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Firm Mantle Plumes and the Nature of the Core–Mantle Boundary Region Earth and Planetary Science Letters 232 (2005) 29–37 www.elsevier.com/locate/epsl Firm mantle plumes and the nature of the core–mantle boundary region Jun KorenagaT Department of Geology and Geophysics, Yale University, P.O. Box 208109, New Haven, CT 06520-8109, USA Received 9 September 2004; received in revised form 22 December 2004; accepted 6 January 2005 Editor: S. King Abstract Recent tomographic imaging of thick plume conduits in the lower mantle, when combined with plume buoyancy flux based on hotspot swell topography, indicates a very high plume viscosity of 1021–1023 Pa s. This estimated plume viscosity is comparable or may even be greater than the viscosity of the bulk lower mantle, the estimate of which ranges from 2Â1021 to 1022 Pa s. Here I show that both very high viscosity and large radii of lower-mantle plumes can be simultaneously explained if the temperature dependency of lower-mantle rheology is dominated by the grain size-dependent part of diffusion creep, i.e., hotter mantle has higher viscosity. Fluid-dynamical scaling laws of a thermal boundary layer suggest that the thickness and topography of the DW discontinuity are consistent with such mantle rheology. This new kind of plume dynamics may also explain why plumes appear to be fixed in space despite background mantle flow and why plume excess temperature is only up to 200–300 K whereas the temperature difference at the core–mantle boundary is likely to exceed 1000 K. D 2005 Elsevier B.V. All rights reserved. Keywords: mantle plumes; seismic tomography; hotspot swells; diffusion creep; grain growth 1. Introduction almost invisible [4]. Traditionally, the Rayleigh– Taylor instability of a hot bottom boundary layer is Seismic imaging of deep mantle plumes has long thought to produce the upwelling of a less viscous been considered as a daunting task [1] because plume plume through a more viscous overlying fluid. conduits are believed to be a narrow feature with a Viscosity contrast between a plume and the ambient radius of much less than 100 km [2,3] and the wave mantle is typically assumed to be on the order of 102– front healing effect makes such a small-scale feature 103, and this contrast results in the formation of a large spherical head followed by a narrow conduit (Fig. 1). It is thus quite surprising that a recent finite- T Tel.: +1 203 432 7381; fax: +1 203 432 3134. frequency tomography has resolved quite a few deep E-mail address: [email protected]. mantle plumes with very large radii, typically ranging 0012-821X/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2005.01.016 30 J. Korenaga / Earth and Planetary Science Letters 232 (2005) 29–37 a) Heff > 0 b) Heff < 0 surface by a plume. The buoyancy flux is calculated from swell excess topography, absolute plate velocity, and density contrast between mantle and seawater, all of which are known with reasonable accuracy. Hawaii has by far the largest buoyancy flux of 8700 kg sÀ1; other hotspots mostly fall in the range of 1000–4000 kg sÀ1 [7]. These estimates are most likely the upper bound for thermal buoyancy flux because not all of swell topography can be attributed to the thermal buoyancy of mantle plumes. Dynamic tomography due to viscous stress [8] as well as compositional Fig. 1. The different sign of the activation enthalpy results in buoyancy resulting from mantle melting [9] may different plume morphology and dynamics [2,19,30]. (a) In the case reduce the estimated flux. In addition, small-scale of positive activation enthalpy, a less viscous plume rises through a convection may facilitate the thinning of lithosphere more viscous fluid. A large spherical head forms followed by a narrow plume conduit. (b) Negative activation enthalpy results in a [10], either independently of or coupled with plume more viscous plume intruding in a less viscous fluid. Plume head influx. It is important to note that this upper bound on and tail have similar radii, and upwelling is more diffuse. plume flux corresponds to the lower bound on plume viscosity estimated in the following, thus making my from 200 to 400 km [5]. The lateral dimension of argument robust. those imaged plumes is one of the most reliable The plume buoyancy flux, M˙ A, is related to the U U features of the tomography. The reported radii are the plume heat flux, Q,asM˙ A=a Q/cp , where a is minimum estimate based on extensive resolution tests thermal expansivity, cp is specific heat at constant (note: the tomographic images presented by [5] pressure, and the superscript U indicates the upper generally show larger radii than these minimum mantle values appropriate for surface expression like estimates because of blurring inherent in tomogra- swell topography. Assuming steady state, buoyancy- phy); if plume conduits are narrower, even finite- driven axisymmetric upwelling through a circular frequency tomography could not image them. conduit, then, the buoyancy flux of a plume and its Although it is sometimes claimed that recent dynamic conduit radius (a) may be related as [3]: models exhibit similarly thick plumes [6], those ÀÁ 2 4 plumes with large radii result from the use of paq0DTp ga M˙ A ¼ ð1Þ temperature-independent viscosity and/or low Ray- Alp leigh number (i.e., very high mantle viscosity) in numerical modeling. As I will demonstrate in the where q0 is reference density, DTp, is the amplitude of following, thick plume conduits, whether created in plume temperature anomaly, g is gravitational accel- numerical models or imaged in seismic tomography, eration, and lp is centerline plume viscosity (much imply a serious conflict with the surface observation lower than ambient viscosity, l0, owing to temper- of plume flux, if dynamics is properly scaled to the ature-dependent viscosity). In the numerical and Earth’s mantle and if plume viscosity is assumed to be theoretical models of [3], linear exponential viscosity lower than the surrounding mantle. The seismically is employed with a parabolic temperature distribution. imaged thick conduits, if they are indeed a solid The total viscosity contrast is given by eul0/lp, and feature as claimed by [5], may require a fundamental Eq. (1) is valid only when eJ1(e is typically 102– rethinking of plume dynamics. 103 in previous studies). The constant A is equal to (a/ U U 2 a )(cp /cp)(log(e)) . The conduit radius is defined here as the radius where the temperature anomaly is 2. Plume buoyancy flux and plume radius one-half its centerline value [3], thus the radius a covers the dominant part of the thermal halo. Note Plume buoyancy flux [7] provides a robust con- that, because viscosity is much lower at the center of straint on the flux of hot material brought to the near the plume conduit, the mechanical conduit is much J. Korenaga / Earth and Planetary Science Letters 232 (2005) 29–37 31 narrower than this thermal halo. What is most relevant far as hotspot swells are regarded as the surface to seismic tomography is the thermal halo, and the expression of imaged mantle plumes, therefore, high definition of the radius a here approximately corre- plume viscosity appears to be an inevitable geo- sponds to the definition of plume radius adopted by dynamical interpretation of the tomography. One may [5] (where seismic velocity anomaly drops less than argue that plume flux may actually be highly time- 0.3%, corresponding to the temperature anomaly of dependent and the assumption of steady-state dynam- 100 K in the lower mantle). ics in Eq. (1) is inappropriate. It is highly unlikely, The most uncertain parameter here is plume however, that all of deep mantle plumes are synchro- viscosity, which can vary by a few orders of nously in a reduced flux state. Moreover, time- magnitudes; the uncertainty of other parameters is dependent behavior (e.g., starting plume) tends to less than a factor of two. This scaling law is compared give rise to greater flux than the steady state [6], so the to the observed correlation between plume flux and use of steady-state formula corresponds to the lower radius in Fig. 2, which suggests that plume viscosity is bound on plume viscosity. It should be noted that, likely to be greater than 1021 Pa s for most of deep- with this approach, heat flux carried by mantle plumes mantle plumes and can be as high as 1023 Pa s in some remains essentially the same as that estimated by cases. In most of previous studies on plume dynamics, Sleep [7], i.e., ~2 TW. Although Montelli et al. [5] plume viscosity has been assumed to be much lower, argued that their tomographic image indicates much typically around 1019 Pa s. With such a low viscosity, larger plume heat flux than previously estimated, the thick plume conduits as inferred from the finite- seeing large radii does not readily imply high heat flux frequency tomography would produce an unaccept- because seismic image alone cannot constrain plume ably high plume flux of 105–106 kg sÀl because the rise velocities. buoyancy flux by Poiseuille-type flow is proportional The inferred plume viscosity, 1021–1023 Pa s, is to the fourth power of the conduit radius (Eq. (1)). As comparable to or may exceed the viscosity of bulk lower mantle (lLM), the estimate of which ranges 21 22 106 from 2Â10 –10 Pa s [11]. For the above assump- µ 19 p=10 Pa s tion of Poiseuille-type flow to be valid, plume must be 20 much less viscous than the surrounding mantle, which 105 10 acts as a rigid wall.
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