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.     

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.     

基于随温度变化的热系数模拟板块俯冲动力学过程

热传导系数和热膨胀系数是影响板块俯冲动力学过程的两个重要参数. 由于地球介质的不均匀性,热系数也会随深度发生变化.然而,这种变化在地球动力学模拟研究中往往被忽略.本文针对随温度变化的热传导系数和热膨胀系数, 模拟板块俯冲的动力学过程,分析热系数、黏度对板块俯冲形态的影响及其对应的地幔对流特征.结果表明,依温度变化的热传导系数和热膨胀系数会影响地幔温度及黏度分布,进而改变板块的俯冲角度;黏度是控制板块俯冲动力学演化过程的重要因素;地幔对流受黏度结构的影响,呈现分层对流及局部多个对流环等多种不同形态的对流场特征.      

Continental growth and volatile exchange during Earth''s evolution

We investigate the thermal and degassing history of the Earth with the help of a parameterized mantle convection model including the volatile exchange between mantle and surface reservoirs. The weakening of mantle silicates by dissolved volatiles is described by a functional relationship between creep rate and water fugacity. We use flow law parameters of diffusion creep in olivine under dry and wet conditions. The mantle degassing rate is considered as directly proportional to the seafloor spreading rate, which is also dependent on the mantle heat flow and the continental area. To calculate the spreading rate, we assume three different continental growth models: constant growth, delayed growth, and the one proposed by Reymer and Schubert (1984, Tectonics, 3: 63–77). The rate of regassing also depends on the seafloor spreading rate, as well as on other factors. Both mechanisms (degassing and regassing) are coupled self-consistently with the help of a parameterized convection model under implementation of a temperature and volatile-content dependent mantle viscosity. We calculate time series for the Earth's evolution over 4.6 Gyr for the average mantle temperature, the mantle heat flow, the mantle viscosity, the Rayleigh number, the Urey ratio, the volatile loss, and the seafloor spreading rate. In those numerical simulations with continental growth from the beginning and a high initial average mantle temperature water is outgassed rapidly. In the delayed continental growth model there is a very early outgassing event and the delayed continental growth has no remarkable influence on the thermal and outgassing history. A similar situation is found for the linear continental growth model but not for the Reymer and Schubert (1984) model.     

Mantle geochemistry: Insights from ocean island basalts

The geochemical study of the Earth's mantle provides important constraints on our understanding of the formation and evolution of Earth, its internal structure, and the mantle dynamics. The bulk Earth composition is inferred by comparing terrestrial mantle rocks with chondrites, which leads to the chondritic Earth model. That is, Earth has the same relative proportions of refractory elements as that in chondrites, but it is depleted in volatiles. Ocean island basalts(OIB) may be produced by mantle plumes with possible deep origins; consequently, they provide unique opportunity to study the deep Earth. Isotopic variations within OIB can be described using a limited number of mantle endmembers, such as EM1, EM2 and HIMU, and they have been used to decipher important mantle processes. Introduction of crustal material into the deep mantle via subduction and delamination is important in generating mantle heterogeneity; however, there is active debate on how they were sampled by mantle melting, i.e.,the role of olivine-poor lithologies in the OIB petrogenesis. The origin and location of high 3He/4He mantle remain controversial,ranging from unprocessed(or less processed) primitive material in the lower mantle to highly processed materials with shallow origins, including ancient melting residues, mafic cumulates under arcs, and recycled hydrous minerals. Possible core-mantle interaction was hypothesized to introduce distinctive geochemical signatures such as radiogenic 186 Os and Fe and Ni enrichment in the OIB. Small but important variations in some short-lived nuclides, including 142 Nd, 182 W and several Xe isotopes, have been reported in ancient and modern terrestrial rocks, implying that the Earth's mantle must have been differentiated within the first 100 Myr of its formation, and the mantle is not efficiently homogenized by mantle convection.     

The structure of convection in the spherical mantle with internal heating

Thermal convection in the mantle is caused by the heat transported upwards from the core and by the heat produced by the internal radioactive sources. According to the data on the heat transfer by the mantle plumes and geochemical evidence, only 20% of the total heat of the Earth is supplied to the mantle from the core, whereas most of the heat is generated by the internal sources. Along with the models that correctly allow for the internal heat sources, there are also many publications (including monographs) on the models of mantle convection that completely ignore the internal heating or the heat flux from below. In this study, we analyze to what extent these approximations could be correct. The analytical distributions of temperature and heat flux in the case of internal heating without convection and the results of the numerical modeling for convection with different intensity are presented. It is shown that the structure of thermal convection is governed by the distribution of the heat flux in the mantle but not by the heat balance, as it is typically implicitly assumed in most works. Heat production by the internal sources causes the growth of the heat flux as a function of radius. However, in the spherical mantle of the Earth, the heat flux decreases with radius due to the geometry. It turned out that with the parameters of the present Earth, both these effects compensate each other to a considerable extent, and the resulting heat flux turns out to be nearly constant as a function of radius. Since the structure of the convective flows in the mantle is determined by the distributions of heat flux and total heat flux, in the Cartesian models of the mantle convection the effective contribution of internal heating is small, and ignoring the heat flux from the core significantly distorts the structure of the convective currents and temperature distributions 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.     

Displacements of ridges and subduction zones in the models of mantle convection with lithospheric plates

In the existing kinematic theory of the tectonics of lithospheric plates, the position and the parameters of plates are assigned a priori in the initial and boundary conditions. However, in the self-consistent dynamic theory, the properties of oceanic plates (as well as the structure of the mantle’s convection) should appear automatically as the solution of the differential equations of energy, mass, and momentum transfer for a viscous fluid. In this case, the viscosity of the mantle’s substance as a function of temperature, pressure, shear stress, and chemical composition must be taken from the data of laboratory measurements. In the present work, the results of the numerical solution of the equations of convection are presented in the problem formulation mentioned above on a simple model of heated viscous fluid with properties that correspond to the mantle’s substance. In this case, to reveal the main reason for the generation of plates and their influence on the convection, a number of simplifications are introduced; in particular, temperature variations in the viscosity in the mantle are disregarded. In spite of the undertaken simplifications, the models show how the rigid lithosphere can be split into separate plates immersed in the mantle, how in the course of evolution the sizes of plates and their number can change, and how in this case the ridges and subduction zones can be displaced.     

地幔对流的数值模拟及其与表面观测的关系

本文从基本的热对流方程出发,并结合地幔对流特点,特别考虑到自重及非线性影响,探讨地幔对流及其与表面观测的关系,发展了相应的数值方法.结果表明,计算得到的长波大地水准面、地表地形、板块速度场水平散度与观测值符合程度较好.上、下地幔的非绝热温度异常与由地震层析得到的地震波速异常显示一定的相关性.地幔内部的流动呈现复杂形态,反映了高瑞利数对流的特征.     

A helium stratified and ingassed lower mantle: resolving the helium paradoxes

It is generally believed a variation of 3He/4He isotopic ratios in the mantle is due to only the decay of U and Th,which produces4 He as well as heat.Here we show that not only3He/4He isotopic ratios but also helium contents can be fractionated by thermal diffusion in the lower mantle.The driving force for that fractionation is the adiabatic or convective temperature gradient,which always produces elemental and isotopic fractionation along temperature gradient by thermal diffusion with higher light/heavy isotopic ratio in the hot end.Our theoretical model and calculations indicate that the lower mantle is helium stratified,caused by thermal diffusion due to*400℃temperature contrast across the lower mantle.The highest3He/4He isotopic ratios and lowest He contents are in the lowermost mantle,which is a consequence of thermaldiffusion fractionation rather than the lower mantle is a primordial and undegassed reservoir.Therefore,oceanicisland basalts derived from the deepest lower mantle with high3He/4He isotopic ratios and less He contents—the long-standing helium paradox,is solved by our model.Because vigorous convection in the upper mantle had resulted in disordered or disorganized thermal-diffusion effects in He,Mid-ocean ridge basalts unaffected by mantle plume have a relatively homogenous and lower!3He/4He isotopic compositions.Our model also predicts that 3He/4He isotopic ratios in the deepest lower mantle of early Earth could be even higher than that of Jupiter,the initial He isotopic ratio in our solar system,because the temperature contrast across the lower mantle in the early Earth is the largest and less4 He had been produced by the decay of U and Th.Moreover,the early helium-stratified lower mantle owned the lowest He contents due to over-degassing caused by the largest temperature contrast.Consequently,succeeding evolution of the lower mantle is a He ingassed process due to secular cooling of the deepest mantle.This explains why significant amount of He produced by the decay of U and Th in the lower mantle were not released,another long-standing heat–helium paradox.     

A preliminary study of the effects of some flow parameters in the generation of poloidal and toroidal energies within a 3-D spherical thermal-convective system with variable viscosity

The effects of variable viscosity on flow dynamics within spherical shells are investigated using a finite-element thermal convection model, and preliminary result for cases with relatively low Rayleigh numbers and small viscosity contrasts are reported. These results demonstrate some general effects of viscosity variation on mantle dynamics, and, in particular, the generation of toroidal energy. Since lateral viscosity variations are necessary in the generation of toroidal motion in a thermally driven convective system, it is not surprising our results show that flows with greater viscosity contrasts produce greater amounts of toroidal energy. Our preliminary study further shows that solutions become more time-dependent as viscosity contrasts increase. Increasing the Rayleigh number is also found to increase the magnitude of toroidal energy. Internal heating, on the other hand, appears to lead to less toroidal energy compared wth bottom heating because it tends to produce a thermally more uniform interior and thus smaller viscosity variations.     

The Myasnikov global theory of the evolution of planets and the modern thermochemical model of the Earth’ls evolution

The thermochemical model of the authors is shown to be naturally related to the general theory of V.P. Myasnikov. A heterogeneous modification of this homogeneous theory is described in light of the present ideas on the differentiation of the mantle substance at the boundary with the core and its eclogitization during submersion from the outer boundary and at the endothermic phase transition at a depth of 670 km. The Earth’ls evolution from an initial hot state is numerically modeled. The evolution is shown to start with an abrupt mantle overturn followed by a long period of steady evolution. Global mantle overturns recur a few times, gradually weaken, and are transformed into regional avalanches. The spatial configuration of overturns is represented by a predominant funnel-shaped sink and a few (three to five) ascending superplumes, which convincingly explains the causes of the formation of supercontinents, the opening of oceans, and the observed asymmetry of the planet. The times of overturns remarkably correlate with geological data on the existence of supercontinents. The processes of core growth, mantle cooling, and crust formation exhibit a clearly expressed stepwise behavior. The supplementation of the endothermic phase transition by chemical transformations favors the overcoming of the phase barrier between the upper and lower mantle, enhances the nonlinearity of mantle convection, and imparts a heterocyclic pattern to the process of evolution. It is shown that the lower mantle plume of chemical origin is fragmented by the phase transition into parts that, interacting with the thermal convection, generate a system of upper mantle plumes. This modeling provides an explanation of the coeval systems of oceanic plateaus and continental traps observed on the surface.     

Convection model of post-glacial uplift

A new approach to analytical and numerical study of the process of the post-glacial uplifting of the Earth’s surface was proposed within the framework of a viscous model. Displacement of the Earth’s surface is considered as the motion of the density boundary due to chemico-density convection. It is shown that the incorporation of the non-Newtonian rheology at observed velocities of post-glacial uplifts requires an obligatory presence of faults in the lithosphere and gives rise to quasi-uniform motion of the mantle material, whose viscosity under the lithosphere is, on the average, sufficiently small and amounts to ～10¹⁹ Pa. The study of the stability of the constructed model of the post-glacial uplift considered as the chemico-density convection relative to the thermal convection shows that the velocity of thermal convection developing in the presence of a quasiuniform mantle flow related to the post-glacial recovery is ～1 m/yr.     

Mantle plumes in the models of quasi-turbulent thermal convection

The process of multiple self-nucleation and ascent of mantle plumes is studied in the numerical models of thermal convection. The plumes are observed even in the simplest isoviscous models of thermal convection that leave aside the more complex rheology of the material, thermochemical effects, phase transformations, etc., which, although controlling the features of plumes, are not necessary for their formation. The origin of plumes is mainly due to the instability of the mantle flows at highly intense (low-viscous) thermal convection. At high viscosity, convective flows form regular cells. As viscosity decreases, the ascending and descending flows become narrower and unsteady. At a further decrease in viscosity, the ascending plumes assume a mushroom-like shape and occasionally change their position in the mantle. The lifetime of each flow can attain 100 Ma. Using markers allows visualizing the evolution of the shape of the mantle plumes.     

A conservative form of the deep convection equations and the efficiency of heat energy conversion in a polytropic mantle model

A wide class of equations is defined for a high pressure and subcritical temperature range of a fluid state whose thermodynamic properties enable the construction of a polytropic model of the mantle. A variant of deep convection equations of the Ogura and Phillips type is substantiated in terms of the polytropic mantle model. The proposed system of the deep convection equations includes fluctuation of the generalized potential temperature, has a quasi-incompressible form, and is transformed into Mihaljan’s system of shallow convection equations with a decrease in the layer depth. This circumstance is of great importance because it validates the use of the same dimensionless parameters as in the shallow convection model. The advantage of the proposed variant of the deep convection equations is its complete conservatism, which allows one to gain constraints on the efficiency of energy conversion in deep mantle processes and the thermal energy power expended on the generation rate of the convection kinetic energy and associated processes. This power is shown to be of the order of half the geothermal flux measured on the Earth’s surface.     

High-P/T experimental studies and water in the silicate mantle

Water (or H) in the silicate mantle is a key element in influencing Earth’s climate, habitability, geochemical evolution, geophysical properties and geodynamical processes, and has received increasing attention in the past decades. Experimental work under simulated high-pressure and high-temperature conditions is a powerful tool in characterizing the species, distribution, storage capacity and various physicochemical impacts of water in the mantle. In recent years, significant approaches have been acquired about some key physical, chemical and dynamical properties of water in the mantle and their various impacts, as a result of extensive studies by high-pressure and temperature experiments, and our knowledge of Earth’s water cycle, especially the deep water cycle, on both temporal and spatial scales has been greatly enhanced. In this paper, a brief review based mainly on experimental studies is presented concerning the current understanding and some recent approaches of water in the silicate mantle, such as the possible origin, amount, storage and the effect on mantle properties.     

Thermal evolution of the Earth: Secular changes and fluctuations of plate characteristics

The average secular cooling rate of the Earth can be deduced from compositional variations of mantle melts through time and from rheological conditions at the onset of sub-solidus convection at the end of the initial magma ocean phase. The constraint that this places on the characteristics of mantle convection in the past are investigated using the global heat balance equation and a simple parameterization for the heat loss of the Earth. All heat loss parameterization schemes depend on a closure equation for the maximum age of oceanic plates. We use a scheme that accounts for the present-day distribution of heat flux at Earth's surface and that does not depend on any assumption about the dynamics of convection with rigid plates, which remain poorly understood. We show that heat supply to the base of continents and transient continental thermal regimes cannot be ignored. We find that the maximum sea floor age has not changed by large amounts over the last 3 Ga. Calculations lead to a maximum temperature at an age of about 3 Ga and cannot be extrapolated further back in time. By construction, these calculations are based on the present-day tectonic regime characterized by the subduction of large oceanic plates and hence indicate that this regime did not prevail until an age of about 3 Ga. According to this interpretation, the onset of rapid continental growth occurred when the current plate regime became stable.     

Using postglacial sea level,crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model.Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.     

Using postglacial sea level, crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model.Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.     

Parameterized thermal model of a mixed mantle convection

IntroductionTectonicevolutionisinfluencedbythermalhistoryoftheEarth.TheEarthhasabout4.6Gahistory.ThermalenergyfromtheinterioroftheEachprovidesthemainpowerfortectonicevolution.ItnotonlycontrolstheformationofthelayeredstructuresinsidetheEarth,butalsopromotesthetectonicmovementsofthesurfaceplatesduringthegeologicalera.ThestudyofthethermalhistoryoftheEarthhaspassedseveralstages.Inearlystudies,onlyconductivemechanism(Lubimova,1958)isdiscussedinthethermalevolution.However,theimpotalceofthermalco…