where combined effects of sediment thermal insulation and lateral heat transfers related to conductivity contrast between crust and mantle are important. EET is reduced by 10 km only, but as rigidity varies with the cube of EET, this corresponds to a diminu-tion of strength by a factor 2. At the end of rifting, temperature increase in the most extended part of litho-sphere leads to a significant drop in EET (from 25 to 10 km for the depth of isotherm 400C and from 45 to 15 km for the depth of isotherm 600C, Figure 6b). This variation nevertheless improves fit of the offshore negative anomaly for DON = 35 km and EET = depth of 600C isotherm (Figure 6a). However, the onshore negative anomaly
remains compatible only with a shallow depth of necking. As Burov and Diament [1995] and Lavier and Steckler [1997] have proposed that EET can be reduced by inelastic behavior related to bending, we have investigated such consequences for Gulf of Guinea continental margin. We used the model of Lavier and Steckler [1997] that derives EET from calculation of YSE and plate curvature. YSE is derived from calculated temperature field and standard parameters for brittle yield limits and power law creep in crust and mantle [Kirby and Kronenberg, 1987], and plate curvature is calculated at DON level. Curvature is impor-tant in two places, below maximum sediment thickness and in coastal domain. This tends mainly to widen the zone of weakness with respect to that obtained with temperature effect only, but does not really improve the quality of the fit. At this stage, we consider therefore that EET is mainly described by depth of a given isotherm and conclude that the best fit DON in the offshore domain is deeper (35 km) than that in the near onshore domain (<10 km). This surprising result can be alternately explained if decoupling exists between margin and conti-nent during rifting, which is also implicit in the interpre-tation of Watts and Steward [1998], who included a low level of necking (7.2 km) that minimizes restoring forces and a very contrasted rigidity between offshore (EET < 10 km) and onshore (EET = 70 km). This decoupling zone could correspond to the Atlantic hinge proposed by Karner et al. [1997] that has been active during the second and third stages of extension (Hauterivian to early Aptian), with respect to an eastern hinge active in the first stage Figure 5. Comparison of observed free air gravity anomalies and model results for the South Gabon
modeled section. Observed data have been averaged within a 100 km wide band around the profile. Models have been obtained for the Airy hypothesis and for a set of DON values (10, 20, and 35 km) and plate rigidities (1021, 1023, and 1025N m).
(Berriasian). While this eastern hinge has demonstrably produced uplift, Atlantic hinge was accompanied by insignificant vertical displacement of the footwall [Karner et al., 1997]. In order to test such an interpre-tation, we introduce a discontinuity in the previous model at x = 1350 km that limits the effect of restoring forces on the western part of the Atlantic hinge (basin). Additionally, we account for possible variations of oce-anic crustal thickness (that was assumed to be uniform in previous models) interpreted as a faulted proto
oce-anic crust by Meyers et al. [1996]. Both modifications lead to a significant improvement of gravity modeling, mostly for DON = 10 – 20 km (Figure 7a).
2.4. Compared Gravity Results on South Gabon and
Congo Fan Sections
[13] The different gravity pattern across the Congo fan
can be interpreted either by a different morphology or by a different mechanical behavior [Watts and Steward, 1998]. Our results show that given the observed gravity range, the Figure 6. (a) Comparison of observed free air gravity anomalies and model results for the South Gabon
modeled section. Observed data have been averaged within a 100 km wide band around the profile. Models have been obtained for the Airy hypothesis and for a set of DON values (10, 20, and 35 km) and variable plate rigidities (EET varies as the depth of 400C or 600 isotherms). (b) Variation of EET (defined as depth of isotherm of 400C or 600C) along the South Gabon margin at the end of rifting and at present time.
best model is obtained for DON = 10 – 20 km and for EET corresponding to the depth of isotherm 400C (Figure 7b). On the other hand, DON = 35 km cannot produce reasonably high-amplitude anomalies at the right location (calculated positive anomaly is 10 mGal instead of observed 40 – 60 mGal). This result is not very different for what we obtained for South Gabon, within the same range of DON and EET values. Observed bathymetry (Figure 8a) and predicted thinning factor (Figure 8b) show that shelf break and crustal hinge are located in the same positions for Gabon and Congo; major differences concern offshore extension of
sediment in the Congo fan that makes slope more gentle than that of South Gabon, and crustal thickness more important in onshore South Gabon (and even more important that the reference value of 35 km we adopted, suggesting that under accretion or previous thickening affects this area as shown in Figure 9). The first difference explains why the offshore gravity low is not well marked, as the second one explains the difference for the onshore gravity low. On the other hand, our modeling does not predict a very important difference in rigidity; rigidity of Congo fan being a little bit more homogeneous than that of South Gabon.
Figure 7. (a) Free air gravity anomalies across the South Gabon margin for the Airy hypothesis and for different depths of necking DON (10, 20, and 30 km). Gray area represents the observation range with a 100 km wide band around profile. Equivalent elastic thickness varies along the margin according to the depth of isotherm 400C and variations of oceanic crustal thickness have been considered. (b) Free air gravity anomalies across the Congo fan for Airy hypothesis and for different depths of necking DON (10, 20, and 30 km). Gray area represents the observation range with a 100 km wide band around profile. Equivalent elastic thickness varies along the margin according to the depth of isotherm 400C and 600C.
[14] Within range of modeling uncertainties (3-D or edge
effects, basin geometry, etc.), both sections lead to a similar range of DON (10 – 20 km) and EET (depth of 400C isotherm, i.e., 20 – 30 km at present time and 10 – 20 km at the end of rifting). Most of previous studies on isostasy of continental margins have concluded for a shallow level of necking [Keen and Dehler, 1997; Lucazeau and Brigaud, 2000; Reemst and Cloetingh, 2000; Stewart et al., 2000; Watts and Steward, 1998], namely, in the upper middle crust (5 – 20 km), and in continental rifts such as lake Baikal, Van der Beek [1997] also proposes a value within middle crust (DON = 20 km). Keen and Dehler [1997] have observed a large range of DON values (3 – 25 km) that they related to the variable durations of extension that allow or not continental lithosphere to cool during rifting. In all cases, whatever the tectonic context (cratons or mobile belts), DON has been located within continental crust, and may support the idea that the continental mantle has little strength, unlike oceanic mantle [Jackson, 2002]. On the other hand, present-day strength has been inter-preted variably on passive margins. Watts [1988] and Watts and Steward [1998] proposed very low EET values (EET < 10 km) for the Baltimore canyon on the American east
coast and South Gabon, respectively, whereas Keen and Dehler [1997] for North Atlantic margins, Stewart et al. [2000] for Namibian margins, Lucazeau and Brigaud [2000] for Campos basin in Brazil, and Watts [2001] for the Mozambique margin have determined higher values (EET in the range 20 – 40 km). In the present study, our interpre-tation of South Gabon gravity differs sensibly from that of Watts and Steward [1998], who used a neutral DON value (DON = 7.2 km) and low rigidity near the Continent Ocean Boundary (COB) to fit the offshore gravity low, while we preferred deeper DON and stronger crust, because this interpretation is also consistent with gravity in the Congo fan. A part of the offshore gravity low on South Gabon section is due to the sediment load of the Congo fan that extends on the oceanic crust and has been recognized in the recent Zaiango experiment [Savoye et al., 2000], and the other part is due to the unevenly distributed crustal thickness in the COB domain [Meyers et al., 1996]. We have found that a variable rigidity across the margin mainly controlled by temperature, in a way similar to that proposed for oceanic lithosphere, reduces strength at the Atlantic hinge zone, and increases gravity edge effect to obtain a better fit; conse-quently, our model also diverges from that of Watts and Steward [1998], who assume a strong continent in that location (EET = 50 – 70 km). However, conventional meas-urements of heat flow, oil exploration data, or gas hydrate bottom-simulating reflectors (F. Lucazeau et al., High-reso-lution heat flow density in lower Congo basin from probe measurements, oil exploration data, and bottom-simulating reflectors, submitted to Geochemistry, Geophysics, and Geosystems, 2003) show that heat flow along the South Gabon section varies from 55 – 60 mW m2 in the deep offshore to 70 – 80 mW m2 on shelf and onshore basins, which is therefore not likely to explain a strong continent in that position.
[15] Our conclusion on the mechanisms of isostasy across
margins in the Gulf of Guinea is that a moderate strength still exists and has existed during the formation of the margin. This strength may correspond to EET in the range of 20 – 30 km, which can potentially ensure interactions between sediment loads and drainage.
3. Estimation of the Different Contributions to Surface Uplift
[16] During the Cenozoic, sediment depocenters have
migrated significantly from the mouths of the Ogooe and Kwanza Rivers to the present Congo fan. Present-day morphology of the continent displays a coastal relief (Figures 1 and 10) that isolates the Congo drainage basin from the margin. This relief has a bulge morphology, whose amplitude relative to average Congo River base level is 250 m (500 m with respect to the longitudinal profile) and width 600 km (Figure 10). It certainly plays a role of a topographic barrier in the present-day dynamics of the Congo River, leading to low sediment delivery [Milliman and Syvitski, 1992], deep incision of the offshore canyon [Babonneau et al., 2002], and variable patterns (erosion or filling) of recent turbiditic channels [Turakiewicz, 2001]. If this relief has existed during Oligocene, it could have played a similar role in the switch of depocenters: any uplift in the downstream part of Ogooe and Kwanza Rivers, Figure 8. (a) Comparison of present bathymetry across the
two sections of margin. Deep offshore morphology in Congo fan differs mainly as a result of the more important volume. (b) Comparison of thinning factor s across the two sections of margin. Initial continental crust thickness is 35 km. Model hypothesis correspond to DON = 20 km and EET equal to the depth of the isotherm 400C.
such as that resulting from interactions with sediment loads, could have controlled migration of depocenters.
[17] Present-day morphology observed on the coastal
domain is however a probable consequence of multiple uplift and erosion phases. Following the Oligocene switch of depocenters, at least a regional uplift [Karner et al., 1997; Lavier et al., 2001], an important denudation of that magnitude has been determined from relics surfaces [Leturmy et al., 2003] and an isostatic unloading in response to that denudation can be identified and quantified. It is therefore possible to reconstruct Oligocene topography by correcting the present-day topography from these different identified contributions and then to consider what process is susceptible to explaining depocenters migration. We will successively review elements for estimating regional uplift, estimate erosion unloading and reconstructed topography, and finally consider the location and magnitude of uplift related to those sediment loads.
3.1. Uplift and Erosion on the Gulf of Guinea Continental Shelf and Coastal Plains
[18] There are many lines of evidence that continental
shelf and coastal plains have been eroded during Neogene. This includes observations of erosional unconformities on the continental shelf during Neogene [e.g., Emery et al., 1975; McGinnis et al., 1993; Se´ranne et al., 1992] and an anomalous coastal plains pattern where progressively older strata are observed on the eastern border [Karner et al.,
1997]. Two major episodes of erosion are recognized: Oligocene erosion affects mainly the continental shelf nearby the shelf break and has been interpreted mainly either as result of submarine currents [Miller et al., 1985] or unloading response to sea level fall [McGinnis et al., 1993]; Miocene erosion (Aquitanian to Burdigalian) affects a broader zone from the shelf break to the coastal plains, and its amplitude is so important (minimum of 500 m) that it should be associated with a regional uplift of South Africa [Harrison et al., 1983; Karner et al., 1997; Lavier et al., 2001; Lithgow-Bertelloni and Silver, 1998; Sahagian, 1988]. Magnitude of Miocene erosion ranges from 500 to 2000 m and has been inferred in different ways, including mineral diagenesis of illite smectite in Cretaceous reservoirs [Walgenwitz et al., 1990], compaction of shale, oil matura-tion patterns, Apatite Fission Tracks analysis (F. Walgenwitz, unpublished reports), sediment packages modeling [Karner et al., 1997], and backstripping reconstruction [Lavier et al., 2001]. Methods based on paleotemperature analysis (diagenesis, fission tracks) predict a cooling of 45 – 90C, which corresponds to 1000 – 2000 m of denu-dation assuming present-day value for thermal gradient (45C km1). As the compaction state of eroded material was probably lower than that exposed now, thermal gradient could have been up to 60C km1, reducing the range to 750 – 1500 m overburial. Modeling techniques can predict amplitude of uplift: Karner et al. [1997] have used a stratigraphic modeling approach and found that about Figure 9. Morphology of the (left) South Gabon margin and (right) Congo fan in the Gulf of Guinea
according to different depths of necking. Equivalent elastic thickness varies along the margin according the depth of isotherm 400C. Thick line on the South Gabon section corresponds to gravimetric Moho and indicates therefore model misfit.
545 m of uplift in early Miocene is required to explain the strata pattern in coastal domain. Lavier et al. [2001] have applied backstripping techniques for two sections in Congo and Angola, and determined that Eocene shelf break should be above seawater before Miocene whereas it probably remains at the same water depth as that observed today: in order to explain this gap, a tectonic uplift of 300 m for the Congo section and 500 m for the Angola section is necessary. In the present work, we have used a direct model of evolution including kinematic necking and
flex-ural isostasy (see section 2). We examine here evolution of bathymetry at the shelf break and in the coastal plain for a Congo section. At the shelf break, in order to obtain present-day fit for bathymetry (60 m), model predicts that past elevation was 300 m above sea level (Figure 11) from Cretaceous to Oligocene. This is consistent with the back-stripping analysis by Lavier et al. [2001], and can be interpreted in the same way. In our model, load represented by the Congo deep sea fan causes flexural subsidence on the shelf during Neogene; because this subsidence is not Figure 10. (a) Longitudinal profile of Congo River (heavy black line) and corresponding ridges
topography (heavy gray line). Dashed line at a constant elevation of 450 m possibly represents a recent uplift. Flexural bulge related to sediment load is represented by a gray surface below the river profile. (b) Location of present Congo River on topographic map. Note that the river has difficulty flowing across the coastal bulge.
compensated by any uplift in the model, prediction of bathymetry before Oligocene at 360 m above present elevation (300 m above sea level) indicates the order of uplift magnitude we have neglected. Additionally, we can estimate eroded material thickness from a palinspastic restoration and include erosion in the modeling process. Differences of predicted bathymetry, depending on whether or not erosion is included in the model, give an order of 450 – 500 m magnitude (Figure 11), both at shelf break and in coastal plains. This difference represents the amount of denudation that should have been balanced by surface uplift
on the continental shelf. On the other hand, unpublished apatite fission track on a transect through Precambrian basement in Gabon (M. Se´ranne, University of Montpellier, personal communication, 2001) does not evidence any track length reduction, which locates the present-day surface below the partial annealing zone (60C). As surface temperature is20 – 25C, this limits a possible denudation to 1000 – 1500 m depending on thermal conductivity of eroded material but does not prove, however, that basement has been denuded up to this maximum limit on the western flank of coastal bulge.
Figure 11. Close up on modeling results across Congo shelf, including or not erosion. (a) Present-day stratigraphy. (b) Section with reconstructed thickness of eroded material (a minimum of 800 m has been removed at the shelf break level). (c) Evolution of elevation at a location on shelf break (thin black lines, X = 1100 km on cross section) and coastal plain (gray lines, to X = 1180 km on cross section). Solid lines are elevations predicted by models that do not incorporate the additional quantity of sediment required by the erosion process, while dashed lines are elevations predicted with this material eroded after 18 Ma. A minimum uplift of 450 – 500 m is required to counterbalance the anomalous elevation of shelf break before the erosion event.
[19] To summarize, denudation on the Gulf of Guinea
continental shelf is estimated between 800 m (minimum thickness from palinspastic restoration) and up to 2000 m (according to paleotemperature reconstructions); surface uplift is estimated between 300 – 350 m (elevation of shelf break) and 450 – 550 m (modeling). This later value is comparable to the internal base level of the Congo River drainage basin (450 m), and both can be related to a very large-scale event supported in the deep mantle [Lithgow-Bertelloni and Silver, 1998]. Uplift can be dated by the main stage of aerial denudation on shelf, between Aquitanian (25 Ma) and Burdigalian (16 Ma) [Lavier et al., 2001]. As sediment supply by the Congo River increases almost continuously from Oligocene [Lavier et al., 2001; Leturmy et al., 2003; Meyers and Rosendahl, 1991], and as erosion within the Congo drainage basin becomes only efficient after the onset of the western branch of the East African Rift system, around 12 – 13 Ma [Leturmy et al., 2003], migration of depocenters before Oligocene occurs likely before upstream organization of Congo drainage basin and is therefore related to changes in the downstream part. A restoration of Oligocene topography is therefore developed in the next paragraph in order to discuss possible changes in the downstream part of drainage.
3.2. Restoration of Oligocene Topography
[20] Oligocene topography can be restored by removing
the different uplift and denudation contributions from present-day topography. Continental shelf denudation is the most difficult to obtain because there is no preserved relic surface, but the estimated range varies from 1000 to 2000 [Walgenwitz et al., 1990]. Where preserved surfaces exist, denudation can be estimated by volume between a smooth surface defined by relics of the old surface and actual topography; this has been done for the whole Congo drainage basin [Leturmy et al., 2003] and also used to determine the subsequent unloading response (Figure 12) as the deflection of 2-D elastic thin plate (see Appendix A2). Density of the unloaded material is that of upper continental crust and EET varies in the range 20 to 80 km (an intermediate value of 50 km is used in Figure 12b). Amplitude of this flexural unloading varies from 200 m to 300 m within coastal bulge, depending on EET value (see also Figure 10). The other uplift contribution is related to regional uplift that affected the stratigraphic pattern on the continental shelf and hypsometry of the continent. As strength of the continent is high [Hartley et al., 1996] and origin of load deeply rooted in the mantle [Lithgow-Bertelloni and Silver, 1998], we can assume a constant value of about 500 m. On the other hand, uplift related to the East African rift system has not been considered. Restored topography (Figure 13) has not been obviously corrected for recent uplifts in southern and eastern parts, but the important aspect is that coastal topography has existed in the down-stream part of the Congo drainage basin, and has a characteristic morphology of a rift shoulder (Figure 13a); this imposes a barrier between continental drainage and margin since onset of rifting. On Figure 13, two possible corridors across this coastal relief also appear, which show that threshold instability in Paleo-Ogooe would necessarily lead to migration of drainage to the present outlet of the Congo River. This would differ from the mechanism
proposed by Driscoll and Karner [1994] for the Amazon, where the mouth migrates progressively in response to the accumulated load.
3.3. Flexural Uplift Associated With Cretaceous and Paleocene Sediment Loads
[21] Migration of depocenters from the mouths of the
Ogooe and Kwanza River to the mouth of Congo River during Oligocene has been evidenced in Leturmy et al. [2003]. As moderate strength of the Gulf of Guinea passive margin has been recognized in the first part of this paper, it is possible that sediment loads in the Ogooe and Kwanza Rivers can produce negative feedbacks and have caused this spectacular switch. In order to estimate location and ampli-tude of the flexural bulge related to Cretaceous and Paleo-cene loads, we have determined the 2-D deflection of a thin elastic plate (Figure 14). EET is 20 km according to previous analysis of isostasy, and calculated effect repre-sents cumulated deflection for that period. Unfortunately, compilation of sediment thickness is limited in the northern part and may introduce some bias there, but it is clear that the location of surface uplift occurs at the limit of a topographic threshold formed by the rift topography, and consequently can represent a dam in the Paleo-Ogooe River even though amplitude is small (of the order of 50 – 100 m); downstream part of the present-day Congo River (in the middle part between location of the two depocenters) is conversely subsiding and can potentially favor a pathway through the topographic barrier. This coincidence however happens later than a paroxysm in sedimentation rates at the end of Cretaceous (Maastrichtian, i.e., 67 – 71 Ma), but sedimentation rates in the Gulf of Guinea have decreased significantly in three locations from 67 to 34 Ma (Figure 15). Similar changes in sedimentation rates during Oligocene have been described by Rust and Summerfield [1990] who noticed an important increase nearby the mouth of the Orange River. Oligocene corresponds also to a major drop (about 60 m) in the relative sea level, and to a climatic switch from greenhouse to icehouse conditions [Lavier et al., 2001; Se´ranne, 1999]. The paleo-Congo River has possibly been endoreic during early Tertiary (67 – 34 Ma) since very low sediment delivery is observed in this interval, then onset of different climatic and eustatic conditions during Oligocene has favored capture of this endoreic basin at the present location of the Congo mouth, providing spectacular increase of sediment rates.
4. Discussion and Conclusion
[22] We have addressed in this paper the problem of
interactions between the Gulf of Guinea continental margin and the Congo drainage basin. This question results from observations that depocenters have migrated from the mouths of the Ogooe and Kwanza River to the present-day fan of the Congo River, in a period of time between Cretaceous end (65 Ma) and Oligocene (35 Ma), after a period of active sedimentation. It also results from obser-vations that at present time, Congo River sediment delivery is low compared to other large drainage basins and to volumes accumulated in the fan, that the main submarine channel on the continental shelf is deeply incised and that the turbiditic system seems unstable during Pleistocene
(alternation of several generations of erosive and construc-tive channels).
[23] Interaction between margin and continental drainage
subsequently addresses problems of lithospheric strength and uplift of the African continent: is continental margin rigid enough to affect the continent by sediment loads on the margin or to be affected by regional uplift in the continent? We have examined both aspects in this paper. The first part is an analysis of the mechanisms of isostasy at two locations with very different gravity signatures, across South Gabon and the Congo fan. Our approach includes modeling of margin thermal evolution, determination of the extensional field that provides a fit for present-day bathymetry, and
calculation of gravity signature from the resulting density field. It also includes regional isostasy as a thin elastic plate loaded by either sediment deposits or permanent forces consecutive to rifting. These latter mechanisms are related to the rheology of the continental margin during rifting that can still remain rigid, and control plastic deformation around the level of maximum strength (or depth of necking DON): as the resulting deformation is not necessarily equivalent to that obtained for Airy isostasy, restoring forces can exist permanently in order to recover an equilibrium state as far as the lithosphere remains strong. These restoring forces are either directed upward if DON is deep or downward if DON is shallow; neutral level (no restoring force) depends on Figure 12. Estimated Tertiary denudation and associated flexural rebound with the Congo drainage
basin. (a) Estimated Tertiary denudation from the surface envelope technique [Leturmy et al., 2003]. (b) Flexural uplift related to erosion unloading (EET has been taken to 20 km). Largest values are observed in the southern parts of coastal relief and East African rift.
density distribution in the range 7 – 10 km. This analysis has large uncertainties as it depends on the quality of basin geometry (decreasing in the deep offshore) and density distribution, on the 2-D assumption that is difficult to verify in most cases and on the model of necking which assumes a continuum where weak faults can affect overall strength. However, it gives a first-order view of lithosphere rheology at both present time (response to sediment load) and time of rifting (DON). On the Gulf of Guinea continental margin, we have found that neither Airy type isostasy (no strength) nor high rigidity (higher than 1024N m) can explain amplitude of gravity edge effect (either too small or too high). We found that a moderate rigidity related to temperature (or equivalent elastic thickness EET defined as depth of 400C isotherm) gives the best results for both modeled sections. The corresponding value of EET is 30 km at present time, decreasing to 20 km at the continental hinge where the cumulative effects of low conductivity sediments insulation and lateral heat transfers across Moho make lithosphere locally hotter. At the end of rifting, EET varies from 20 km near the continent to 10 km at the ocean limit where crustal thinning and temperature anomaly are at maximum.
DON is found in the range 10 – 20 km, which is consistent with calculation of EET at time of rifting: in term of rheological structure, this means that the strength of the continental lithosphere is limited to the crustal part only, and increases as a simple function of temperature. We also have tested a more elaborated model for determining EET that includes flexural stress and subsequent inelastic deforma-tion, but changes in both EET and gravity appear insignif-icant in this case. Our interpretation for South Gabon is slightly different from a previous one by Watts and Steward [1998]: this comes from the difficulty of matching gravity low offshore and gravity low onshore. There is no other way to explain gravity low onshore than having DON very shallow, but at the same time, it is difficult to fit gravity low offshore except having deep offshore basin very weak. This is not consistent with what is modeled on the other section (Congo), and we preferred a model in which both sections have a similar behavior in term of rheology, with some discontinuity at the hinge of South Gabon section. Our model predicts that there are only few crustal thinning differences between two sections, except in onshore Congo where thinning affects the continent further east. This explains the presence or not of gravity low onshore, and on the other hand, offshore gravity low is important in South Gabon only where volume and geometry of sediment pack-ages are different from that of the Congo fan. Predicted crustal geometries have been however confirmed by unpub-lished seismic results, an old ESP survey in South Gabon (S. Le Douaran, ELF unpublished report, 1989) and a recent OBS survey in the Congo fan [Contrucci et al., 2003].
[24] The second part of the paper is dedicated to the
analysis of uplifts that can affect continental shelf and coastal domain (including a coastal topographic ‘‘bulge’’ Figure 13. Topography restored at the end of Eocene. This
topography has been calculated by removing erosion unloading (see Figure 12b) and a constant 500 m uplift from the envelop of present-day topography [see Leturmy et al., 2003]. (a) Topographic profile along the present-day Congo River. (b) Map of the restored topography (present-day coastline and Congo River are also shown on this map).
Figure 14. Cretaceous sediment thickness and associated flexural bulge (EET = 20 km) superposed on restored Oligocene topography. Flexural uplift is maximum in the downstream parts of Ogooe and Kwanza (50 – 100 m) and disappears in the present-day downstream part of Congo River.
parallel to the coastline). There are different lines of evidence for a recent regional uplift, including (1) Congo basin morphology either immature or more mature but recent (13 Ma) in the western branch of the East African rift [Leturmy et al., 2003], (2) elevated base level of the Congo River around 450 m, (3) reconstruction of the shelf break before Miocene, and (4) truncation and organization of sediment strata on coastal plains that require about 500 m of uplift. This uplift, as well as those related to volcanic activity on Sao Tome or the East African rift, are younger than migration of depocenters and have obviously not controlled this process. Assuming that this uplift extends at regional scale because of its origin in the deep mantle and the probably high strength of the African continent, and that surface denudation and related unloading uplift can be calculated in any point of the Congo drainage basin using preserved relic surfaces, we tried to reconstruct a paleoto-pography for Oligocene: on coastal domain, an asymmetric topography typical of continental rifts shoulders has been reconstructed. This forms a topographic barrier between continent interior and continental margin that may have promoted a switch in drainage organization. Sediment loads deposited during upper Cretaceous create a specific pattern of uplift related to the flexural bulge associated with deformation of an elastic plate: because of the existence of two depocenters, the maximum values (50 – 100 m) are expected in the downstream part of the Ogooe and Kwanza and can potentially interfere with rift topography to create
dams in drainage. On the other hand, uplift is expected to be minimum in the downstream part of the Congo River and therefore can potentially promote future development of this system. However, sediment record shows that a sediment gap exists from 65 to 35 Ma within the whole Gulf of Guinea, and that sedimentation becomes important again everywhere in Oligocene, and similarly in the Orange domain. This could suggest first that the Congo basin has been endoreic from Maastrichtian to Oligocene and Second that the switch has been controlled by global causes such as sea level drop or climatic change. Maastrichtian peak of sedimentation observed in the Ogooe depocenter can be clearly related to Senonian inversion that affected the northern part of the Congo drainage basin [Guiraud and Bosworth, 1997] and clearly shows that drainage area of the Ogooe was greater then the present-day one, and occupied part of the present-day Congo drainage. It demonstrates also that this inversion is not the cause of sealing in the Ogooe, and it leaves an interaction hypothesis possible.
[25] Finally, if this interaction has been at the origin of a
possible switch before Oligocene, similar consequences can happen at present time in the Congo River. We reported on Figure 10a location and amplitude of flexural bulge related to Tertiary sediment load in the Congo. This uplift occurs in a region of narrow pathways, where cataracts and pools are numerous, and can contribute together with climatic forcing to observed instabilities in the turbiditic system of the Congo.
Appendix A
A1. Thermomechanical Model
[26] This model described the 2-D thermal evolution of a
rift or passive margin that deforms under a prescribed kinematics field (distribution of extension factors, accretion of oceanic material) and where sediment can progressively accumulate and compact. Elements of our model have been described by Latil-Brun and Lucazeau [1988]. Some aspects and additional modifications are included here. For geo-dynamics and sediment process, related advection of heat is directly taken into account by a Lagrangian formulation (no need of additional term in the heat equation):
@ @x lxðx; y; t; TÞ @T @x þ @ @y lxðx; y; t; TÞ @T @y þ A x; tð Þ r x; y; t; Tð ÞC x; yð Þ@T @t ¼ 0; ðA1Þ
where lx and ly are horizontal and vertical thermal
conductivity, respectively; A(x, t) is radiogenic heat production;r(x, y, t, T ) is density; C(x, y) is specific heat; T is temperature; and t is time.
[27] Conductivity (l) varies as a function of temperature
(T ) in continental crust according to
l Tð Þ ¼ l Tð LabÞ 1þ a T Tð LabÞ
; ðA2Þ
where l(TLab) is conductivity at laboratory temperature
conditions anda is a coefficient of the order of 5 104C1 [Wells, 1980].
Figure 15. Sedimentation rates at different locations of the Gulf of Guinea continental margin. These rates have been determined as surface averages along three sections represented in the inset: North Gabon, Angola, and Congo. Sedimentation rates in North Gabon are represented by a light gray color limited by a dotted line, in Angola by a medium gray color limited by a solid line, and in Congo by a black color limited by a dashed line. During Cretaceous, main influx of sediment is observed in North Gabon and Angola sections (in connection with the importance of Ogooe and Kwanza Rivers at that time) and during Tertiary in Congo and Angola sections (mainly represented by Congo River deposits).
[28] In the mantle, radiative heat transfer counterbalances
the decrease of conductive heat transfer: here we used the model of Schatz and Simmons [1972]:
lL¼ 418 31þ 0:2TABS ; lR¼ 0:0023 Tð ABS 500Þ; TABS>500K; lmantle¼ lLþ lR: ðA3Þ
Sediment thermal conductivity is noticeably lower than that of basement, because of the high porosity and the low conductivity of water or air filling the pores. An empirical geometric model provides a good approximation of the bulk conductivity:
lbulk¼ l1matrix=l
water: ðA4Þ
Thermal conductivity of matrix and water are determined in a way similar as explained by Chapman et al. [1984].
[29] Density depends on temperature changes according
to
r Tð Þ ¼ r Tð LabÞ 1 a T T½ ð LabÞ; ðA5Þ
where a is the coefficient of thermal expansion (3 105 C1). Continental crust has been stratified in three layers of varying heat production and density (Table 1). Sediment density depends on sediment type and compac-tion: in our experiment it ranges typically between 2350 and 2450 kg m3.
[30] Deformation of continental lithosphere associated
with rifting corresponds to pure shear as defined formerly in the McKenzie [1978] stretching model;b(x) is the stretch-ing parameter defined for each column of the mesh: it is obtained by an iterative process fitting the present-day bathymetry with a maximum RMS less than 100 m. As rifting has a finite duration t, it is better to define the strain _e as
_e¼ ln bð Þ=t: ðA6Þ
The possibility that crustal thinningb(x) is different from the upper mantle thinningd(x) (Figure 3) has not been used in the modeling here. Boundary conditions are usually isother-mal on top and bottom, and no heat flux through the vertical boundaries. In case of oceanic accretion, oceanic type material is added next to the last column of the mesh (Figure 3), and the vertical boundary condition is transformed to an isothermal type (solidus temperature of magma).
[31] Processes of sedimentation and compaction are
in-cluded in the model by the incorporation of new elements
on the top that have thickness and physical properties related to their state of compaction. It is assumed that compaction follows a simple law in such a way that porosity decreases exponentially with depth [Sclater and Christie, 1980]: zð Þ ¼ 0exp z zc ; ðA7Þ
where 0is the surface porosity and zc is the compaction
depth that both depend on lithology.
[32] Both Airy and regional isostasy can be accounted for.
In Airy case, lithostatic pressure at a certain depth below lithosphere bottom is same as that of a reference lithosphere (initial lithosphere). In case of density variations between the two states, subsidence or uplift accommodates the difference of weight. Change in elevation SAirywith respect
to the initial state is
SAiry¼ Z zL z0 r z; tð Þdz Z zL z0 r z; 0ð Þdz ra rw ð Þ ; ðA8Þ
whereraandrware density of asthenosphere and of water,
respectively, and z0 and zL are top and bottom of the
lithosphere, respectively.
[33] If lithosphere has some strength, loads are
compen-sated over a wider spatial domain than the local application point. Depth of necking (DON) is considered as a parameter value zneck, for which surface depression (necking
subsi-dence) Sneckis given by [Kooi et al., 1992]
Sneck¼ 1
1 b
zneck: ðA9Þ
In case of Airy type isostasy, a similar expression for surface depression SAirycan be obtained:
SAiry¼ Ecrust 1 1 b ra rc ra rw : ðA10Þ
Force that attempts to restore the isostatic equilibrium is simply proportional to the difference in Airy subsidence and necking subsidence. Neutral level is obtained for equal values for Sneckand SAiry.
[34] Two types of loads can therefore permanently act on
lithosphere: surface load of sediments and restoring load related to necking. A thin plate approximation provides a solution for the deflection w(x) created by these loads P(x):
@2ðD xð Þ@2wÞ
@x4 þ ra rfilling
gw¼ P xð Þ; ðA11Þ
where g is the gravitational acceleration,rinfillis the density
of basin fill, and D is the flexural rigidity. Equation (A11) is solved by a finite difference algorithm [Hassani, 1989].
[35] D(x) is related to an equivalent elastic thickness
(EET) h(x) by
D xð Þ ¼ Eh xð Þ
3
12 1ð n2Þ; ðA12Þ
Table 1. Continental Crust Stratification and Properties
Upper Crust Middle Crust Lower Crust
Top, km 0 3 15 Bottom, km 3 15 35 Heat production,mW m3 1.5 1 0.3 Thermal conductivity, W m1C1 3 3 3 Specific heat, J kg1C1 3400 3400 3400 Density, kg m3 2700 2800 2900
where n is the Poisson coefficient and E is the Young modulus.
A2. Model for 2-D Elastic Thin Plate
[36] Two-dimensional elastic plate response to surface
loads has been computed using a finite element code [Ravaut et al., 1997]. The governing equation is
D @ 4 w @x4þ 2 @4w @x2@y2þ @4w @y4 þ ra rfilling gw¼ P x; yð Þ: ðA13Þ
P(x, y) is the distribution of load and D is a constant value of rigidity. Boundary conditions are free slip conditions therefore rejected far from the investigated domain.
[37] Acknowledgments. This work has been funded by a TFE research project (‘‘Projet Grand Fond’’) through a visiting grant for F.L. and a postdoc grant for P.L. Riad Hassani provided the 2-D elastic thin plate finite element code. The Cretaceous and Tertiary isopach maps are derived from a TFE synthesis by P. Unternehr and H. Pigeyre. The 2-D thermo-mechanical and gravity modeling have been included in the in-house TFE software MARGE. The authors want to thanks TFE for providing some of the data and authorize publication. Discussions with Michel Se´ranne and Michel Lopez, comments from reviewers Jean Braun and Julio Friedmann, and revision of English by Alan Burns have contributed helpfully to the final form of this paper. IPGP contribution 1909.
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![Figure 13. Topography restored at the end of Eocene. This topography has been calculated by removing erosion unloading (see Figure 12b) and a constant 500 m uplift from the envelop of present-day topography [see Leturmy et al., 2003]](https://thumb-eu.123doks.com/thumbv2/123doknet/14768398.589693/16.888.76.436.102.596/topography-restored-topography-calculated-removing-unloading-constant-topography.webp)
