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Upper Mantle Viscosity and Dynamic Subsidence of Curved Continental Margins

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Upper Mantle Viscosity and Dynamic Subsidence of Curved Continental Margins ARTICLE Received 18 Oct 2012 | Accepted 19 May 2013 | Published 18 Jun 2013 DOI: 10.1038/ncomms3036 Upper mantle viscosity and dynamic subsidence of curved continental margins Victor Sacek1 & Naomi Ussami1 Continental rifting does not always follow a straight line. Nevertheless, little attention has been given to the influence of rifting curvature in the evolution of extended margins. Here, using a three-dimensional model to simulate mantle dynamics, we demonstrate that the curvature of rifting along a margin also controls post-rift basin subsidence. Our results indicate that a concave-oceanward margin subsides faster than a convex margin does during the post-rift phase. This dynamic subsidence of curved margins is a result of lateral thermal conduction and mantle convection. Furthermore, the differential subsidence is strongly dependent on the viscosity structure. As a natural example, we analyse the post-rift stratigraphic evolution of the Santos Basin, southeastern Brazil. The differential dynamic subsidence of this margin is only possible if the viscosity of the upper mantle is 42–3 Â 1019 Pa s. 1 Instituto de Astronomia, Geofı´sica e Cieˆncias Atmosfe´ricas, Universidade de Sa˜o Paulo, Rua do Mata˜o 1226, Sa˜o Paulo 05508-090, Brazil. Correspondence and requests for materials should be addressed to V.S. (email: [email protected]). NATURE COMMUNICATIONS | 4:2036 | DOI: 10.1038/ncomms3036 | www.nature.com/naturecommunications 1 & 2013 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3036 he post-rift tectonic subsidence of divergent margins is promoted by the thermal conduction. These concepts are mainly explained by the thermal contraction of a thinned applied to study the evolution of the southeastern Brazilian Tlithosphere and its isostatic response to cooling due to margin. vertical heat flow1,2 in a one-dimensional model. Although lithospheric cooling is mainly guided by this vertical heat flow Results through the margin, two-dimensional (2D) numerical models3–5 Differential subsidence and upper mantle viscosity. In our show that lateral thermal conduction has an important role in numerical simulations, we assumed a temperature- and pressure- controlling the rate of subsidence. For the same amount of dependent Newtonian rheology, with the viscosity Z given by the lithospheric stretching, a 2D model predicts faster subsidence Arrhenius law: than a one-dimensional model does4. A 2D model depends on the E þðz=DÞV E þ V horizontal temperature gradient, which is a function of lateral Zðz; TÞ¼Z0Âexp À ð1Þ variations in lithospheric thickness. T=DT þ T0 1 þ T0 Another important process that controls subsidence of the where E and V are the (non-dimensional) activation energy and margin is mantle advection beneath the lithosphere6,7, which is volume, respectively, z is depth, D is the thickness of the model, also a function of mantle viscosity. Lateral variations in T is temperature, DT is the decrease in temperature from the base lithospheric thickness across the margin induce small-scale of the model to the surface, T ¼ 0.21 is a non-dimensional 8 0 convection , which increases heat transfer to the thinned constant and Z0 ¼ Z(D,DT) is the viscosity at the base of the lithosphere and adjacent areas9. One consequence of this model. The temperature profile is linear with depth to the base of process is a transient uplift of the flanks of the rift and a the lithosphere, and the lithospheric stretching factor2 b varies decrease in the subsidence rate of the adjacent stretched from 1 to 3 (Fig. 1a). This implies that the thickness of the lithosphere10. In this case, the isostatic effect of the additional thinned lithosphere is 1/b of its original thickness. In plan view, heat introduced into the stretched lithosphere due to the small- the transition from the continent to the stretched margin is scale mantle convection acts against the subsidence caused by curved and contains a concave-oceanward segment and a convex vertical and lateral heat conduction. Therefore, the cumulative segment (Fig. 1b). Additional information is found in the subsidence depends on the competing effects of conductive and Methods section. We analysed the subsidence in three locations advective heat transport within the margin. of the margin with b ¼ 3: location A is in the concave segment, Although previous 2D models of continental margin sub- location C is in the convex segment and location B is between sidence have shown the importance of incorporating a horizontal locations A and C. 20 dimension and convective processes into the study of subsidence, In the first simulation, for a mantle with Z0 ¼ 5 Â 10 Pa s, little attention has been given to the influence of the assumed E ¼ 30 and V ¼ 0 (Fig. 2a, first column), the rate of subsidence planar shape of the rifting, with a few exceptions11–12. Several decreases from the concave segment towards the convex segment portions of divergent marginal basins around the world have (from A to C), and the difference in subsidence between locations curved segments, and 2D models may not adequately describe C and A increases over time, reaching 4250 m during the post- their subsidence histories. Examples include the southeastern rift evolution of the margin when assuming a water-filled basin Brazilian margin and its conjugate, the western African margin. (Fig. 2a, third column). This result implies that the subsidence is To study the thermal evolution of a stretched margin following faster in the concave segment than in the convex segment during rifting, we used the three-dimensional (3D) finite element code the post-rift phase, generating more space to accommodate CitcomCU13,14 to simulate convection in the upper 660 km of the the sediments in the concave segment. The load of the sediments Earth. Using different numerical simulations, we observe that the filling this accommodation space triples the differential sub- subsidence pattern of a curved margin is sensitive to the viscosity sidence caused only by the water load. Despite the fact that the structure of the upper mantle. For a viscous upper mantle, the lithosphere has the same stretching factor at the three locations subsidence is mainly guided by the thermal conduction, which is along the margin, the subsidence histories of these sites are more efficient in the concave segment of the margin than in the distinct due to more efficient cooling of the stretched lithosphere convex one. Therefore, a differential subsidence is expected along through lateral conduction in the concave segment. In addition, a curved margin. For a less-viscous upper mantle, the influence of the small-scale convection induced beneath the stretched litho- advection in the thermal structure of the mantle becomes sphere is more vigorous in the concave segment than for any increasingly important and reduces the differential subsidence other geometrical configuration, with advection beneath 0 3.0 1,200 1 23 100 2.5 200 C 800 2.0 300 B Convex-oceanward (km) (km) segment 400 1.5 A 400 500 Conacave-oceanward 1.0 600 segment 0 0.0 0 500 1,000 1,500 0 400 800 1,200 1,600 (°C) (km) Figure 1 | Initial configuration of the numerical model. (a) Temperature profile for the unstretched continental lithosphere (solid line) and stretched lithosphere with b ¼ 3 (dashed line). (b) Map of stretching factor b, ranging from 1 to 3. The subsidence history of the margin is analysed at locations A, B and C with b ¼ 3. 2 NATURE COMMUNICATIONS | 4:2036 | DOI: 10.1038/ncomms3036 | www.nature.com/naturecommunications & 2013 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3036 ARTICLE Initial viscosity Velocity profile Vertical movement 250 profile at t ≈ 70 Myr relative to print B a 200 0 0.2 b 100 200 150 d c = 0.1 300 0 5×1020 Pa s 100 400 0.0 V = 0.0 m 500 E =20 E =30 Depth (km) e 600 E = 30.0 50 Relat. uplift (km) Relat. –0.1 V V 0123 45 0 0.2.5 5. 0. 2.5 5. 1.0 × 1021 0 0.2 0 5.0 × 1020 100 –50 (Pa s) 1.0 × 1020 200 0.1 = –100 300 0 18 19 20 21 22 5×1020 Pa s 10 10 10 10 10 400 0.0 500 V = 2.5 Viscosity (Pa s) Depth (km) E = 30.0 600 uplift (km) Relat. –0.1 012 3 45 Figure 3 | Mean difference in subsidence between locations A and C. The mean difference in subsidence, taken for the time interval 50–100 Myr, 0 0.2 100 is given as a function of the non-dimensional activation energy E, the 200 0.1 non-dimensional activation volume V and the viscosity Z0. The viscosity = 300 0 indicated on the horizontal axis is at the base of the lithosphere. 400 1×1020 Pa s 0.0 500 V = 0.0 The letters a–e indicate the respective model in Fig. 2. Depth (km) 600 E = 30.0 Relat. uplift (km) Relat. –0.1 0 123 45 0 0.2 thermal conduction, resulting in 100–150 m of differential 100 subsidence between locations A and C during the post-rift 200 0.1 0 = evolution of the margin (Fig. 2b–d, third column) for a 300 21 1×10 Pa s water-filled basin. 400 V = 5.0 0.0 500 E = 30.0 The interaction of small-scale mantle convection with the Depth (km) 600 uplift (km) Relat. –0.1 lithosphere also produces oscillations in subsidence along the 0 1 2 3 45 margin over periods of a few millions of years (Myr), with a 0 0.2 peak-to-peak amplitude of a few metres to tens of metres.
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