应用Lane-Emden方程分析下月幔厚度与月核半径大小

文中取圈层结构和球对称形态为月球的基本结构假设,并以月球平均密度和无量纲惯性矩作为约束,数值求解月球Lane-Emden方程,得到下月幔厚度和月核大小的变化范围.结果表明月核的密度在4.7 ~7.0 g/cm3范围内变化时,月核半径的变化范围为704~356 km,相应的月幔厚度的变化范围约为33～381 km,月核占月球总质量的百分比在0.6%～7%之间变化.所得结果可为后续的关于月球内部结构的研究提供一定的参考.     

基于神经网络方法获得最优化月球内部结构模型

由于观测手段有限,目前对月球内部结构的认识还存在很大的不确定性,至今仍没有一个被广泛认可的内部结构模型,且现有对月球内部结构模型的研究几乎很少关注观测值对观测精度的影响.本研究采用混合密度神经网络方法得到了月球内部结构模型的后验概率密度分布,获得了平均月球内部结构模型(Mean模型)、最大后验概率对应的月球内部结构模型...     

On the admissible range for the mass and inertia moments of the liquid core: II. Results of numerical calculations

We analyze the present-day data on the periods of free oscillations and amplitudes of the forced nutations of the Earth for evaluating the admissible range of the mass and moment of inertia for the liquid core. The initial model for this study is taken in the form of the model distribution of density and mechanical Q parameters of the mantle suggested in (Molodenskii, 2010; 2011a; 2011b). This model was constructed by the steepest descent method in the space of 64 parameters, which determine the distribution of density and parameters of mechanical Q in the mantle, liquid outer core, and solid inner core of the Earth. We assumed the Q parameter of the mantle and inner solid core to be constant and sought for the density variations for the simplest two-parameter model of the piecewise-linear functions with the jumps on the boundary between the liquid core and the mantle and at the olivine-spinel phase transition at a depth of 670 km in the mantle. After this, the computations were repeated for the other distributions of Q (which were also assumed to be unchanged) that correspond to their limiting admissible values. Using this approach, we managed to find the most probable values of the mass and moment of inertia of the liquid core and determine the admissible range of their values. According to our estimates, the ratios of the mass and moments of inertia of the liquid core to the mass and moment of inertia of the whole Earth fall in the intervals 0.317996 ± 0.00065 and 0.110319 ± 0.00022, respectively. These values are lower than the corresponding values for the PREM model (0.322757 and 0.112297) by (1.48 ± 0.30)% and (1.76 ± 0.35)%, respectively. The interpretation of these results requires the revision and thorough analysis of the data on the admissible temperature range of the liquid core and (or) its chemical composition.     

Mascons and the moon's orientation

This letter reports the discovery of a relation between the moments of inertia of the mascons (taken about the moon's center) and the moon's moments of inertia. It is found that the principal axes of the mascons alone are nearly parallel to those of the moon. Possible explanations of this parallelism are discussed. If the mascons are associated with a layer of uncompensated basalt on the moon's nearside, then the parallelism can be adequately explained on the grounds that the mascons and basalts together determined the moon's orientation. On the other hand, the third-order harmonics of the moon's gravity field indicate that the excess mass controlling the moon's orientation is on the farside. It thus appears that the mascons have been emplaced in special sites whose position was controlled by the processes which produced the farside highlands.     

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.     

Creep of crystals: J.P. Poirier,Cambridge University Press, 1985, xii + 260 pp., £27.50, US$ 49.50, ISBN 0-521-26177-5

Fractional crystallization behaviour of a magma ocean extending to lower mantle depths was deduced from estimations of melting relations for the deep mantle and the density relationships between ultrabasic liquid and mantle minerals. The accretional growth of the Earth necessarily involves a molten zone (magma ocean) in the outer layer of the growing Earth. The fractionation by melting during accretion results in primary stratification composed of a molten ultrabasic upper mantle (magma ocean), a perovskite-rich lower mantle, and an iron core. A certain amount of Al₂O₃ and CaO was removed from the magma ocean and retained in the lower mantle due to eclogite fractionation in the early stage of accretion and the perovskite fractionation in the later stage of accretion. Models of the stratification of the upper mantle arising from fractional crystallization of the magma ocean and subsequent convective disturbance were deduced on the basis of estimations of melting relations for the deep mantle and the density relationships between the ultrabasic liquid and mantle minerals. The stratification of the mantle, which is consistent with geophysical constraints is as follows; the upper mantle is composed of two layers, the upper olivine-rich layer and the lower garnet-rich layer with a thickness around 200 km, and the lower mantle with a perovskite-rich composition. In this model, both the 400 and 650 km discontinuities are the chemical boundaries.     

对月球重力场特征的理解

依据克莱门汀号和月球勘探者号月球探测器所获得的数据所建立最新的地球重力模型和地形模型,为人类深入了解月球内部性质及其演化特征,提供新的平台.M.T. Zuber (1994) 和 M. A. Wieczorek (1998) 所建立的月壳全球模型,为利用最新月球着力资料研究月球内部构造和演化,揭示月球上独特的“物质瘤”之成因等科学问题,开凿了先河.本文通过对现有的月球重力和地形数进行分析和计算,提出作者对月球内部物质分布特征的理解和一些认识.从宏观角度看,月球布格重力异常与月球地形起伏是相关的,统计结果表明它们呈弱负相关,从均衡角度来说,在月球停止大规模内部物质运动之前,月球壳幔可能已基本达到均衡;从Mascon深度估算结果来看,一些大型的Mascon基本属于玄武岩浆“充填”型的,少数Mascon可能与月幔柱有关,如东方海Mascon.     

Large impact craters and the moon's orientation

This paper investigates the idea that large impact events have caused the moon to change its orientation in space. It is found that the very largest impact events, such as those which formed Imbrium and Orientale, probably did reorient the moon. This reorientation is primarily due to the change in the moon's moments of inertia consequent upon crater formation. The impulse delivered by the impact can at most unlock the moon's synchronous rotation for a few thousand years, and is thus not of major importance. The moon will attain its new orientation in less than a few times 10⁴ years as a result of tidal friction. Since the large craters eventually are filled by isostatic rebound and extrusive igneous activity, the moon may eventually regain its original orientation unless other phenomena cause new changes in the distribution of mass on its surface.     

月球内部构造研究综述

回顾了月震观测的历史,归纳出月震的特点,并将月震分成热震、浅震和深震三种类型加以.分析总结出一个比较完整的月球内部构造模型.在此基础上,详细介绍了如何根据月震观测资料确定月壳和月幔.本文还对月核存在的可能性加以阐述,指出由于月球1100 km以下数据的缺乏,到目前为止没有确切的证明月核存在的证据.最后,紧密关注月球构造研究的最新进展,给出了月核可能存在的形式：半径为352 km（成分为纯Fe）或者374 km（成分为Fe-FeS晶体）.     

Thermal and chemical evolution of the terrestrial magma ocean

The Earth is likely to have experienced a magma ocean stage during accretion. Thermal and chemical evolution of magma ocean is investigated based on a one-dimensional two-phase-flow heat and mass transfer model. Differentiation at lower mantle pressure depends on the type of magma ocean and surrounding atmosphere. If the magma ocean is formed by the blanketing effect of a solar-type proto-atmosphere, extensive differentiation proceeds at lower mantle pressure. If the magma ocean is formed by the blanketing effect of an impact-induced steam atmosphere, no differentiation at lower mantle pressure is likely. If a very deep magma ocean is formed by a giant impact, whether differentiation proceeds at lower mantle pressure or not depends on grain size, viscosity of melt and/or properties of a transient atmosphere. On the contrary, chemical differentiation likely proceeds at upper mantle pressure irrespective of magma ocean type. A shallow magma ocean can remain for 100 200 My without any heating processes.     

Temperatures in the lunar interior and some implications

Data on the electrical conductivity of olivine and pyroxene obtained under redox conditions similar to those that exist in the moon indicate that the moon is at temperatures near the melting point at depths of 600–900 km. This temperature profile, combined with information on the distribution of radioactive elements and evidence of extensive differentiation of the moon, lead to the conclusion that the moon accreted at temperatures between 600–1000°C. This high accretion temperature can be reconciled with the presence of FeS and the probable FeO/MgO ratio in the lunar interior if the moon accreted from material which was depleted in H₂ relative to the solar nebula.     

Inversion of seismic and gravity data for the composition and core sizes of the Moon

We model the internal structure of the Moon, initially homogeneous and later differentiated due to partial melting. The chemical composition and the internal structure of the Moon are retrieved by the Monte-Carlo inversion of the gravity (the mass and the moment of inertia), seismic (compressional and shear velocities), and petrological (balance equations) data. For the computation of phase equilibrium relations and physical properties, we have used a method of minimization of the Gibbs free energy combined with a Mie-Gr@uneisen equation of state within the CaO-FeO-MgO-Al₂O₃-SiO₂ system. The lunar models with a different degree of constraints on the solution are considered. For all models, the geophysically and geochemically permissible ranges of seismic velocities and concentrations in three mantle zones and the sizes of Fe-10%S core are estimated. The lunar mantle is chemically stratified; different mantle zones, where orthopyroxene is the dominant phase, have different concentrations of FeO, Al₂O₃, and CaO. The silicate portion of the Moon (crust + mantle) may contain 3.5–5.5% Al₂O₃ and 10.5–12.5% FeO. The chemical boundary between the middle and the lower mantle lies at a depth of 620–750 km. The lunar models with and without a chemical boundary at a depth of 250–300 km are both possible. The main parameters of the crust, the mantle, and the core of the Moon are estimated. At the depths of the lower mantle, the P and S velocities range from 7.88 to 8.10 km/s and from 4.40 to 4.55 km/s, respectively. The radius of a Fe-10%S core is 340 ± 30 km.     

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.     

27.3-day and 13.6-day atmospheric tide

An analysis of time variations in the earth's length of day (LOD) for 25 years (1973-1998) versus at- mospheric circulation changes and lunar phase is presented. It is found that, on the average, there is a 27.3-day and 13.6-day period oscillation in global zonal wind speed, atmospheric geopotential height, and LOD following alternating changes in lunar phase. Every 5-9 days (6.8 days on average), the fields of global atmospheric zonal wind and geopotential height and LOD undergo a sudden change in rela- tion to a change in lunar declination. The observed atmospheric oscillation with this time period may be viewed as a type of atmospheric tide. Ten atmospheric tidal cases have been analyzed by comparing changes in LOD, global zonal wind speed and atmospheric geopotential height versus change in lunar declination. Taken together these cases reveal prominent 27.3-day and 13.6-day tides. The lunar forcing on the earth's atmosphere is great and obvious changes occur in global fields of zonal wind speed and atmospheric geopotential height over the equatorial and low latitude areas. The driving force for the 27.3-day and 13.6-day atmospheric tides is the periodic change in lunar forcing during the moon's revolution around the earth. When the moon is located on the celestial equator the lunar declination equals zero and the lunar tidal forcing on the atmosphere reaches its maximum, at this time the global zonal wind speed increases and the earth's rotation rate decreases and LOD increases. Conversely, when the moon reaches its most northern or southern positions the lunar declination is maximized, lunar tidal forcing decreases, global zonal wind speed decreases, earth's rotation rate increases and LOD decreases. 27.3-day and 13.6-day period atmospheric tides deserve deeper study. Lunar tidal forcing should be considered in models of atmospheric circulation and in short and medium range weather forecasting.     

全球地表热流的产生与分布

全球地表热流是反映地球内部热与动力学过程的一种主要能流.本文在三维球坐标框架下，就几个不同的粘度模型分别研究地幔内部密度异常(基于全球地震层析结果)以及板块运动激发的地幔流动的热效应及其对于观测地表热流产生和分布特征的贡献.由于地幔动力系统具有较高的Pe数，可以期望由板块运动激发的地幔流动将强烈地扰动地幔内部初始传导状态下的温度场以及地表热的热流分布.结果表明，与地幔内部密度异常产生的热效应相比，运动的板块及其激发的地幔流动在全球地表观测热流的产生和分布特征上起着更为重要的作用.观测到的大洋中脊处的高热流在很大程度上可以归因于板块激发的地幔流动的热效应.计算的平均温度剖面较好地揭示了岩石圈和D″层的温度特征，即温度随深度的剧烈变化，这与我们目前通过其他手段对岩石圈和D″层的温度结构了解是一致的.一个下地幔粘度比上地幔高出30倍的粘度结构(文中使用的粘度模型2)较之其余模型的拟合程度似乎更好.     

Comparison of dynamical and geometrical shape of the moon

The dynamical shape of the moon is described by means of the parameters of its gravity field and principal moments of inertia. These data are derived from the lunar artificial satellites (“Luna-10”, “Orbiters 1–4”), and astronomical measurements of the physical librations.The geometrical shape of the moon is determined from measurements of absolute heights of the lunar surface.The differences of dynamical and geometrical figures of the moon are analysed, and their possible interpretation is discussed.     

Cretaceous length of day perturbation by mantle avalanche

These last 10 years, numerical models of mantle convection have emphasized the role of the 670 km endothermic phase change in generating avalanches that trigger catastrophic mass transfers between upper and lower mantle. On the other hand, scientists have emphasized the concomitance of large-scale worldwide geophysical and tectonic events, which could find their deep thermal roots in the huge mass transfers induced by the avalanches. In particular, the paleontological records show two periods of length of day (l.o.d.) shortening between 420 and 360, and 200 and 80 Myr BP. This last event is synchronous with a strong true polar wander and a global warming of the upper mantle. In order to study the potential effects of the avalanche on the main component of the Earth’s rotation, the Liouville equation has been solved and the l.o.d. evolution has been calculated from the perturbations of the inertia tensor. The results show that the inertia tensor of the Earth’s is mainly sensitive to the global transfers through the 670 km discontinuity. The l.o.d. perturbations will be synchronous with the global thermal effects of the avalanche. These theoretical results allow proposing a self-consistent physical mechanism to explain periods of the Earth’s rotation acceleration. Within this context, the l.o.d. shortening during the Cenozoic and Cretaceous brings one more clue to the possible participation of a mantle avalanche in generating the concomitant large scale events which have occurred during this very particular period of the Earth’s history.     

Geochemical constraints on the model of the composition and thermal conditions of the Moon according to seismic data

A new method of reconstruction of the temperature profile in the lunar mantle from the velocities of seismic P- and S-waves for different models of chemical composition is developed. The procedure of the solution of an inverse problem is realized with the help of the minimization of the Gibbs free energy and the equations of state of a mantle substance, taking into account phase transformations, anharmonicity, and the effects of inelasticity. The geophysical and geochemical constraints on composition and temperature distribution in Moon’s mantle are established. The upper mantle can be composed of olivine pyroxenite, depleted by low-volatile oxides (∼2 wt % of CaO and Al₂O₃). On the contrary, the lower mantle must be enriched by low-volatile oxides (∼4–6 wt % of CaO and Al₂O₃). Its composition can be represented by a mineral association of the olivine + clinopyroxene + garnet or olivine + orthopyroxene + clinopyroxene + garnet type, which is close in composition to pyrolite. The temperature distribution at depths 50–1000 km are approximated by the equation: T(°C) = 351 + 1718[1–exp (−0.00082H)]. The constraints inferred make it possible to conclude that the published values of the velocities of P- and S-waves for the lunar mantle, obtained by processing the data of seismic experiments of the Apollo lunar mission are inconsistent with each other at depths below 300 km. Otherwise, the variations in the velocities of P- and S-waves disturb the symmetry between the petrological model (composition), the temperature profile, and the seismic profile.     

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.     

Mantle regulation of core cooling: A geodynamo without core radioactivity?

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.