T42A-01 10:20h
HIGH HEAT FLUX AND LOW EXCESS TEMPERATURE IN MANTLE PLUMES INFERRED FROM NON-ADIABATICITY IN INTERNALLY HEATED MANTLE CIRCULATION MODELS
Heat transfer across the core mantle boundary (CMB) is fundamentally important to the Earth's internal energy budget, but the amount of heat entering the mantle from the core is poorly known. Classic arguments based on the dynamic topography over mantle hotspots suggest a rather modest core contribution to the mantle energy budget, on the order of 5-10%. Recent geodynamic studies, however, favor significantly higher values to overcome problems of insufficient internal mantle heat generation, and to satisfy constraints on power requirements of the geodynamo and the thermal history of the core. Here we use a high resolution mantle dynamics model to show that the non-adiabatic mantle geotherm which arises from internal mantle heating has a dramatic effect in lowering the excess temperature of hot upwelling plumes by systematically decreasing plume temperatures relative to ambient mantle away from the CMB. This non-adiabatic effect of internally heated mantle flow may explain the unusually low plume excess temperatures inferred from the petrology of hotspot lavas, and implies current estimates of the core heat flux based on hotspot topography should be raised perhaps by a factor of three.
T42A-02 10:35h
Plume Heat Flux, Core Heat Flux, and the Style of Mantle Convection
The style of mantle convection (i.e., whole mantle convection versus layered mantle convection) is an important question that affects nearly every aspect of the Earth's evolution. Although geochemical observations have long suggested a layered mantle with more enriched mantle material in the bottom layer to provide a significant amount of heat to the top layer, the nature of such a layering remains unclear. An important observation that may help constrain the style of mantle convection is the plume heat flux [Davies, 1999]. Plume heat flux is estimated as $\sim$ 3.5 TW, or 10% of the surface heat flux, and which is also believed to be roughly equal to the heat flux out of the core [Davies, 1988; Sleep, 1990]. However, Labrosse [2002] argued that plume heat flux may only account for a small fraction of the core heat flux based on 3-D Cartesian isoviscous thermal convection models. Here by formulating 3-D spherical mantle convection with different depth- and temperature-dependent viscosity, we examine the dependence of ratios of plume heat flux to the surface heat flux and bottom heat flux on internal heating rate, mantle rheology, and Rayleigh number. We found that without a depth-dependent viscosity, mantle convection is required to be driven mostly ($>$50%) by basal heating, in order to produce the observed ratio (10%) of plume heat flux to surface heat flux. A large fraction of the bottom heat flux is consumed to heat the cold slabs that reach the bottom boundary and does not lead to plume heat flux, consistent with Labrosse [2002]. Since it is unlikely that the core can supply this amount of heat flux ($>$18 TW), these calculations with no depth-dependent viscosity support the layered mantle convection in which both the core and the bottom layer of the mantle can provide this amount of heat for the top layer. With a depth-dependent viscosity (X30 jump at 670 km depth plus X10 gradual increase), both the ratios of plume heat flux to surface heat flux and bottom heat flux increase for a given amount of internal heating rate. Plume heat flux is more comparable to core heat flux. Therefore, to use plume heat flux as a constraint on core heat flux and the style of mantle convection is critically dependent on mantle viscosity structure.
T42A-03 10:50h
Bounds on the energy budget of the core from geodesy and geomagnetism.
There is much renewed interest in the energetics of the core because of its relevance to the thermal history of the Earth and the ability for magnetic field generation to take place over geological time. Here we present the results of calculations to place lower bounds on both the Ohmic dissipation and the entropy production rate. To do so we adopt the constraints arising from geodetic studies of the Earth's nutations. Buffett and coworkers deduce the field strength at the core-mantle and inner-core boundaries necessary to produce the required dissipation mechanism to account for the out-of-phase response of the Earth to the planetary driving mechanisms. We use these in tandem with geomagnetic constraints in a variational procedure to determine precise lower bounds on the quantities of interest. Whilst these lower bounds are, by their very nature, underestimates of the true dissipations, the results are actually approaching (within an order of magnitude) several recent estimates of the Ohmic dissipation. We will discuss the results, areas of uncertainty and possible future avenues of investigation.
T42A-04 11:05h
Models of the Earth's thermal and magnetic evolution
The thermal and hence magnetic evolution of the Earth's core is coupled by the heat flow at the CMB to convection in the mantle. We use numerical and parameterized models of convection in the Earth's mantle in conjunction with energy and entropy conservation models for the core to study the effects of convection style in the mantle on the core's thermal and magnetic evolution. Different scenarios for mantle convection which satisfy modern-day constraints such as surface heat flow and bulk silicate Earth composition are considered. We analyze the effects that various viscosity profiles, phase change parameters and degrees of internal heating in the mantle have on the heat flow at the CMB and the magnetic field generated in the core. The results from numerical and parameterized models are compared, with the former displaying strong short-timescale variations. We find that mantle avalanches can significantly affect the generation of the magnetic field. Models with a small degree of internal heating in the core allow for a sustained geodynamo even before the time of inner-core formation. In addition, we discuss the possibility of extending our analyses to other terrestrial bodies.
T42A-05 11:20h
Continental Insulation, Mantle Cooling, and the Surface Area of Oceans and Continents
It is generally assumed that continents, acting as thermal insulation above the convecting mantle, inhibit the Earth's internal heat loss. We present theory, numerical simulations, and laboratory experiments to test the validity of this intuitive and commonly used assumption. A scaling theory is developed to predict heat flow from a convecting mantle partially covered by stable continental lithosphere. The theory predicts that parameter regimes exist for which increased continental insulation has no effect on mantle heat flow and can even enhance it. Partial insulation leads to increased internal mantle temperature and decreased viscosity. This, in turn, allows for the more rapid overturn of oceanic lithosphere and increased oceanic heat flux. Depending on the ratio of continental to oceanic surface area, global mantle heat flow can remain constant or even increase as a result. Theoretical scaling analyses are consistent with results from numerical simulations and laboratory experiments. Applying our results to the Earth we find, in contrast to conventional understanding, that continental insulation does not generally reduce global heat flow. Such insulation can have a negligible effect or even enhance mantle cooling, depending on the magnitude of the temperature dependence of mantle viscosity. The implication of this result for the Earth's thermal evolution will be discussed.
T42A-06 11:35h
The Role of Continents and of the Wavelength of Mantle Convection on the Earth's Cooling
The long standing problem of the cooling of the Earth lies in the fact that the geophysical approach, using parameterized models of convection, leads to a too fast cooling of the Earth at the beginning of its history. The geochemical estimates of concentrations in radioactive elements in the mantle then appear too low to explain the observed present mantle heat loss. This problem has been addressed recently through new approaches aiming at increasing the sensitivity to initial conditions, by lowering the exponent $\beta$ in the scaling law between the heat flux $Q$ out of the mantle and its Rayleigh number: $Q=C\ Ra^{\beta}$. In the present study, we propose an alternative solution, focusing not on the exponent $\beta$ but on the pre-factor $C$. We show that this coefficent depends on the wavelength of convection and we build up a scaling law that gives the dependence of $C$ on this wavelength for two-dimensional models. In a previous study (Grign{\'e} and Labrosse, 2001), the insulating effect of continents has been introduced in models of Earth's cooling, considering no modification of the dynamics of the mantle due to continents. The mantle circulation can however be expected to depend on the position of continents at the surface of the Earth. Long wavelengths dominate when continents are aggregated in one supercontinent, whereas shorter cells must be present when continents are more homogeneously spread at the surface. The variations of the wavelength of convection with the Wilson cycle can then be implied to induce important variations of the heat flow out of the Earth. Noting that the wavelength has decreased over the past 400 Ma after a continental breakup, it can be proposed that the present day mantle heat loss is anomalously high compared to a monotonous trend that would not take into account the variations of the length scale of convection over time, which renders simple parameterized models of thermal evolution inaccurate for quantitative predictions. The effect of continents on the length scale of mantle convection, associated with their insulating effect, can then bring a possible explanation to the problem of the Earth's cooling.
T42A-07 11:50h
Record of Earth's Secular Cooling in Mantle Xenoliths from the Continental Lithosphere
The time-scale for diffusive heat transport in a 250 km thick rock column is 2 Gy, showing that cratonic lithosphere is potentially able to record secular changes of mantle temperature. In the lithospheric mantle, in-situ radiogenic heat production also decays with a characteristic time of about 3 Gy. Thus, the thermal structure of Archean lithosphere is not in equilibrium with the instantaneous rate of radiogenic heat generation and with heat supply at the base of the lithosphere. One consequence is that temperatures in the lithospheric mantle are not steady and continuously decrease with time. Comparison of xenolith (P,T) arrays with time-dependent thermal models allows constraints on time-changes of basal heat flux (or temperature) and on heat production in the lithospheric mantle. Model results depend strongly on lithosphere thickness. Using values of cooling rates determined from isotopic desequilibrium profiles in mantle minerals (F. Albarede, Geophys. Res. Lett. 30, 1015, 2003; R.M. Bedini et al., Earth Planet Sci. Lett. 223, 99-111, 2004) considerably tightens the solution range. All models that are consistent with xenolith (P,T) arrays from the Kaapval craton, South Africa, and with available heat flow and heat production measurements have been determined using a Monte-Carlo procedure. Taking no account of cooling rate estimates but requiring that lithosphere thickness is larger than 200 km, the characteristic decay time for the basal heat flux must be larger than 1.1 Gy. With larger values of lithosphere thickness, such as those obtained from seismological studies, this characteristic decay time increases to very large values exceeding 6 Gy, which would imply no significant change of basal heat flux. Taking into account available cooling rate estimates, there are no solutions with significant variations of basal heat flux for all values of lithosphere thickness. These results suggest that thermal conditions beneath cratons have changed very little since Archean times, and show that much can be learnt about Earth's thermal evolution by studying samples from thick continental lithosphere.
T42A-08 12:05h
Lithospheric thickness and heat flux beneath cratons
We apply a physically constrained Monte Carlo inversion of surface wave data to study lithospheric structure beneath cratons in Canada, Siberia, and Australia. We, first, invert available surface heat-flow measurements to estimate crustal geotherms and to bound the temperatures in the uppermost mantle. These bounds are then applied as a constraint on the seismic surface wave inversion. We reformulate the inversion by replacing the seismic parameterization with physical parameters that describe the thermal state and evolution of the upper mantle. These parameters include the temperature in the uppermost mantle directly beneath Moho, the mantle temperature gradient (or mantle heat flux), and the potential temperature of the sublithospheric convecting mantle. We also apply a priori constraints based on the condition that melting temperatures were not reached in the crust in Proterozoic times as well as other theoretical considerations. The combination of seismic and thermal data is based on the interconversion between temperature and seismic velocity. The inversion is formulated as a Monte-Carlo sampling of model space that results in an ensemble of models that fit the data, which provides estimates of uncertainties in the model parameters. Results are presented as the distribution of mantle heat flux and lithospheric thickness. Although variations in these parameters are not well correlated with surface tectonic history within cratons, they are anticorrelated with each other. This is consistent with the hypothesis that the old cratonic lithosphere and the underlying astenosphere are in thermal equilibrium and the heat flux through the deep lithosphere is governed by small-scale sublithospheric convection.