T41H-01 08:00h
Energetic and convectional aspects of the EH Earth paradigm
Isotopic (stable and radiogenic), as well as highly reduced characteristics indicate that EH (iron rich enstatite) chondrites, are the most likely building material for the Earth-Moon system.(Javoy 1995) Each new isotopic study in the recent years has reinforced that conclusion. The mineralogical and chemical composition of this Earth building material introduces several fundamental changes relative to the routinely and imprecisely named "chondritic composition" used up to now to describe the energetics of the Earth. This material is silicon and iron-rich, and much poorer in the main refractory radioactive elements (U, Th) than generally thought. This results in a distinctly different composition of the upper and lower mantle. The upper mantle keeps the general characteristics described previously while the lower mantle is richer in silicon and iron. The lower mantle mineralogy is essentially that of a Mg-Fe perovskite, denser by a few percent than the upper mantle material under identical P-T conditions. The core contains 7 to 9 % Si, 3 to 4 % O and little if any S. The oxidized iron distribution between upper and lower mantle and the core was established during the first 30 to 40 million years of the Earth history through the reaction : SiO2 +3 Fe = FeSi +2 FeO The radioactive content of the lower mantle has been almost 50% lower than that of the upper mantle during the first 2.5 billion years of the Earth's history. This enables the early setting of a stable two-level convection system in the mantle whose behaviour has been modeled successfully. The fine tuning of the Earth global composition around the average EH composition now awaits only improvements in high resolution geophysical data on the lower mantle. Javoy M. Geophys. Res. Let. 2219-2222, 1995.
T41H-02 08:20h
Flux estimates from tomographic plume images yield evidence for chemical stratification in the mantle.
We performed a new resolution analysis of the plumes visible in P wave tomography (Montelli et al, {\it Science 303},338, 2004), using realistic plume sizes matched to the observed ones, and including estimates of both the thermal and the volume flux. This experiment revealed 15 segments of lower mantle plumes that are sufficiently well resolved to estimate the plume flux. To do so we solve the Stokes equation, assuming that there is an approximate local equilibrium between the thermochemical buoyancy and the viscous drag.\To handle the large uncertainties in physical model parameters, we generated an ensemble of 600,000 earth model parameter combinations, varying viscosity, excitation enthalpy, geotherm, thermal expansivity, $\partial V_p/\partial T$, melting temperature, iron content, attenuation and heat capacity. For commonly accepted values of the viscosity of the lower mantle around $5 \times 10^{22}$ Pa\ s, the heat flux through the plumes is unacceptably high unless the buoyancy of the hot material is reduced by a denser component, most likely iron (as in our modeling).\For five of the well resolved plume segments, located beneath the hotspots of Afar, Kerguelen, Tahiti, Cape Verde and La Reunion, independent estimates of the buoyancy flux are available, which allow us to find combinations of `acceptable' model parameters, in particular the iron content and the viscosity. For Afar, Cape Verde and Tahiti this results in a maximum likelihood estimate of the extra iron along a line given by $\Delta X_{Fe} = 12.3 - 0.5\log \eta$ % (viscosity $\eta$ in Pa s), typically requiring $\Delta X_{Fe} = 1%$, or an iron enrichment of about 10% in the plume (Kerguelen and Reunion plot above and below this line, respectively). We use this to estimate the flux in other plumes.\It is possible that the buoyancy flux as estimated by the topographic swell underestimates the flux at depth because some of the plume flux is used to maintain the asthenosphere, as originally proposed by Morgan in 1972, allowing for lower $\Delta X_{Fe}$ or $\eta$. But even then our findings seems to support the hypothesis that the region above the Earth's core has a chemical composition that is distinct from the rest of the mantle. Iron enrichment of plumes would also explain the absence of plume heads in the tomographic images and leads to an alternative explanation of flood basalts: a starting plume will tap into the top of the lower mantle reservoir and be only slightly enriched in iron, leading to very high values of heat and volume flux, as our calculations indicate.
T41H-03 08:35h
A critical analysis of Earth's heat loss and secular cooling
Earth's rate of heat loss is about twice as large as the amount of heat generated by radioactive decay, which provides a strong constraint on mantle convection models. Here, we evaluate how theoretical models compare with heat flow data. Most studies rely on a parameterized law for convective heat transfer, of the form $Q=f(l)Ra^{1/3}T^{4/3}$, where non-dimensional heat flux $Q$ is written as a function of Rayleigh number $Ra$ and non-dimensional temperature $T$. Coefficient $f$ is controlled by the planform of mantle convection and depends on dominant wavelength $l$. Earth's heat loss depends on mantle temperature and maximum lithospheric age, as well as a shape function for the heat flux distribution. The spatial distribution of heat flux density at the surface is also characteristic of the planform and regime of convection. Comparing the observed distribution to theoretical predictions for a range of convection models illustrates the peculiar characteristics of Earth's convective regime. Earth's heat loss is sensitive to the maximum lithospheric age and to the distribution shape function. The simplest model, such that neither has changed by large amounts over geological history, predicts small secular cooling rates and yields the observed difference between present-day heat loss and heat production.
T41H-04 08:50h
Recycling the lid: The influence of subduction and stirring on convection in a fluid with a temperature-dependent viscosity with applications to planetary mantle convection
We use two-dimensional numerical simulations to study the dynamics and steady-state heat transfer properties of ${\rm Rayleigh-B\'enard}$ convection with additional large-scale stirring imposed externally from above in a fluid with a temperature-dependent viscosity. Our results show that the forced subduction and stirring of an otherwise stagnant cold boundary layer (i.e. "stagnant lid") influences both upper and lower boundary layer dynamics as well as the global heat transfer properties of the flow. The specific nature of the effects depends on the imposed velocity, $V$, the total viscosity ratio, $\lambda_t$, and the mechanical boundary conditions in the system. Quantitatively, Nu increases from the stagnant lid value with $V$, but the nature and magnitude of the increase depends strongly on $\lambda_t$. In addition, for a given $V > 0$ and $\lambda_t$, we find that the average thickness of the hot lower boundary layer, $\delta$, depends on the hot boundary viscosity ratio, $\lambda_h$. As $ \lambda_h$ is increased from 1 to around 10, horizontal flow in the thermal boundary layer causes $\delta$ to decrease from critical to a minimum thickness that depends on $\lambda_t$. Plumes are suppressed and heat transfer is due to large-scale flow. As $ \lambda_h$ is increased from order 10 to $10^3$, however, the hot boundary layer becomes viscously decoupled from the overlying large-scale flow and $\delta$ increases to the critical thickness for the lower boundary layer to reach local marginal stability. Low viscosity cavity plumes form as a result and are responsible for the majority of the heat transfer from the hot boundary. Our results are applied to understand mantle convection in the presence of steady or episodic plate tectonics characteristic of the Earth and possibly Venus. This application suggests that the morphology and dynamics of mantle upwellings on Earth may depend on the presence of plate subduction and that the dynamics and morphology of upwellings on Venus may have been time- and space-variable, as a result of episodic subduction.
T41H-05 09:05h
Scaling the heat flux through a thermal boundary layer
Heat transfer by thermal convection is almost exclusively controlled by the nature of boundary layers: thermal interfaces within the mantle thus act on the cooling of the Earth as preponderant features. Forty years ago, L. N. Howard proposed a simple model describing time-dependent heat transfer at high Rayleigh number with the fast convective destabilization of a thermal boundary layer after a slow conductive growth. The time-averaged thickness of the boundary layer is linked to the duration of the conductive stage and allows the computation of the local Rayleigh number $Ra_{\delta}$, linked to the stability of the boundary layer. A scaling relationship for the heat flux as a function of the Rayleigh number is obtained in the form $Nu=(Ra/Ra_{\delta})^{1/3}$. It must be emphasized that this 'critical' local value is different than the classical critical value controlling the stability of the whole layer. We aim at re-evaluating Howard's model, modifying several aspects of the boundary layer characteristics and testing the predictions on convective flows: the description of Rad, as a function of the globally defined Ra and of thermal and mechanical conditions within the boundary layer, should help to refine the scaling laws for heat transfer. We use a simple numerical procedure to solve the linear stability problem for a cooled layer with various heating modes, boundary conditions and viscosity laws. These results are then compared to 3D calculations for thermal convection, concerning both the onset of convective instabilities and fully-developed, time-dependent, convective motion.
T41H-06 09:20h
The Surface Heat Flow Constraint Upon Mantle Convection and Earth Evolution
Although the primary impact of the mantle convection process, apart from its role as prime mover of surface plate tectonics, is through the control it exerts upon the rate of radial heat transport, little or no use is normally made of the constraint upon convection models provided by surface heat flow measurements. In this paper we will both review and extend a range of recent analyses in which observed surface heat flow has been employed as a target in the modelling process. The models that have been employed in this way include those based upon seismic tomographic imaging of mantle lateral heterogeneity, a priori models of convective mixing based upon direct solution of the governing field equations, and finally models of the thermal evolution of the Earth in which the convection process is "parameterized". As we will discuss, the constraint upon such models that is provided by the spherically averaged mantle derived contribution to the surface heat flow is both non-trivial and extremely useful. Additional important information is also provided by the observed age dependence of this field as is well known.
T41H-07 INVITED 09:40h
How do we Reconcile the Heat Budget of the Core with the Power Requirements for the Geodynamo?
Regeneration of the magnetic field by convection in the core places demands on heat flow into the base of the mantle. If the heat flow is too low, thermal convection is shut off and the rate of generation of compositional buoyancy by solidification of the core becomes too low to sustain the geodynamo. Conversely, a large heat flow causes rapid growth of the inner core, so that convection prior to the appearance of the inner core must be sustained by thermal buoyancy alone. The attendant requirements on primordial heat become more severe as the age of the inner core decreases. Present-day estimates of temperature in the core suggest that the heat flow into the base of the mantle is 6 to 12 TW, which is sufficient to supply 1 to 2 TW of power to the geodynamo. However, when this range of heat flow is used in thermal history calculations we obtain a young inner-core age and an implausibly hot core temperature prior to 3 Ga. More reasonable thermal histories can be obtained using a lower heat flow if the power requirements for the geodynamo are substantially reduced (say 0.1 to 0.2 TW). On the other hand, a low heat flow appears to be incompatible with estimates of temperature in the core. There are two ways to reconcile the heat budget of the core with the power requirements for the geodynamo. First, we can add radiogenic heat sources to the core. These additional heat sources would slow the cooling of the core for a prescribed heat flow and extend the age of the inner core. Approximately 200 ppm of K in the core is sufficient to avoid unrealistic temperatures at early times. Alternatively, we can reduce heat loss from the core by accumulating radioactive isotopes into a layer that surrounds the core. Such a layer could form by segregating dense oceanic crust at the base of the mantle or by partitioning radioactive isotopes into a deep partial melt.