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1.
Using density–pressure relationships for mantle silicate and core alloy closely matching PREM we have constructed six models of the Earth in different evolutionary states. Gravitational energies and elastic strain energies are calculated for models with homogeneous composition, separated mantle and liquid core, separated inner and outer cores with the inner core either liquid or solid and models with increased densities, representing cooling of either the mantle or core. In this way we have isolated the gravitational energy released by each of several evolutionary processes and subtracted the consequent increase in strain energy to obtain the net energy released as heat or geodynamo power. Radiogenic heat (∼7.8×1030 J) is found to contribute only about 25% of the total heat budget, the balance originating as residual gravitational energy from the original accretion and from core separation (14×1030 J). The total energy of compositional convection, driven by inner core formation, is 3.68×1028 J and this is the most important (or even the only) energy source for the dynamo for the most recent 2 billion years. It appears unlikely that the inner core existed much before that time. The total net (gravitational minus strain) energy released in the core by the process of inner core formation, 11.92×1028 J, is not much less than the thermal energy released in this process, 15.1×1028 J. In the mantle the net (gravitational minus strain) energy released by thermal contraction is about 20% of the heat release. All of the numerical results are presented in a manner that allows simple rescaling to any revised density estimates.  相似文献   

2.
If the interpretation of the D″ layer at the base of the mantle as a thermal boundary layer, with a temperature increment in the order of 800 K, is correct, then the formation of deep-mantle plumes to vent material from it appears inevitable. We demonstrate quantitatively that the strong temperature dependence of viscosity guides the upward flow into long-lived chimneys that are ~ 20 km in diameter near the base of the mantle and decrease in width with progressive upward softening and partial melting of plume material. The speed of flow up the axis of the plume is correspondingly fast; 1.6 m y?1 at the base and 4.8 m y?1 at 670 km depth. Thermal diffusive spreading of a heated plume is compensated by a slow horizontal convergence of mantle material toward the chimney in response to the lower pressure there. This convergence, which contributes only a small increment to the flux of material up the plume, also serves to throttle the flow in the chimney. The global plume mass flux necessary to transport 1.6 × 1012 W of core heat upward through the mantle is 1.8 × 106 kg s?1. At its base, plume material is probably still significantly below its solidus or eutectic temperature, but substantial partial melting is very likely as it rises. We speculate that a small fraction of this fluid component eventually emerges at the surface in “hot spots”, with the fate of the remainder being unknown. The behaviour and properties of D″ and of plumes are closely coupled. Not only are plumes a necessary consequence of a thermal boundary layer, but their existence is impossible without that layer.  相似文献   

3.
The feasibility of a precessionally driven dynamo is investigated. The relative orientation of the angular-velocity vectors of the mantle and core and the precession vector of the earth are determined from a torque balance. The core and mantle are acted upon by separate gravitational torques and mutual interaction torques resulting from pressure, viscous and magnetic stresses at the core-mantle interface. The viscous and magnetic torques are determined using the results of a detailed analysis of the Ekman-Hartmann and magnetic diffusion layers generated at the core-mantle interface by the misalignment of the mantle and core angular-velocity vectors. The dissipative torques are found to be weaker by a factor of 10?4 than those estimated by Malkus (1968) and Stacey (1973), resulting in only 3.5 · 107 W being extracted from the rotational kinetic energy of the earth by these mechanisms. Furthermore, it is found that all of this energy is dissipated in the boundary layers at the core-mantle interface and none is available to drive the geodynamo.  相似文献   

4.
Lower mantle heterogeneity could cause deviations from axial symmetry in geodynamo properties. Global tomography models are commonly used to infer the pattern of core–mantle boundary heat flux via a linear relation that corresponds to a purely thermal interpretation of lower mantle seismic anomalies, ignoring both non-thermal origins and non-resolved small scales. Here we study the possible impact on the geodynamo of narrow thermal anomalies in the base of the mantle, originating from either compositional heterogeneity or sharp margins of large-scale features. A heat flux boundary condition composed of a large-scale pattern and narrow ridges separating the large-scale positive and negative features is imposed on numerical dynamos. We find that hot ridges located to the west of a positive large-scale core–mantle boundary heat flux anomaly produce a time-average narrow elongated upwelling, a flow barrier at the top of the core and intensified low-latitudes magnetic flux patches. When the ridge is located to the east of a positive core–mantle boundary heat flux anomaly, the associated upwelling is weaker and the homogeneous dynamo westward drift leaks, precluding persistent intense low-latitudes magnetic flux patches. These signatures of the core–mantle boundary heat flux ridge are evident in the north–south component of the thermal wind balance. Based on the pattern of lower mantle seismic tomography (Masters et al., 2000), we hypothesize that hot narrow thermal ridges below central Asia and the Indian Ocean and below the American Pacific coast produce time-average fluid upwelling and a barrier for azimuthal flow at the top of the core. East of these ridges, below east Asia and Oceania and below the Americas, time-average intense geomagnetic flux patches are expected.  相似文献   

5.
The “anomalous” layer in the lowermost mantle, identified as D″ in the notation of K.E. Bullen, appears in the PREM Earth model as a 150 km-thick zone in which the gradient of incompressibility with pressure, dKdP, is almost 1.6, instead of 3.2 as in the overlying mantle. Since PREM shows no accompanying change in density or density gradient, we identify D″ as a thermal boundary layer and not as a chemically distinct zone. The anomaly in dKdP is related to the temperature gradient by the temperature dependence of Ks, for which we present a thermodynamic identity in terms of accessible quantities. This gives the numerical result (?Ks/?T)P=?1.6×107 Pa K?1 for D″ material. The corresponding temperature increment over the D″ range is 840 K. Such a layer cannot be a static feature, but must be maintained by a downward motion of the lower mantle toward the core-mantle boundary with a strong horizontal flow near the base of D″. Assuming a core heat flux of 1.6 × 1012 W, the downward speed is 0.07 mm y?1 and the temperature profile in D″, scaled to match PREM data, is approximately exponential with a scale height of 73 km. The inferred thermal conductivity is 1.2 W m?1 K?1. Using these values we develop a new analytical model of D″ which is dynamically and thermally consistent. In this model, the lower-mantle material is heated and softened as it moves down into D″ where the strong temperature dependence of viscosity concentrates the horizontal flow in a layer ~ 12 km thick and similarly ensures its removal via narrow plumes.  相似文献   

6.
This paper is a non-mathematical review, summarising the work in this field.Estimates are made of the power needed to maintain the electric currents which give the main geomagnetic field. The observed surface field needs at least 2×108 W, but unobservable fields may need much more; a toroidal field of peak value 10 or 50nT would need 1010 or 2.5×1011 W.Ways of obtaining this power from the Earth's rotation, particularly through precession, are considered and rejected.Thermal power sources have the disadvantages that there is inherent thermodynamic inefficiency in driving the dynamo, and that a significant fraction of the heat input will be carried away by conduction rather than convection. Radioactivity will only be important if there is a substantial amount of potassium in the core. If this is not the case the core might be cooling; cooling at 20K per 109 yr would release specific heat at a rate of 1012 W. If the cooling causes the inner core to grow by freezing from the liquid core, then an additional 1012 W would be released from the latent heat of freezing. These heat fluxes might support a dynamo having a small toroidal field.If, as seems likely, the solid inner core is significantly denser than the liquid, such cooling would also release 0.6×1012 W of gravitational energy, giving compositional convection which would drive the dynamo very efficiently and give a large toroidal field.  相似文献   

7.
Convection in the Earth’s core is usually studied in the Boussinesq approximation in which the compressibility of the liquid is ignored. The density of the Earth’s core varies from ICB to CMB by approximately 20%. The question of whether we need to take this variation into account in core convection and dynamo models is examined. We show that it is in the thermodynamic equations that differences between compressible and Boussinesq models become most apparent. The heat flux conducted down the adiabat is much smaller near the inner core boundary than it is near the core-mantle boundary. In consequence, the heat flux carried by convection is much larger nearer the inner core boundary than it is near the core-mantle boundary. This effect will have an important influence on dynamo models. Boussinesq models also assume implicitly that the rate of working of the gravitational and buoyancy forces, as well as the Ohmic and viscous dissipation, are small compared to the heat flux through the core. These terms are not negligible in the Earth’s core heat budget, and neglecting them makes it difficult to get a thermodynamically consistent picture of core convection. We show that the usual anelastic equations simplify considerably if the anelastic liquid approximation, valid if αT?1, where α is the coefficient of expansion and T a typical core temperature, is used. The resulting set of equations are not significantly more difficult to solve numerically than the usual Boussinesq equations. The relationship of our anelastic liquid equations to the Boussinesq equations is also examined.  相似文献   

8.
It has been suggested that there exists a stably stratified electrically conducting layer at the top of the Earth's outer fluid core and that lateral temperature gradients in the lower mantle is capable of a driving thermal-wind-type flow near the core–mantle boundary. We investigate how such a flow in a stable layer could influence the geomagnetic field and the geodynamo using a very simple two-dimensional kinematic dynamo model in Cartesian geometry. The dynamo has four layers representing the inner core, convecting lower outer core, stable upper core, and insulating mantle. An α2 dynamo operates in the convecting outer core and a horizontal shear flow is imposed in the stable layer. Exact dynamo solutions are obtained for a range of parameters, including different conductivities for the stable layer and inner core. This allows us to connect our solutions with known, simpler solutions of a single-layer α2 dynamo, and thereby assess the effects of the extra layers. We confirm earlier results that a stable, static layer can enhance dynamo action. We find that shear flows produce dynamo wave solutions with a different spatial structure from the steady α2 dynamos solutions. The stable layer controls the behavior of the dynamo system through the interface conditions, providing a new means whereby lateral variations on the boundary can influence the geomagnetic field.  相似文献   

9.
Although vigorous mantle convection early in the thermal history of the Earth is shown to be capable of removing several times the latent heat content of the core, we are able to construct a thermal evolution model of the Earth in which the core does not solidify. The large amount of energy removed from the model Earth's core by mantle convection is supplied by the internal energy of the core which is assumed to cool from an initial high temperature given by the silicate melting temperature at the core-mantle boundary. For the smaller terrestrial planets, the iron and silicate melting temperatures at the core-mantle boundaries are more comparable than for the Earth, and the cores of these planets may not possess enough internal energy to prevent core solidification by mantle convection. Our models incorporate temperature-dependent mantle viscosity and radiogenic heat sources in the mantle. The Earth models are constrained by the present surface heat flux and mantle viscosity. Internal heat sources produce only about 55% of the Earth model's present surface heat flow.  相似文献   

10.
By treating the lithosphere as a diffusive boundary layer to mantle convection, the convective speed or mantle creep rate, ??, can be related to the mantle-derived heat flux, Q?. If cell size is independent of Q?2 then ??Q?. (If cell size varies with Q?, then a different power law prevails, but the essential conclusions are unaffected.) Then the factthat for constant thermodynamic efficiency of mantle convection, the mechanical power dissipation is proportionalto Q?, gives convective stress σ ∝ Q??1, i.e. the stress increases as the convection slows. This means an increasing viscosityor stiffness of the mantle which can be identified with a cooling rate in terms of a temperature-dependent creep law. If we suppose that the mantle was at or close to its melting point within 1 or 2 × 108 years of accretionof the Earth, the whole scale of cooling is fixed. The present rate of cooling is estimated to be about 4.6 × 10?8 deg y?1 for the average mantle temperature, assumed to be 2500 K, but this very slow cooling rate represents a loss ofresidual mantle heat of 7 × 1012 W, about 30% of the total mantle-derived heat flux. This conclusion requires theEarth to be deficient in radioactive heat, relative to carbonaceous chondrites. A consideration of mantle outgassing and atmospheric argon leads to the conclusion that the deficiency is due to depletion of potassium, and that the K/U ratio of the mantle is only about 2500, much less than either the crustal or carbonaceous chondritic values. Thetotal terrestrial potassium is estimated to be about 6 × 1020 kg. Acceptance of the cooling of the Earth removes the necessity for potassium in the core.  相似文献   

11.
A mechanism for the production of a chemical change in the mantle, from primordial silicate compositions above the 650 km discontinuity to differentiated compositions below, is reviewed. Some consequences of this are the stabilization of two layer convection with a temperature contrast between the anhydrous mantle solidus and the geotherm which, at 650 km depth, is lower than any other location in the mantle. With thermal contributions from the concentration of the heat producing elements U, Th and K below the 650 km mantle boundary layer and the higher geotherms in the past, widespread or catastrophic melting may have taken place at this location. An episodic breach of this boundary layer by extensive heat and mass transport may have periodically destroyed any simple two-layer convection geometry in the mantle. Such episodic injections of mass and energy into the upper mantle from below may have been the mechanism responsible for episodes of enhanced surface tectonism and thermal activity which appear to be recorded in apparent polar wandering paths and radiometric ages of continental rocks.  相似文献   

12.
Numerical experiments have been carried out on two-dimensional thermal convection, in a Boussinesq fluid with infinite Prandtl number, at high Rayleigh numbers. With stress free boundary conditions and fixed heat flux on upper and lower boundaries, convection cells develop with aspect ratios (width/depth) λ? 5, if heat is supplied either entirely from within or entirely from below the fluid layer. The preferred aspect ratio is affected by the lateral boundary conditions. If the temperature, rather than the heat flux, is fixed on the upper boundary the cells haveλ ≈ 1. At Rayleigh numbers of 2.4 × 105 and greater, small sinking sheets are superimposed on the large aspect ratio cells, though they do not disrupt the circulation. Similar two-scale flows have been proposed for convection in the earth's mantle. The existence of two scales of flow in two-dimensional numerical experiments when the viscosity is constant will allow a variety of geophysically important effects to be investigated.  相似文献   

13.
The case for radioactivity in the core based on the power requirements of the geodynamo is re-evaluated. Previous calculations of mantle regulation of core thermal evolution have used an inappropriate formula. New calculations with a more appropriate formula yield lower core heat loss in the past, thus mitigating the implication of unreasonably high past core and mantle temperatures. Multiple thermal evolutions leading to present heat flows are also demonstrated, depending on the efficiency of mantle removal of core heat, some with moderately high past core heat loss and some with low and steady core heat loss. The latter would permit a low- or moderate-power dynamo without core radioactivity. Key uncertainties are the efficiency of core cooling by the mantle, the thermal conductivity of the core and the energy or entropy flow required to maintain the dynamo. The present rate of heat loss from the core is argued to be still rather uncertain, and a commonly used estimate of the thermal conductivity of the core is shown plausibly to be too high and in any case to be uncertain by perhaps a factor of 2. The geochemical difficulties associated with postulating radioactive heat sources in the core are stressed.  相似文献   

14.
The rheology of the lower mantle of the Earth is examined from the viewpoint of solid state physics. Recent developments in high-pressure research suggest that the lower mantle contains a considerable amount of (Mg, Fe)O with Fe/Mg + Fe = 0.2–0.3. The pressure and temperature dependences of diffusion in (Mg, Fe)O are estimated by the theory of diffusion in ionic solids. Of the materials composing the lower mantle, (Mg, Fe)O may be the “softest”, and therefore the rheology of the lower mantle may be that of (Mg, Fe)O, unless the framework effect is important.Temperatures in the lower mantle are inferred from the depths of phase transitions and the melting temperatures of the core materials. A thermal boundary layer at the base of the mantle is suggested. The physical mechanisms of creep are examined based on a grain size-stress relation and non-Newtonian flow is shown to be the dominant flow mechanism in the Earth's mantle.The effective viscosity for the temperature models, with and without the thermal boundary layer, is calculated for constant stress and constant strain rate (with depth). For constant strain rate, which may be appropriate for discussing the mechanics of descending slabs, the increase in effective viscosity with depth is smaller than for the constant-stress case, which may be appropriate for discussing the flow induced by the surface motion of plates.The relatively small depth gradient of viscosity, for constant strain rate, suggests that the lower mantle could also participate in convection. The effective viscosity increases with depth, however, by at least 102 to 103 from the top to the bottom of the lower mantle, for a reasonable range of activation volumes and temperatures. There will be a low-viscosity layer at the base of the mantle, in contrast to the high-viscosity layer at the top of the mantle (plates), if a thermal boundary layer is present. The constant Newtonian viscosity inferred from rebound data may be an apparent feature resulting from the difference in deformation mechanisms between isostatic rebound and large-scale flow.  相似文献   

15.
We propose a thermal model of the subducting Ionian microplate. The slab sinks in an isothermal mantle, and for the boundary conditions we take into account the relation between the maximum depth of seismicity and the thermal parameter Lth of the slab, which is a product of the age of the subducted lithosphere and the vertical component of the convergence rate. The surface heat-flux dataset of the Ionian Sea is reviewed, and a convective geotherm is calculated in its undeformed part for a surface heat flux of 42 mW m–2, an adiabatic gradient of 0.6 mK m–1, a mantle kinematic viscosity of 1017 m2 s–1 and an asthenosphere potential temperature of 1300°C. The calculated temperature-depth distribution compared to the mantle melting temperature indicates the decoupling limit between lithosphere and asthenosphere occurs at a depth of 105 km and a temperature of 1260°C. A 70–km thick mechanical boundary layer is found. By considering that the maximum depth of the seismic events within the slab is 600 km, a Lth of 4725 km is inferred. For a subduction rate equal to the spreading rate, the corresponding assimilation and cooling times of the microplate are about 7 and 90 Myr, respectively. The thermal model assumes that the mantle flow above the slab is parallel and equal to the subducting plate velocity of 6 cm yr–1, and ignores the heat conduction down the slab dip. The critical temperature, above which the subduced lithosphere cannot sustain the stress necessary to produce seismicity, is determined from the thermal conditions governing the rheology of the plate. The minimum potential temperature at the depth of the deepest earthquake in the slab is 730°C.  相似文献   

16.
Groundwater circulation is known to be one of the agents responsible for the redistribution of geothermal energy by acting as a source or sink in the course of its movement through porous media. Heat transport in groundwater systems is considered to be a coupled process and the theory based on this was used to analyse temperature profiles of 30 thermally stable observation wells in a deep, semi-confined aquifer system in the Tokyo Metropolitan area. Vertical water fluxes in the semi-confined aquifers and the associated upward heat fluxes were estimated from a heat flux equation that describes convection and conduction processes of heat transport in one dimension. The vertical downward water fluxes in Shitamachi lowland, Musashino and Tachikawa terraces were 0.69.26.91 × 10?9, 1.46-70.92 × 10?9 and 2.61.2204 × 10?9 m/s, respectively. A vertical upward water flux of 1.80-33.60 × 10?9 m/s was estimated in Shitamachi lowland. The water flux generally decreased with increasing depth for observation wells which intercepted more than one semi-confining layer. The estimated upward heat fluxes for Shitamachi lowland, Musashino and Tachikawa terraces were 0.32-1.12, 0.49-1.21 and 1.00-11.62 W/m2, respectively. The heat flux was highest in Tachikawa terrace where a major fault, the Tachikawa fault, is located. Generally, the estimated heat flux was higher in the semi-confining layers than in the aquifers. Areas with heat sources and sinks as well as groundwater flow patterns in the semi-confined aquifers were revealed by heat flux and temperature distributions in the study area.  相似文献   

17.
The emplacement of kimberlites in the North American and African continents since the early Palaeozoic appears to have occurred during periods of relatively slow motion of these continents. The distribution of kimberlites in time may reflect the global pattern of convection, which forces individual plates to move faster or slower at different times. Two-dimensional numerical experiments on a convecting layer with a moving upper boundary show two different regimes: in the first, when the upper boundary velocity is high, heat is transferred by the large-scale circulation and in the second, when the upper boundary velocity is lower, heat is predominantly transferred by thermal plumes rising from the lower boundary layer. For a reasonable mantle solidus, this second regime can give rise to partial melting beneath the moving plate, far from the plate boundaries. The transition between these modes takes place over a small range of plate velocities; for a Rayleigh number of 106 it occurs around 20 mm yr?1. We suggest that the generation of kimberlite magmas may result from thermal plumes incident on the base of a slowly moving plate.  相似文献   

18.
We have obtained altogether heat flux data of 23 drill holes including 2 observational holes of thermal flow in the Haicheng seismic area. These data show roughly thermal structure of the crust in eastern Liaoning and in the Haicheng seismic area. The results indicate that there is higher value of heat flow in the belt north by east from Liaoyang to Xiongyue, the average thermal flux being 8.29× 10−2J/m2·s (2.0 hfu). The average thermal fulx in the Haicheng seismic area is 9.22×102J/m2·s (2.2 hfu). Comparing with other known geophysical data of the Haicheng seismic area, we give a geophysical section of comprehensive interpretation. We suppose the low-velocity layer in the lower crust of the Haicheng seismic area is a result from intrusion of large-scale uper mantle substance. High temperature and low velocity mean that the layer has the nature of plastic mechanics. The focal region of the Haicheng earthquake is situated right in the upper part of that plastic layer. Obviously, this result is significant for studying the seismogenic process of the Haicheng earthquake and other intra-plate earthquakes. We attempt to emphasize that observation of heat flow is necessary for earthquake study. Gu Haoding did the actual writing.  相似文献   

19.
Convection in the Earth's core is driven much harder at the bottom than the top. This is partly because the adiabatic gradient steepens towards the top, partly because the spherical geometry means the area involved increases towards the top, and partly because compositional convection is driven by light material released at the lower boundary and remixed uniformly throughout the outer core, providing a volumetric sink of buoyancy. We have therefore investigated dynamo action of thermal convection in a Boussinesq fluid contained within a rotating spherical shell driven by a combination of bottom and internal heating or cooling. We first apply a homogeneous temperature on the outer boundary in order to explore the effects of heat sinks on dynamo action; we then impose an inhomogeneous temperature proportional to a single spherical harmonic Y 2² in order to explore core-mantle interactions. With homogeneous boundary conditions and moderate Rayleigh numbers, a heat sink reduces the generated magnetic field appreciably; the magnetic Reynolds number remains high because the dominant toroidal component of flow is not reduced significantly. The dipolar structure of the field becomes more pronounced as found by other authors. Increasing the Rayleigh number yields a regime in which convection inside the tangent cylinder is strongly affected by the magnetic field. With inhomogeneous boundary conditions, a heat sink promotes boundary effects and locking of the magnetic field to boundary anomalies. We show that boundary locking is inhibited by advection of heat in the outer regions. With uniform heating, the boundary effects are only significant at low Rayleigh numbers, when dynamo action is only possible for artificially low magnetic diffusivity. With heat sinks, the boundary effects remain significant at higher Rayleigh numbers provided the convection remains weak or the fluid is stably stratified at the top. Dynamo action is driven by vigorous convection at depth while boundary thermal anomalies dominate in the upper regions. This is a likely regime for the Earth's core.  相似文献   

20.
The behavior of the main magnetic field components during a polarity transition is investigated using the α2-dynamo model for magnetic field generation in a turbulent core. It is shown that rapid reversals of the dipole field occur when the helicity, a measure of correlation between turbulent velocity and vorticity, changes sign. Two classes of polarity transitions are possible. Within the first class, termed component reversals, the dipole field reverses but the toroidal field does not. Within the second class, termed full reversals, both dipole and toroidal fields reverse. Component reversals result from long term fluctuations in core helicity; full reversals result from short term fluctuations. A set of time-evolution equations are derived which govern the dipole field behavior during an idealized transition. Solutions to these equations exhibit transitions in which the dipole remains axial while its intensity decays rapidly toward zero, and is regenerated with reversed polarity. Assuming an electrical conductivity of 3 × 105 mho m?1 for the fluid core, the time interval required to complete the reversal process can be as short as 7500 years. This time scale is consistent with paleomagnetic observations of the duration of reversals. A possible explanation of the cause of reversals is proposed, in which the core's net helicity fluctuates in response to fluctuations in the level of turbulence produced by two competing energy sources—thermal convection and segregation of the inner core. Symmetry considerations indicate that, in each hemisphere, helicity generated by heat loss at the core-mantle boundary may have the opposite sign of helicity generated by energy release at the inner core boundary. Random variations in rates of energy release can cause the net helicity and the α-effect to change sign occasionally, provoking a field reversal. In this model, energy release by inner core formation tends to destabilize stationary dynamo action, causing polarity reversals.  相似文献   

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