Core cooling by subsolidus mantle convection

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.     

Plume heat flow is much lower than CMB heat flow

Plumes rising from the core–mantle boundary (CMB) are often assumed to transport most, or all, of the heat conducted across the CMB. Here this assumption is explored using numerical convection models in idealized geometries that lead to a single plume under steady-state or near steady state conditions. Plume heat transport is calculated for different internal heating rates using two methods and compared to the CMB heat flux. For these conditions, it is found that the heat flux transported by plumes in the upper mantle is only a fraction of the core heat flux and, thus, core heat flow estimates derived from observed hotspots could be multiplied by a factor of several.     

On the admissible range of the radial temperature gradient and Brünt-Väisäla frequency in the mantle and core: I. Main relations

The question of ambiguity in the solution of the inverse problem for determining the Brünt-Väisäla frequency in the Earth’s mantle from the entire set of the up-to-date data on seismicity, free oscillations, and forced nutations of the Earth, as well as the data on the Earth’s total mass and total moment of inertia, is considered. Based on the results of a series of numerical experiments, the band of admissible distributions of the Brünt-Väisäla frequency and mantle density with depth is calculated. This estimate is used for investigating the convective and gravitational stability of the different regions of the mantle against relatively small adiabatic and nonadiabatic perturbations. The generalization of the known Rayleigh criterion of convective stability of homogeneous and a nonself-gravitating incompressible viscous fluid for the case of a compressible self-gravitating fluid is given. A system of the ordinary eight-order differential equations with complex coefficients and homogeneous boundary conditions, whose eigenvalues determine the transition from the stable state to instability, is obtained. Examples of the numerical determination of these eignevalues are presented. For interpreting the data about the band of the admissible distributions of the Brünt-Väisäla frequency with depth, the notion of the effective bulk modulus of the medium at different depths is introduced. This quantity governs the depth changes in temperature in a convecting mantle and allows us to make a conclusion about the role of heat conduction and the radial heterogeneity of the mantle composition without imposing any constraints on the convection mechanism. It is shown that within the present-day observation errors in the frequencies of the Earth’s free oscillations, the simplest reasonable model is that in which the ratio of the effective bulk modulus to its adiabatic value in the lower and middle mantle is 1.043 ± 0.05. The closeness of this value to unity indicates that convection in the lower and middle mantle is fairly close to adiabatic. At the same time, when the analysis only relies on seismic data and on the information about the periods of the free oscillations of the Earth, there is a significant uncertainty in the models of the effective bulk modulus distribution in the upper mantle and crust. This uncertainty precludes us from making purely empirically derived conclusions that reliably and unambiguously describe the role of the effects of heat conduction and radially heterogeneous material composition in the convection in the upper mantle.     

Geophysical observations pertaining to solid-state convection in the terrestrial planets

We present a broad-based review of the observational evidence that pertains to or otherwise implies solid-state convection to be occurring (or have occurred) in the interiors of the terrestrial planets.For the Earth, the motion of the plates is prima facie evidence of large-scale mantle convection. Provided we understand upper-mantle thermal conductivity correctly, heat flow beneath the old ocean basins may be too high to be transported conductively from the upper mantle through the base of the lithosphere and therefore convection on a second smaller scale might be operative. The horizontal scale of plate dimensions implies, due to typical cell aspect ratios observed in convection, that the motion extends to the core-mantle boundary. Improved global data coverage and viscoelastic modeling of isostatic rebound due to Pleistocene deglaciation imply a uniform mantle viscosity, and thus indicate that whole-mantle convection could exist. Additionally, there is some seismic evidence of lithospheric penetration to depths deeper than 700 km. We discuss some salient features and assumption boundedness of arguments for convection confined to the upper mantle and for convection which acts throughout the mantle since the vertical length scale has a profound effect upon the relevance of geophysical observations. The horizontal form of mantle convection may be fully three-dimensional with complex planform and, therefore, searching for correlative gravity patterns in the ocean basins may not be useful without additional geophysical constraints. Many long-wavelength gravity anomalies may arise from beneath the lithosphere and must be supported dynamically, although thermal convection is not a unique explanation. Topography is an additional geophysical constraint, but for wavelengths greater than a few hundred kilometers, a general lack of correlation exists between oceanic residual gravity and topography, except at specific locations such as Hawaii. Theoretical calculations predict a complex relationship between these two observational types. Oceanic gravity data alone shows no regular planform and there is no correlation with any small-scale convective pattern predicted by laboratory experiments.All of the observational evidence argues against Martian plate tectonics occurring now or over much of the history of this planet, but lack of plate tectonics is not an argument against interior convection. The Tharsis uplift on Mars may have resulted from convective processes in the mantle, and the present-day gravity anomaly associated with Tharsis must be supported by the finite strength of the lithosphere or by mantle convection. Stresses imparted by the present topographic load would be greater than a kilobar, in excess of long-term finite strength. Observed fracture patterns are probably a direct result of this load, and the key question concerns the level of resultant strain relief. The global topographic and geomorphic dichotomy between the northern and southern hemisphere required a solid-state flow process to create the accompanying center-of-figure to center-of-mass offset.Lunar heat flow values, in analogy with oceanic heat flow on the Earth, strongly imply a convective mechanism of heat transport in the interior which, based on seismic Q values, is limited to the lower mantle. The presence of moonquakes in this region does not preclude solid-state convective processes. Lunar conductivity profiles provide no information on convection because of the difficulty in conductivity modeling, uniqueness of models, and the uncertainty in the conductivity-temperature relationship. The excess oblateness of the lunar figure over the hydrostatic value does not require convective support; in fact, such a mechanism is unlikely.The presence of a dipole magnetic field on Mercury does not provide a constraint on mantle convection unless its existence can be inextricably linked to a molten core. The non-hydrostatic shape of the equatorial figure, required for the observed $\text{3}\text{2}$ resonance between Mercury's rotational and orbital periods, is most likely related to surface processes, as opposed to convection. The $\text{3n}\text{2}$ resonance implies escape from a 2n resonance and, therefore, is related to the question of a molten core. Further dynamical data is needed to constrain interior models.Interpretation of limited radar imagery for the surface of Venus is enigmatic in terms of plate tectonics and therefore interior convection. Linear tensional and possibly compressional features are observed, but there are also crustal regions which appear to show large impact structures and are thus geologically old and may not have been recycled.     

小行星撞击对地球的上地幔对流的影响

本文分别基于数值结果和地质学模型,在假定地球的上地幔存在稳定Rayleigh-Bénard对流的基础上,模拟了直径为10 km（陨石坑直径约180 km,以Chicxulub为例）和直径为100 km（陨石坑直径约1000 km）的小行星撞击对地球的上地幔对流格局的影响.本文将直径10 km小行星的撞击效果等效为热异常,将直径100 km小行星的撞击效果等效为热异常和速度异常（主要指陨石坑底部的回弹）的叠加.计算结果表明,当小行星的直径在10 km左右时,撞击对上地幔对流的影响十分微弱,热扰动时间仅2—3 Ma;而当小行星的直径达到100 km时,撞击就会对上地幔对流产生强烈影响.这时,对流从扰动到新的稳态有一定模式可循（依次为：调整、多个对流环、调整、稳定）,扰动的持续时间受黏度和撞击点位置影响,同时稳定后地幔热柱会向着撞击点的方向产生一定的位移.     

Thermal evolution of Venus

The theory of three-dimensional and finite-amplitude convection in a viscous spherical shell with temperature and pressure dependent physical parameters is developed on the basis of a modified Boussinesq fluid assumption. The lateral dependences of the variables are resolved through their spherical harmonic representations, whereas their radial and time dependences are determined by numerical procedures. The theory is then applied to produce thermal evolution models for Venus. The emphasis is on illustrating the effects of certain physical parameters on the thermal evolution rather than proposing a specific thermal history for the planet. The main conclusions achieved in this paper are (1) a significant portion of the present temperature in the mantle and heat flux at the surface of Venus is probably owing to the decay of a high temperature established in the planet at the completion of its core formation, (2) the effective Rayleigh number of the mantle is so high that even the lower order modes of convection cool the planet sufficiently and maintain an almost adiabatic temperature gradient in the convecting region and high temperature gradients in the thermal boundary layers, (3) the convection is oscillatory with avalanche type properties which induces oscillatory features to the surface heat flux and the thickness of the crustal layer, and (4) a planetary model with a recycling crust cools much faster than those with a permanently buoyant crust.The models presented in this paper suggest that Venus has been highly convective during its history until ～ 0.5 Ga ago. The vigorous convection was bringing hot and fresh material from the deep interior to the surface and dragging down the crustal slags, floating on the surface, in to the mantle. The rate of cooling of the planet was so high that its core has solidified. In the last 0.5 Ga the vigour of convection diminished considerably and the crustal slags developed into a global and permanently buoyant crustal layer. The tectonic style on Venus has, consequently, changed from the recycling of crustal plates to hot spot volcanics. At the present time the planet is completely solid, except in the upper part of its mantle where partial melting may occur.     

Tectonic episodicity and convective feedback mechanisms

The evolution of the Earth is characterized by irreversible processes: radioactive decay of the major heat-producing elements, thermal convection and chemical segregation. The prevailing heating from within and the temperature dependence of the viscosity are essential for thermal convection. In the present paper, the chemical and thermal evolution of the mantle and the generation of the continent material are represented by a two-dimensional and finite-difference Boussinesq convection model. We have incorporated the above-mentioned principal features in this model, a geochemical paper by Hofmann (1988, Earth Planet. Sci. Lett., 90: 297–314) constituting our starting point for the distribution of the radionuclides. The concentration of the radionuclides and the viscosity are functions of the location and time developing according to our system of differential equations. Although the real Earth is a much more complex system, we have dared to make a comparison with observed geophysical and geological data; we obtain a depleted upper mantle and acceptable values for the heat flow on the surface of the Earth as well as for the distribution of temperature, viscosity and of the velocity of creep in the mantle. The ups and downs of the convective vigour of the model roughly resemble the supercontinental cycles, the world-wide distribution of mineral dates in time, the sea-level variations and the variations of a number of geochemical parameters.     

Geoneutrinos and the energy budget of the Earth

The total energy loss of the Earth is well constrained by heat flux measurements on land, the plate cooling model for the oceans, and the buoyancy flux of hotspots. It amounts to 46 ± 2 TW. The main sources that balance the total energy loss are the radioactivity of the Earth's crust and mantle, the secular cooling of the Earth's mantle, and the energy loss from the core. Only the crustal radioactivity is well constrained. The uncertainty on each of the other components is larger than the uncertainty of the total heat loss. The mantle energy budget cannot be balanced by adding the best estimates of mantle radioactivity, secular cooling of the mantle, and heat flux from the core. Neutrino observatories in deep underground mines can detect antineutrinos emitted by the radioactivity of U and Th. Provided that the crustal contribution to the geoneutrino flux can be very precisely calculated, it will be possible to put robust constraints on mantle radioactivity and its contribution to the Earth's energy budget. Equally strong constraints could be obtained from a deep ocean observatory without the need of crustal correction. In the future, it may become possible to obtain directional information on the geoneutrino flux and to resolve radial variations in concentration of heat producing elements in the mantle.     

Convection of a fluid with strongly temperature and pressure dependent viscosity

Plate tectonics on the Earth is a surface manifestation of convection within the Earth’s mantle, a subject which is as yet improperly understood, and it has motivated the study of various forms of buoyancy-driven thermal convection. The early success of the high Rayleigh number constant viscosity theory was later tempered by the absence of plate motion when the viscosity is more realistically strongly temperature dependent, and the process of subduction represents a continuing principal conundrum in the application of convection theory to the Earth. A similar problem appears to arise if the equally strong pressure dependence of viscosity is considered, since the classical isothermal core convection theory would then imply a strongly variable viscosity in the convective core, which is inconsistent with results from post-glacial rebound studies. In this paper we address the problem of determining the asymptotic structure of high Rayleigh number convection when the viscosity is strongly temperature and pressure dependent, i.e. thermobaroviscous. By a method akin to lid-stripping, we are able to extend numerical computations to extremely high viscosity contrasts, and we show that the convective cells take the form of narrow, vertically-oriented fingers. We are then able to determine the asymptotic structure of the solution, and it agrees well with the numerical results. Beneath a stagnant lid, there is a vigorous convection in the upper part of the cell, and a more sluggish, higher viscosity flow in the lower part of the cell. We then offer some comments on the possible meaning and interpretation of these results for planetary mantle convection.     

Comparison of Early Evolutions of Mimas and Enceladus

Thermal history of Mimas and Enceladus is investigated from the beginning of accretion to 400 Myr. The numerical model of convection combined with the parameterized theory is used. The following heat sources are included: short lived and long lived radioactive isotopes, accretion, serpentinization, and phase changes. The heat transfer processes are: conduction, solid state convection, and liquid state convection. We find that temperature of Mimas’ interior was significantly lower than that of Enceladus. If Mimas accreted 1.8 Myr after CAI then the internal melting and differentiation did not occur at all. Comparison of thermal models of Mimas and Enceladus indicates that conditions favorable for the start of tidal heating lasted for a short time (~10⁷ yr) in Mimas and for ~10⁸ yr in Enceladus. This could explain the Mimas—Enceladus paradox. In fact, in view of the chronology based on cometary impact rate, one cannot discard a possibility that also Mimas was for some time active and it has the interior differentiated on porous core and icy mantle.     

Thermal histories of the core and mantle

Recognition that the cooling of the core is accomplished by conduction of heat into a thermal boundary layer (D″) at the base of the mantle, partly decouples calculations of the thermal histories of the core and mantle. Both are controlled by the temperature-dependent rheology of the mantle, but in different ways. Thermal parameters of the Earth are more tightly constrained than hitherto by demanding that they satisfy both core and mantle histories. We require evolution from an early state, in which the temperatures of the top of the core and the base of the mantle were both very close to the mantle solidus, to the present state in which a temperature increment, estimated to be ～ 800 K, has developed across D″. The thermal history is not very dependent upon the assumption of Newtonian or non-Newtonian mantle rheology. The thermal boundary layer at the base of the mantle (i.e., D″) developed within the first few hundred million years and the temperature increment across it is still increasing slowly. In our preferred model the present temperature at the top of the core is 3800 K and the mantle temperature, extrapolated to the core boundary without the thermal boundary layer, is 3000 K. The mantle solidus is 3860 K. These temperatures could be varied within quite wide limits without seriously affecting our conclusions. Core gravitational energy release is found to have been remarkably constant at ～ 3 × 10¹¹ W. nearly 20% of the core heat flux, for the past 3 × 10⁹ y, although the total terrestrial heat flux has decreased by a factor of 2 or 3 in that time. This gravitational energy can power the “chemical” dynamo in spite of a core heat flux that is less than that required by conduction down an adiabatic gradient in the outer core; part of the gravitational energy is used to redistribute the excess heat back into the core, leaving 1.8 × 10¹¹ W to drive the dynamo. At no time was the dynamo thermally driven and the present radioactive heating in the core is negligibly small. The dynamo can persist indefinitely into the future; available power 10¹⁰ y from now is estimated to be 0.3 × 10¹¹ W if linear mantle rheology is assumed or more if mantle rheology is non-linear. The assumption that the gravitational constant decreases with time imposes an implausible rate of decrease in dynamo energy. With conventional thermodynamics it also requires radiogenic heating of the mantle considerably in excess of the likely content of radioactive elements.     

地球形成和演化过程中的分异能计算方法研究

地球形成初期,构成地球的物质在组成上是大致均一的.目前地球的地核-地幔-地壳圈层结构,是由分异作用形成的.分异过程释放的能量称为分异能.Sorokhtin和Chilingarian等人从行星吸积的定义出发,导出了基于地球内部密度分布的势能计算公式,计算出的分异能大小为1.698×1031J.本文采用计算球体势能的思路,导出分异能计算的解析公式和数值计算公式,通过求取原始地球模型与均匀分层模型、PREM模型的势能差计算分异能.两种方法的计算结果分别为1.535×1031J和1.698×1031J.前者与Sorokhtin等的结果相近,后者与之相同.本文初步分析了方法间的异同以及造成结果偏差的主要原因.     

The cooling Earth: A reappraisal

By treating the lithosphere as a diffusive boundary layer to mantle convection, the convective speed or mantle creep rate, $\text{?}\text{?}$, can be related to the mantle-derived heat flux, $\text{Q}\text{?}$. If cell size is independent of $\text{Q}\text{?}{}^2$ then $\text{?}\text{?}\text{∝}\text{Q}\text{?}$. (If cell size varies with $\text{Q}\text{?}$, 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 $\text{Q}\text{?}$, gives convective stress $\text{σ ∝}\text{Q}\text{?}{}^{\mathrm{?1}}$, 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.     

Detecting thermal boundary control in surface flows from numerical dynamos

The geomagnetic field and secular variation exhibit asymmetrical spatial features which are possibly originating from an heterogeneous thermal control of the Earth's lower mantle on the core. The identification of this control in magnetic data is subject to several difficulties, some of which can be alleviated by the use of core surface flow models. Using numerical dynamos driven by heterogeneous boundary heat flux, we confirm that within the parameter space accessible to simulations, time average surface flows obey a simple thermal wind equilibrium between the Coriolis and buoyancy forces, the Lorentz, inertial and viscous forces playing only a secondary role, even for Elsasser numbers significantly larger than 1. Furthermore, we average the models over the duration of three vortex turnovers, and correlate them with a longer time average which fully reveals the signature of boundary heterogeneity. This allows us to quantify the possibility of observing mantle control in core surface flows averaged over a short time period. A scaling analysis is performed in order to apply the results to the Earth's core. We find that three vortex turnovers could represent between 100 and 360 years of Earth time, and that the heat flux heterogeneity at the core-mantle boundary could be large enough to yield an observable signature of thermal mantle control in a time average core surface flow within reach of the available geomagnetic data.     

Models for the origin and composition of the earth,and the hypothesis of potassium in the Earth's core

Progress in understanding the condensation of planetary constituents from a solar nebula necessitates a re-examination of models for the origin and composition of the Earth. All models which appear to be viable require the Earth to have an Fe–FeS core and the full, or nearly full, solar (i.e. chondritic) K/Si ratio. The crust and upper mantle do not contain the requisite potassium for the entire Earth to have the solar K/Si ratio. Therefore, these models require that much of the Earth's potassium, about 80–90%, must be in the deep interior—in the lower mantle or in the core.The hypothesis that a substantial fraction of the Earth's potassium is in the Fe–FeS core is based on the chalcophilic behavior of potassium. Data including the stability of K₂S, the occurrence of potassium in sulfide phases in meteorites and in metallurgical systems, and most importantly, experiments on potassium partitioning between solid silicates and Fe–FeS melts support this hypothesis. The present data appear to require at least several percent of the Earth's total potassium to be in the core. Incorporation of much larger amounts of potassium into the core, possibly most of the 80–90% of the Earth's potassium which is postulated to be in the deep interior, is not contradicted by the present data. Additional experimental data, at high pressures, are required before quantitative estimates of the core's potassium content can be made.It is likely that⁴⁰K is a significant heat source in the core. Decay of⁴⁰K is a plausible energy source to drive core convection to maintain the geomagnetic field, and to drive mantle convection and seafloor spreading.     

Formation,history and energetics of cores in the terrestrial planets

The cores of the terrestrial planets Earth, Moon, Mercury, Venus and Mars differ substantially in size and in history. Though no planet other than the Earth has a conclusively demonstrated core, the probable cores in Mercury and Mars and Earth's core show a decrease in relative core size with solar distance. The Moon does not fit this sequence and Venus may not. Core formation must have been early (prior to ～4 · 10⁹ yr. ago) in the Earth, by virtue of the existence of ancient rock units and ancient paleomagnetism and from UPb partitioning arguments, and in Mercury, because the consequences of core infall would have included extensional tectonic features which are not observed even on Mercury's oldest terrain. If a small core exists in the Moon, still an open question, completion of core formation may be placed several hundred million years after the end of heavy bombardment on tectonic and thermal grounds. Core formation time on Mars is loosely constrained, but may have been substantially later than for the other terrestrial planets. The magnitude and extent of early heating to drive global differentiation appear to have decreased with distance from the sun for at least the smaller bodies Mercury, Moon and Mars.Energy sources to maintain a molten state and to fuel convection and magnetic dynamos in the cores of the terrestrial planets include principally gravitational energy, heat of fusion, and long-lived radioactivity. The gravitational energy of core infall is quantifiable and substantial for all bodies but the Moon, but was likely spent too early in the history of most planets to prove a significant residual heat source to drive a present dynamo. The energy from inner core freezing in the Earth and in Mercury is at best marginally able to match even the conductive heat loss along an outer core adiabat. Radioactive decay in the core offers an attractive but unproven energy source to maintain core convection.     

Seismic tomography and continental drift

Based on data of seismic tomography, the structure of the mantle flows of the contemporary Earth and the continental drift are calculated. Results of calculation of the contemporary motion of continents and their future drift for 150 Myr are presented. The present-day positions of six continents and the nine largest islands are taken as an initial state. The contemporary temperature distribution in the mantle is calculated according to the data of seismic tomography. The 3-D distribution of seismic wave velocities is converted into the density distribution and then into the temperature distribution. The Stokes equation is numerically solved for flows in a viscous mantle with floating continents for the given initial temperature distribution. In this way, the velocities of convective flows are determined in the entire present-day mantle and the surface distribution for the Earth’s heat flux is obtained. The reliability of the calculated flows in the mantle is estimated by the comparison of the calculated velocities of the contemporary continents and oceanic lithosphere with data of satellite measurements. Further, evolutionary equations of convection with floating continents were numerically solved. The calculated structure of mantle flows, temperature distribution, and position of continents are presented for a time moment 150 Myr in the future. The resulting successive changes in the position of continents in time show how islands (in particular, Japan and Indonesia) will be attached to continents and how continents will converge, exhibiting a tendency toward the formation of a new supercontinent in the southern hemisphere of the Earth.     

Regionalized models for the thermal evolution of the Earth

Traditional models for the heat loss in oceanic and continental regions are combined into a regionalized model for the thermal evolution of the Earth. The need for regionalization is obvious when one considers that the mantle loses 3 to 4 times as much heat per unit area in oceanic regions than in continental areas. The present-day rate of heat loss together with a geochemical estimate of the concentration of heat-producing elements in the Earth fixes the response time of the thermally convecting mantle. The response time in turn can be used to select the most reasonable representation for mantle convection in terms of the sensitivity of viscosity on temperature and layering versus mantle-wide circulation. Present geochemical estimates of the bulk composition of the Earth are most easily reconciled with the observed heat flow if the mantle is layered and its rheology is slightly less temperature dependent than generally assumed. The layered system can produce sufficiently high temperatures to explain the high-magnesian komatiites of the Archean. One difficulty with the models is that they predict widespread melting at shallow depth in the early stages of Earth history but do not address how such melting affects and alters the heat transfer mechanisms.     

Gravitational energy of core evolution: implications for thermal history and geodynamo power

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.