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9.08 Thermal Evolution of the Mantle G 9.08 Thermal Evolution of the Mantle G. F. Davies, Australian National University, Canberra, ACT, Australia ª 2007 Elsevier B.V. All rights reserved. 9.08.1 Introduction 197 9.08.1.1 Cooling and the Age of Earth 197 9.08.1.2 A Static Conductive Mantle? 198 9.08.2 The Convecting Mantle 198 9.08.2.1 A Reference Thermal History 200 9.08.3 Internal Radioactivity and the Present Cooling Rate 202 9.08.4 Variations on Standard Cooling Models 203 9.08.4.1 Effect of Volatiles on Mantle Rheology 203 9.08.4.2 Two-Layer Mantle Convection 204 9.08.4.3 Static Lithosphere Convection, and Venus 205 9.08.5 Coupled Core–Mantle Evolution and the Geodynamo 206 9.08.6 Alternative Models of Thermal History 208 9.08.6.1 Episodic Histories 208 9.08.6.2 Strong Compositional Lithosphere 209 9.08.7 Implications for Tectonic Evolution 210 9.08.7.1 Viability of Plate Tectonics 211 9.08.7.2 Alternatives to Plate Tectonics 212 9.08.7.3 History of Plumes 212 9.08.8 Conclusion 214 References 214 9.08.1 Introduction age emerged. This was done by William Thomson, better known as Lord Kelvin, who played a key role The thermal evolution of Earth’s interior has fea- in the development of thermodynamics, notably as tured fundamentally in the geological sciences, and the formulator of the ‘second law’. it continues to do so. This is because Earth’s internal Kelvin actually calculated an age for the Sun first, heat fuels the driving mechanism of tectonics, and using estimates of the gravitational energy released by hence of all geological processes except those driven the Sun’s accretion from a nebular cloud, the heat at the surface by the heat of the Sun. The thermal content of the present Sun, and the rate of radiation of evolution also featured famously in a nineteenth- heat, concluding that the Sun was likely to be younger century debate about the age of Earth. than 100 Ma and most unlikely to be older than 500 Ma (Kelvin, 1862). The following year Kelvin calculated an age of Earth using different physics (Kelvin, 1863). He 9.08.1.1 Cooling and the Age of Earth reasoned that the known geothermal gradient of about –1 According to Hallam (1989), from the time when the 20Ckm near Earth’s surface would have declined origin of Earth was considered by scientists of the from an essentially infinite gradient at the time of European Enlightenment it was conceived as having Earth’s formation. Making use of Fourier’s law to started hot, notably in the nebular theories of Kant solve the resulting thermal diffusion problem (Davies, and Laplace. This led to conjectures and very rough 1999) he obtained an age between 20 and 400 Ma with estimates of how long it may have taken to cool his most probable value being 98 Ma. There ensued down, and thus to estimates of the age of Earth. several decades of heated debate between and among However, it was not until Fourier had formulated geologists and physicists, with Kelvin’s last estimate his ‘law’ of conduction and the science of thermody- (Kelvin, 1899)beingonly24Ma. namics was established that a quantitatively reliable, A number of Kelvin’s assumptions were challenged though physically inappropriate, estimate of Earth’s duringthecourseofthislongcontroversy,themost 197 198 Thermal Evolution of the Mantle telling challenge in retrospect coming from The through a liquid because a liquid does not have any Reverend Osmond Fisher (Fisher, 1881) who pointed shear strength. A second argument is that Earth’s out that if Earth’s interior were ‘plastic’ (meaning in response to tidal forces implies quite high rigidity. some degree fluid), then a much greater reservoir of Finally, Earth has, on average, a slightly greater equa- heatwouldbetappedandtheresultingagecouldbe torial bulge than is accounted for by its rotation, and much greater. Fisher’s point was that conduction alone this was intepreted to imply that the mantle has a would have cooled only the outer few hundred kilo- viscosity (a fluid’s resistance to flow) sufficiently high meters of Earth, whereas a circulating fluid could bring to preclude significant internal motion. Against this, heat from much deeper as well, so it would take longer the concept of a deformable ‘asthenosphere’ extending for the larger amount of heat to be removed at the down for several hundred kilometers was widely held currently observed rate. Fisher’s point did little to among geologists as necessary to accommodate the settle the nineteenth-century controversy, but it considerable movements they inferred to have returned in a slightly different guise a century later. occurred in the crust (Barrell, 1914). The controversy with Kelvin was finally settled The initial presumption used to reconcile the through the discovery of radioactivity, which pro- observed heat flow with a static mantle was that the vided a previously unknown source of heat within radioactivity must be confined to within about 20 km Earth, so heat could be replenished as it is lost of the surface, and observations in continental areas through the surface, and the flow of heat thus main- support this (Jeffreys, 1976). The implication is that tained for much longer than Kelvin’s estimates. The most of the heat emerging from continental crust is actual determination of Earth’s age relied on exploit- generated there and can readily be conducted to the ing a different aspect of radioactivity, the production surface. The amount of heat coming from deeper was of daughter isotopes. This task was pursued most presumed or implied to be very small. However, this notably by Holmes from early in the twentieth cen- encounters the problem that heat flow from ocean tury (Holmes, 1911, 1913) but not completed to basins is greater than from continents, but the thin, general satisfaction until meteorites were dated by less radioactive oceanic crust can account for only a the lead–lead method and Earth was shown to fit small fraction of the total (Sclater et al., 1980). within the meteorite trend (Patterson, 1956). The A later presumption was that thermal conductiv- age of Earth is still determined only indirectly. ity must increase substantially with depth, so that a sufficient heat flow could be sustained for a much greater time. This possibility was bolstered by the 9.08.1.2 A Static Conductive Mantle? proposal that radiative transfer of heat could be The discovery of the heat generated by radioactivity important in the mantle (Clark, 1957). The idea is provided Earth with an enduring source of heat, but that if mantle minerals are sufficiently transparent, it created another problem by breaking the consis- then the blackbody radiation of the hot materials tency in Kelvin’s argument between age and the could transmit significant distances. Since the trans- removal of heat by conduction. If heat escapes from mission would be like a random walk it constitutes a Earth’s interior by conduction, then Kelvin’s argu- diffusion process and so can be described by an ment would still seem to require Earth to be less than enhanced effective conductivity. However, the pre- 100 My old, otherwise the surface heat flow would be sence of iron in minerals tends to reduce the much less than is observed. Put another way, if Earth transparency of the minerals at the relevant wave- is 4.5 Gy old, roughly 100 times Kelvin’s estimate, lengths (Shankland et al., 1979). Thus, it was not at all then the geothermal gradient ought to be 10 times obvious that radiative transfer could resolve the issue. less than the 15–20CkmÀ1 commonly observed in There have been recent claims for a significant effect deep mines and boreholes. This is because in the (Hofmeister, 2005), though if they are significant it relevant thermal diffusion process the heat flow would probably only be for the deepest mantle. (and the temperature gradient) declines in propor- tion to the square root of time (Davies, 1999). Until the 1960s, it was most generally held that 9.08.2 The Convecting Mantle Earth’s mantle is solid and unyielding (Jeffreys, 1976). This conclusion was based on several lines of evidence, The emergence of plate tectonics in the 1960s the most obvious being that the mantle transmits seis- directly implied that at least the upper part of the mic shear waves, and shear waves cannot propagate mantle is mobile. In 1969 Goldreich and Toomre Thermal Evolution of the Mantle 199 (1969) pointed out that the excess bulge at the equa- Subsequently several groups realized, more-or- tor varied about as much with longitude as with less independently, that the relationship could be latitude, so the old explanation that it was a fossil used to calculate the thermal evolution of the Earth from past faster rotation could not be correct. In their without assuming that heat loss is equal to heat pro- reinterpretation, the Earth adjusts its rotation to bring duction. Sharpe and Peltier (1978, 1979) were the its largest bulges to the equator, and this implies an first, although they implemented it in terms of an ‘upper’ bound on viscosity that is quite compatible enhanced thermal diffusion, which does not accu- with a mobile mantle. With later interpretations of rately represent the internal temperature profile. postglacial rebound constraints and positive geoids Others soon used it to characterize the total heat over subduction zones, the current picture is that the transport in terms of a representative internal tem- 20 upper mantle has a viscosity of (1–3) Â 10 Pa s perature (Cassen et al., 1979; Schubert, 1979; while the lower mantle is perhaps 30 times more Schubert et al., 1979a, 1979b, 1980; Stevenson and viscous than this (Hager, 1984; Mitrovica, 1996; Turner, 1979; Davies, 1980; Stacey, 1980).
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