Geophys. J. Int. (2002) 149, 179–189 On the state of sublithospheric upper mantle beneath a supercontinent Jun Korenaga1,∗ and Thomas H. Jordan2 1Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, USA. E-mail: [email protected] 2Department of Earth Sciences, University of Southern California, Los Angeles, USA Accepted 2001 October 25. Received 2001 October 17; in original form 2000 November 5 SUMMARY An assumption of isothermal and static asthenosphere as the normal state of sublithospheric mantle, as commonly employed in studies of terrestrial magmatism, may be physically im- plausible for a system cooled from above. The growth of an unstable thermal boundary layer at the base of the lithosphere can lead to small-scale convection, so asthenosphere is expected to be usually convecting. A first-order estimate based on the energetics of convection sug- gests that mantle upwelling rate associated with such small-scale convection is on the order of 10 cm yr−1 for asthenospheric viscosity of 1018–1019 Pa s. To investigate the potential role of such sublithospheric convection in anomalous magmatism associated with rifting of the super- continent Pangaea, a simple upper-mantle convection problem with thick cratonic lithosphere is considered through finite element modelling. Strong three dimensionality is exhibited in our solutions, and the planform of convection is largely affected by the bottom topography of con- tinental lithosphere. Our model also suggests that differential cooling, imposed by a variation in lithospheric lid thickness, may lead to large-scale convection, which brings uncooled, ‘hot’ material from the base of thick lithosphere to shallow asthenosphere. The potential importance of such sublithospheric convection in magmatism during continental rifting is discussed. Key words: continental margins, hotspots, mantle convection, upper mantle. necking can result in vigorous, small-scale mantle convection, which 1 INTRODUCTION may account for the observed voluminous rifting magmatism. As Continental rifting during the dispersal of the supercontinent Keen & Boutilier (1995) showed, however, such sharp necking is Pangaea was often accompanied by massive magmatism as evi- unlikely in the deformation of ductile mantle. Intense lithospheric denced by the frequent occurrence of flood basalts and thick ig- necking is fundamental for this type of mechanism, as is assumed neous crust emplaced along a number of rifted margins (White & a priori even in the most recent efforts for this type of modelling McKenzie 1989; Holbrook & Kelemen 1993; Coffin & Eldholm (Boutilier & Keen 1999; Keen & Boutilier 2000). 1994). The thickness of igneous crust formed at such volcanic rifted Both types of explanations, i.e. plume models and necking mod- margins is typically 20–30 km (White et al. 1987; Mutter & Zehnder els, implicitly assume that the ‘normal’ state of asthenospheric man- 1988; Holbrook et al. 1994). Because normal oceanic crust, which tle is isothermal and thus static. Anything that cannot be explained most likely results from decompressional melting of passively up- by the passive upwelling of mantle with normal potential tempera- welling mantle with normal potential temperature (∼1300◦C) (Klein ture, therefore, seems to require some special mechanism. Even if & Langmuir 1987; McKenzie & Bickle 1988; Kinzler & Grove asthenospheric mantle was indeed isothermal at some time, however, 1992), is only 6–7 km thick (e.g. White et al. 1992), the voluminous cooling from above results in the growth of a thermal boundary layer, magmatism implied by several times thicker igneous crust formed which may eventually become unstable and lead to sublithospheric, during rifting has been commonly attributed to the upwelling of small-scale convection (Foster 1965; Parsons & McKenzie 1978; unusually hot mantle originating in a large plume head (White & Buck & Parmentier 1986; Davaille & Jaupart 1994), after which McKenzie 1989; Richards et al. 1989; Hill et al. 1992). On the other the resultant thermal structure is no longer isothermal. Static and hand, continents seem to rift at pre-existing weak zones such as cra- isothermal asthenosphere, therefore, seems to be a rather extreme tonic edges (Wilson 1966; Anderson 1994). Mutter et al. (1988) pro- case, despite the fact that it is commonly assumed to be normal in posed that a sharp lateral thermal gradient produced by lithospheric studies of terrestrial magmatism. If asthenospheric mantle is usu- ally convecting, then, how does this affect our inferences regarding ∗Now at Department of Earth and Planetary Science, University of mantle dynamics based on the products of melting? The impor- California, Berkeley, USA. tance of small-scale convection may be significant, particularly for C 2002 RAS 179 180 J. Korenaga and T. H. Jordan magmatism during continental rifting. Unlike mid-ocean ridge mag- Using values appropriate for the shallow upper mantle, i.e. −5 3 3 −6 2 −1 matism, which may be adequately modelled with steady-state, pas- α = 3 × 10 , ρ0 = 3.3 × 10 kg m , κ = 10 m s , k = sive mantle upwelling driven by large-scale plate motion (e.g. 3.3Wm−1 K−1, and g = 9.8ms−2, the velocity scale expected for McKenzie & Bickle 1988), continental rifting is essentially a tran- small-scale convection with a depth extent of 150 km is calculated as sient process, in which an initially null surface divergence evolves a function of asthenospheric viscosity, for several values of surface into finite-rate spreading. The dynamic aspect of pre-existing sub- heat flux (Fig. 1a). With the above thermal conductivity and a tem- lithospheric convection may be important in calculating the amount perature difference of 1300 K across the rigid lithosphere, heat fluxes of melt generated during rifting, because, when the convective up- of 40–10 mW m−2 approximately correspond to lithospheric thick- welling rate exceeds the surface divergence rate, this can produce nesses of 100–400 km, respectively. The viscosity of the astheno- ‘excess’ magmatism due to rapid mantle fluxing through the melting sphere is probably in a range of 1018–1019 Pa s, based on laboratory zone. This type of active mantle upwelling has been proposed to be studies (Karato & Wu 1993; Hirth & Kohlstedt 1996) and geophysi- important in recent studies on continental rifting magmatism (e.g. cal observations (Pasay 1981; Weins& Stein 1985; Hager & Clayton Kelemen & Holbrook 1995; Korenaga et al. 2000). 1989). Though the depth extent of this weak asthenosphere is not The rheology of the Earth’s mantle is characterized by strongly well-known, mantle viscosity is expected to increase with depth be- temperature-dependent viscosity. Because most of the tempera- cause of its non-zero activation volume (e.g. Karato & Wu 1993). ture variation occurs in nearly rigid lithosphere, the energetics of Indeed, the mantle transition zone (400–670 km) seems to have a small-scale convection beneath lithosphere (or stagnant-lid convec- higher viscosity, of 1020–1021 Pa s, and a further increase in viscos- tion) can be approximated by that of isoviscous convection (e.g. ity is also indicated for the lower mantle (Hager et al. 1985; Hager Solomatov 1995). Based on the boundary layer theory (e.g. Turcotte & Schubert 1982), the velocity scale of such small-scale convection, U, can be expressed as a function of surface heat flux, q, as (Korenaga 2000) αρ gκ D2q U ∼ 0 , (1) 8µk where α is thermal expansivity, ρ0 is a fluid density at some refer- ence temperature, g is gravitational acceleration, κ is the thermal diffusivity, D is the depth extent of convection, µ is fluid viscosity and k is the thermal conductivity. Cellular convection with a unit aspect ratio is assumed in deriving the above scaling law. In this case, the temperature difference across the thermal boundary layer, T , is related to the surface heat flux as q 1/4 3/4 8κµ q Tq ∼ . (2) αρ0g k The thickness of the stagnant lid controls heat flux at the top of the convecting domain. Thicker lithosphere can transfer less heat, so the strength of sublithospheric convection is reduced with increasing lid thickness. Eq. (1) is only conditionally applicable to stagnant-lid convec- tion, because the generation of negative buoyancy for small-scale convection is constrained by temperature-dependent viscosity. The thickness of the cold thermal boundary layer that can participate in convection is limited by a viscosity ratio corresponding to the tem- perature drop across the unstable boundary layer, and the viscosity ratio is about 3 for marginally stable convection and can be as high as 10 for fully developed convection (Davaille & Jaupart 1993). The temperature dependency of mantle rheology can be modelled by the following Arrhenius law (e.g. Weertman 1970), E E µ(T ) = µ0 exp − (3) RT RT0 where E is activation energy, R is the universal gas constant and µ0 is reference viscosity at temperature T0, for which we use the interior temperature of the convecting domain. Denoting p = log(µmax/µ0), where µmax is the highest viscosity in the unstable boundary layer, Figure 1. (a) Velocity scale of isoviscous convection subject to a given the maximum temperature drop allowed in the boundary layer may surface heat flux (eq. 1) is plotted as a function of viscosity. The depth be expressed as, scale of convection is set as 150 km. (b) Temperature drop across cold pRT2 thermal boundary layer (eq. 2) is compared with the maximum temperature T ∼− 0 (4) drop imposed by temperature-dependent viscosity (straight lines, eq. 4). The p E reference temperature T0 is set as 1573 K. Cases for two values of activation −1 when Tp T0. The velocity scale derived for isoviscous convec- energy (200 and 400 kJ mol ) and the logarithmic viscosity contrast of 1.0 tion (1) can be applied to stagnant-lid convection, if Tq < |Tp|. (corresponding to the viscosity contrasts of 3) are illustrated. C 2002 RAS, GJI, 149, 179–189 Sublithospheric mantle convection 181 & Clayton 1989; Simons & Hager 1997; Forte & Mitrovica 1996).