The Deviation of the Lunar Center of Mass to the East of the Direction toward the Earth. A Mechanism Based on Rounding of the Figure of the Moon

It is known that the center of mass (CM) of the Moon does not coincide with its geometrical center of figure (CF), and that the CF–CMline deviates to the Southeast of the direction toward the center of the Earth. An investigation of this phenomenon, which has remained incompletely understood, has been carried out in two stages. One mechanism can explain part of the eastward shift of the lunar CM as being due to tidal evolution of the lunar orbit. A second mechanism is considered here, which relates this shift of the lunar CM with evolution of the shape of the Moon. A differential equation describing the shift of the lunar CMto the East in the course of the physically inevitable rounding of its shape as it moves away from the Earth is derived and solved. This mechanism not only explains the eastward shift of the lunar CM, but also predicts that the oblateness of the Moon could have been appreciable at earlier epochs, reaching values ε ≈ 0.31. The theory of figures of equilibrium in a tidal gravitational field is used to determine how close to the Earth the Moon could have formed.     

Tectonomagmatic evolution of the Earth and Moon

The Earth and Moon evolved following a similar scenario. The formation of their protocrusts started with upward crystallization of global magmatic oceans. As a result of this process, easily fusible components accumulated in the course of fractional crystallization of melt migrating toward the surface. The protocrusts (granitic in the Earth and anorthositic in the Moon) are retained in ancient continents. The tectonomagmatic activity at the early stage of planet evolution was related to the ascent of mantle plume of the first generation composed of mantle material depleted due to the formation of protocrusts. The regions of extension, rise, and denudation were formed in the Earth above the diffluent heads of such superplumes (Archean granite-greenstone domains and Paleoproterozoic cratons), whereas granulite belts as regions of compression, subsidence, and sedimentation arose above descending mantle flows. The situation may be described in terms of plume tectonics. Gentle uplifts and basins (thalassoids) in lunar continents are probable analogues of these structural elements in the Moon. The period of 2.3–2.0 Ga ago was a turning point in the tectonomagmatic evolution of the Earth, when geochemically enriched Fe-Ti picrites and basalts typical of Phanerozoic within-plate magmatism became widespread. The environmental setting on the Earth’s surface changed at that time, as well. Plate tectonics, currently operating on a global scale, started to develop about ∼2 Ga ago. This turn was related to the origination of thermochemical mantle plumes of the second generation at the interface of the liquid Fe-Ni core and silicate mantle. A similar turning point in the lunar evolution probably occurred 4.2–3.9 Ga ago and completed with the formation of large depressions (seas) with thinned crust and vigorous basaltic magmatism. Such a sequence of events suggests that qualitatively new material previously retained in the planets’ cores was involved in tectonomagmatic processes at the middle stage of planetary evolution. This implies that the considered bodies initially were heterogeneous and were then heated from above to the bottom by propagation of a thermal wave accompanied by cooling of outer shells. Going through the depleted mantle, this wave generated thermal superplumes of the first generation. Cores close to the Fe + FeS eutectics in composition were affected by this wave in the last turn. The melting of the cores resulted in the appearance of thermochemical superplumes and corresponding irreversible rearrangement of geotectonic processes.     

Not so rare Earth? New developments in understanding the origin of the Earth and Moon

A widely accepted model for the origin of the Earth and Moon has been a somewhat specific giant impact scenario involving an impactor to proto-Earth mass ratio of 3:7, occurring 50-60 Ma after T₀, when the Earth was only half-accreted, with the majority of Earth's water then accreted after the main stage of growth, perhaps from comets. There have been many changes to this specific scenario, due to advances in isotopic and trace element geochemistry, more detailed, improved, and realistic giant impact and terrestrial planet accretion modeling, and consideration of terrestrial water sources other than high D/H comets. The current scenario is that the Earth accreted faster and differentiated quickly, the Moon-forming impact could have been mid- to late in the accretion process, and water may have been present during accretion. These new developments have broadened the range of conditions required to make an Earth-Moon system, and suggests there may be many new fruitful avenues of research. There are also some classic and unresolved problems such as the significance of the identical O isotopic composition of the Earth and Moon, the depletion of volatiles on the lunar mantle relative to Earth's, the relative contribution of the impactor and proto-Earth to the Moon's mass, and the timing of Earth's possible atmospheric loss relative to the giant impact.     

Accretion of Moon and Earth and the emergence of life.

The discrepancy between the impact records on the Earth and Moon in the time period, 4.0-3.5 Ga calls for a re-evaluation of the cause and localization of the late lunar bombardment. As one possible explanation, we propose that the time coverage in the ancient rock record is sufficiently fragmentary, so that the effects of giant, sterilizing impacts throughout the inner solar system, caused by marauding asteroids, could have escaped detection in terrestrial and Martian records. Alternatively, the lunar impact record may reflect collisions of the receding Moon with a series of small, original satellites of the Earth and their debris in the time period about 4.0-3.5 Ga. The effects on Earth of such encounters could have been comparatively small. The location of these tellurian moonlets has been estimated to have been in the region around 40 Earth radii. Calculations presented here, indicate that this is the region that the Moon would traverse at 4.0-3.5 Ga, when the heavy and declining lunar bombardment took place. The ultimate time limit for the emergence of life on Earth is determined by the effects of planetary accretion--existing models offer a variety of scenarios, ranging from low average surface temperature at slow accretion of the mantle, to complete melting of the planet followed by protracted cooling. The choice of accretion model affects the habitability of the planet by dictating the early evolution of the atmosphere and hydrosphere. Further exploration of the sedimentary record on Earth and Mars, and of the chemical composition of impact-generated ejecta on the Moon, may determine the choice between the different interpretations of the late lunar bombardment and cast additional light on the time and conditions for the emergence of life.     

Irreversible evolution of tectono-magmatic processes at the Earth and Moon: Petrological data

The tectono-magmatic evolution of the Earth and Moon started after the solidification of their magmatic “oceans”, whose in-situ crystallization produced the primordial crusts of the planets, with the composition of these crusts depending on the depths of the “oceans”. A principally important feature of the irreversible evolution of the planetary bodies, regardless of their sizes and proportions of their metallic cores and silicate shells, was a fundamental change in the course of their tectono-magmatic processes during intermediate evolutionary stages. Early in the geological evolution of the Earth and Moon, their magmatic melts were highly magnesian and were derived from mantle sources depleted during the solidification of the magmatic “oceans”; this situation can be described in terms of plume tectonics. Later, geochemically enriched basalts with high concentrations of Fe, Ti, and incompatible elements became widespread. These rocks were typical of Phanerozoic within-plate magmatism. The style of tectonic activity has also changed: plate tectonics became widespread at the Earth, and large depressions (maria) started to develop at the Moon. The latter were characterized by a significantly thinned crust and basaltic magmatism. These events are thought to have been related to mantle superplumes of the second generation (thermochemical), which are produced (Dobretsov et al., 2001) at the boundary between the liquid core and silicate mantle owing to the accumulation of fluid at this interface. Because of their lower density, these superplumes ascended higher than their precursors did, and the spreading of their head parts resulted in active interaction with the superjacent thinned lithosphere and a change in the tectonic regime, with the replacement of the primordial crust by the secondary basaltic one. This change took place at 2.3–2.0 Ga on the Earth and at 4.2–3.9 Ga on the Moon. Analogous scenarios (with small differences) were also likely typical of Mars and Venus, whose vast basaltic plains developed during their second evolutionary stages. The change in the style of tectonic-magmatic activity was associated with important environmental changes on the surfaces of the planets, which gave rise to their secondary atmospheres. The occurrence of a fundamental change in the tectono-magmatic evolution of the planetary bodies with the transition from depleted to geochemically enriched melts implies that these planets were originally heterogeneous and had metal cores and silicate shells enriched in the material of carbonaceous chondrites. The involvement of principally different material (that had never before participated in these processes) in tectono-magmatic processes was possible only if these bodies were heated from their outer to inner levels via the passage of a heating wave (zone) with the associated cooling of the outermost shells. The early evolutionary stages of the planets, when the waves passed through their silicate mantles, were characterized by the of development of super-plumes of the first generation. The metallic cores were the last to melt, and this processes brought about the development of thermochemical super-plumes.     

Core formation in the Earth and Moon: new experimental constraints from V, Cr, and Mn

The mantles of the Earth and Moon are similarly depleted in V, Cr, and Mn relative to the concentrations of these elements in chondritic meteorites. The similar depletions have been used as evidence that the Moon inherited its mantle from the Earth after a giant impact event. We have conducted liquid metal-liquid silicate partitioning experiments for V, Cr, and Mn from 3 to 14 GPa and 1723 to 2573 K to understand the behavior of these elements during planetary core formation. Our experiments have included systematic studies of the effects of temperature, silicate composition, metallic S-content, metallic C-content, and pressure. Temperature has a significant effect on the partitioning of V, Cr, Mn, with all three elements increasing their partitioning into the metallic liquid with increasing temperature. In contrast, pressure is not observed to affect the partitioning behavior. The experimental results show the partitioning of Cr and Mn are hardly dependent on the silicate composition, whereas V partitions more strongly into depolymerized silicate melts. The addition of either S or C to the metallic liquid causes increased metal-silicate partition coefficients for all three elements. Parameterizing and applying the experimental data, we find that the Earth’s mantle depletions of V, Cr, and possibly Mn can be explained by core formation in a high-temperature magma ocean under oxygen fugacity conditions about two log units below the iron-wüstite buffer, though the depletion of Mn may be due entirely to its volatility. However, more oxidizing conditions proposed in recent core formation models for the Earth cannot account for any of the depletions. Additionally, because we observe no pressure effect on the partitioning behavior, the data do not require the mantle of the Moon to be derived from the Earth’s mantle, although this is not ruled out. All that is required to create depletions of V, Cr, and Mn in a mantle is a planetary body that is hot enough and reducing enough during its core formation. Such conditions could have existed on the Moon-forming impactor.     

General regularities in the distribution of seismic events on the Earth and on the Moon

Doklady Earth Sciences -     

Moon and Earth : compositional differences inferred from siderophiles,volatiles, and alkalis in basalts

We have compared RNAA analyses of 18 trace elements in 25 low-Ti lunar and 10 terrestrial oceanic basalts. According to Ringwood and Kesson, the abundance ratio in basalts for most of these elements approximates the ratio in the two planets.Volatiles (Ag, Bi, Br, Cd, In, Sb, Sn, Tl, Zn) are depleted in lunar basalts by a nearly constant factor of 0.026 ± 0.013, relative to terrestrial basalts. Given the differences in volatility among these elements, this constancy is not consistent with models that derive the Moon's volatiles from partial recondensation of the Earth's mantle or from partial degassing of a captured body. It is consistent with models that derive planetary volatiles from a thin veneer (or a residuum) of C-chondrite material; apparently the Moon received only 2.6% of the Earth's endowment of such material per unit mass.Chalcogens (Se and Te) have virtually constant and identical abundances in lunar and terrestrial basalts, probably reflecting saturation with Fe(S, Se, Te) in the source regions.Siderophiles show diverse trends. Ni is relatively abundant in lunar basalts (4 × 10^?3 × Cl-chondrites), whereas Ir, Re, Ge, Au are depleted to 10^?4?10^?5× Cl. Except for Ir, these elements are consistently enriched in terrestrial basalts: Ni 3 × , Re 370 ×, Ge 330 × , Au 9 × . This difference apparently reflects the presence of nickel-iron phase in the lunar mantle, which sequesters these metals. On Earth, where such metal is absent, these elements partition into the crust to a greater degree. Though no lunar mantle rock is known, an analogue is provided by the siderophile-rich dunite 72417 (~0.1% metal) and the complementary, siderophile-poor troctolite 76535. The implied metal-siderophile distribution coefficients range from 10⁴ to 10⁶, and are consistent with available laboratory data.The evidence does not support the alternative explanation advanced by Ringwood—that Re was volatilized during the Moon's formation, and is an incompatible element (like La or W⁴⁺) in igneous processes. Re is much more depleted than elements of far greater volatility: (Re/U)_Cl～- 4 × 10^?6 vs (T1/U)_Cl = 1.3 × 10^?4, and Re does not correlate with La or other incompatibles.Heavy alkalis (K, Rb, Cs) show increasing depletion with atomic number. Cs/Rb ratios in lunar basalts, eucrites, and shergottites are 0.44, 0.36, and 0.65 × Cl, whereas the value for the bulk Earth is 0.15–0.26. These ratios fall within the range observed in LL and E6 chondrites. supporting the suggestion that the alkali depletion in planets, as in chondrites, was caused by localized remelting of nebular dust (= chondrule formation). Indeed, the small fractionation of K, Rb and Cs, despite their great differences in volatility, suggests that the planets, like the chondrites, formed from a mixture of depleted and undepleted material, not from a single, partially devolatilized material.     

The split fate of the early Earth,Mars, Venus,and Moon

Plate tectonics shaped the Earth, whereas the Moon is a dry and inactive desert, Mars probably came to rest within the first billion years of its history, and Venus, although internally very active, has a dry inferno for its surface. Here we review the parameters that determined the fates of each of these planets and their geochemical expressions. The strong gravity field of a large planet allows for an enormous amount of gravitational energy to be released, causing the outer part of the planetary body to melt (magma ocean), helps retain water on the planet, and increases the pressure gradient. The weak gravity field and anhydrous conditions prevailing on the Moon stabilized, on top of its magma ocean, a thick buoyant plagioclase lithosphere, which insulated the molten interior. On Earth, the buoyant hydrous phases (serpentines) produced by reactions between the terrestrial magma ocean and the wet impactors received from the outer solar system isolated the magma and kept it molten for some few tens of million years. The planets from the inner solar system accreted dry: foundering of wet surface material softened the terrestrial mantle and set the scene for the onset of plate tectonics. This very same process also may have removed all the water from the surface of Venus and added enough water to its mantle to make its internal dynamics very strong and keep the surface very young. Because of a radius smaller than that of the Earth, not enough water could be drawn into the Martian mantle before it was lost to space and Martian plate tectonics never began. The radius of a planet is therefore the key parameter controlling most of its evolutional features.     

Escape of atmospheric gases from the Moon

The escape rate of atmospheric molecules on the Moon is calculated. Based on the assumption that the rates of emission and escape of gases attain equilibrium, the ratio of molecular number densities during day and night, n_0d/n_0n, can be explained. The plausible emission rate of helium and radioactive elements present in the Moon has also been calculated.     

单剪条件下主应力大小及主应力轴方向

对单剪条件下的应力莫尔圆变化过程进行详细分析,将莫尔圆从初始状态到破坏状态的大、小主应力变化过程看做由若干个等增量步组成,从而推导出任意剪应力状态与初始状态对应的小主应力差值与两者大主应力差值的比为一常数,该常数可以根据初始状态莫尔圆和破坏时对应的莫尔圆确定。推导出单剪条件下任意剪应力对应的大、小主应力及主应力轴方向的表达式。讨论了土体材料参数及法向应力对主应力轴偏转过程的影响以及大、小主应力与剪应力的关系。结果表明：在土体材料参数一定的条件下,主应力轴方向由应力比唯一确定;法向应力一定,土体的摩擦角越小,相同剪应力对应的主应力偏转角越大;剪切起始阶段,主应力变化缓慢,随着剪应力增大,主应力急剧变化至土样破坏时保持不变。     

Determination of the strain ellipsoid from measurements on any three sections

An ellipsoid is defined by, and may be re-constructed from, any three sections through it. In the field, calculation of the strain ellipsoid from general sections (two-dimensional strain ellipses determined from measured strain markers) is complicated by the fact that, due to experimental error and/or strain inhomogeneity, the three ellipses may not come from the same ellipsoid. The ellipses must first be adjusted to make them compatible. A method is suggested by which an adjustment ellipse is determined analytically for each of the three sections. Application of these adjustment ellipses makes the three sections compatible, and the strain ellipsoid may be determined. The principal axes of the ellipsoid are derived from the ellipsoid matrix by eigenvector analysis. Examples are given of practical applications of this method.     

A unified model for hydrogen in the Earth and Moon: No one expects the Theia contribution

The Moon is thought to have formed after a planetary embryo, known as Theia, collided with the proto-Earth 4.5 billion years ago. This so-called Giant Impact was the last major event during Earth’s accretion, and its effects on the composition of the Earth and the newly forming Moon would be measureable today. Recent work on lunar samples has revealed that the Moon’s water was not lost as a result of this giant impact. Instead, the Moon appears to contain multiple hydrogen reservoirs with diverse deuterium-to-hydrogen (D/H) ratios. For the first time, we incorporate hydrogen isotopic measurements of lunar samples to help constrain the composition of Theia. We show that the Moon incorporated very low-D/H (δD ≈ -750‰) materials that only could have derived from solar nebula H₂ ingassed into the magma ocean of a large (∼0.4 M_E) planetary embryo that was largely devoid of chondritic water. We infer Theia was a very large body comparable in size to the proto-Earth, and was composed almost entirely of enstatite chondrite-like material. These conclusions limit the type of impact to a “merger” model of similarly-sized bodies, or possibly a “hit-and-run” model, and they rule out models that mix isotopes too effectively.     

椭球体的视电阻率特征

椭球体是最具代表性的典型三维地电体之一,它三个轴的长短经过变化后可以和多种形状的地电体相似。因此,实现了椭球体电阻率的求解,就可以模拟绝大多数三维地电体的电阻率曲线。从拉普拉斯方程的求解出发,得到了均匀空间中存在的水平椭球体异常表达式,并用简单加倍的方法得到了均匀半空间中水平椭球体的视电阻率公式,结合倾斜旋转椭球体的视电阻率公式的规律,得到了倾斜椭球体的视电阻率公式,再进行一系列简化得到板状体。最后分析对比了均匀电场中旋转椭球体和板状体的视电阻率曲线的形态和规律。结论表明:旋转椭球体与板状体的视电阻率曲线的走向大体相似,且板状体的曲线相比旋转椭球体较缓和。对于低阻情况,在异常体顶部附近的视电阻率异常为零,异常体的倾向一侧有极小值,反倾向一侧有极大值,曲线随倾角α的增大而逐渐变陡。对于高阻情况,视电阻率的极大值出现在异常体顶部附近,两侧有极小值,倾向一侧的曲线较缓和而反倾向一侧的曲线较陡峭,随着倾角α的增大,视电阻率异常变大。     

Highly siderophile elements in the Earth, Moon and Mars: Update and implications for planetary accretion and differentiation

The highly siderophile elements (HSE) pose a challenge for planetary geochemistry. They are normally strongly partitioned into metal relative to silicate. Consequently, planetary core segregation might be expected to essentially quantitatively remove these elements from planetary mantles. Yet the abundances of these elements estimated for Earth's primitive upper mantle (PUM) and the martian mantle are broadly similar, and only about 200 times lower than those of chondritic meteorites. In contrast, although problematic to estimate, abundances in the lunar mantle may be more than twenty times lower than in the terrestrial PUM. The generally chondritic Os isotopic compositions estimated for the terrestrial, lunar and martian mantles require that their long-term Re/Os ratios were within the range of chondritic meteorites. Further, most HSE in the terrestrial PUM also appear to be present in chondritic relative abundances, although Ru/Ir and Pd/Ir ratios are slightly suprachondritic. Similarly suprachondritic Ru/Ir and Pd/Ir ratios have also been reported for some lunar impact melt breccias that were created via large basin forming events.Numerous hypotheses have been proposed to account for the HSE present in Earth's mantle. These hypotheses include inefficient core formation, lowered metal-silicate D values resulting from metal segregation at elevated temperatures and pressures (as may occur at the base of a deep magma ocean), and late accretion of materials with chondritic bulk compositions after the cessation of core segregation. Synthesis of the large database now available for HSE in the terrestrial mantle, lunar samples, and martian meteorites reveals that each of the main hypotheses has flaws. Most difficult to explain is the similarity between HSE in the Earth's PUM and estimates for the martian mantle, coupled with the striking differences between the PUM and estimates for the lunar mantle. More complex, hybrid models that may include aspects of inefficient core formation, HSE partitioning at elevated temperatures and pressures, and late accretion may ultimately be necessary to account for all of the observed HSE characteristics. Participation of aspects of each process may not be surprising as it is difficult to envision the growth of a planet, like Earth, without the involvement of each.     

文化视角下的地球科学

从文化视角来审视地球科学, 或将地球科学作为一种文化现象来研究, 地球科学至少包含三方面的内容: 一是地学研究方法或思维逻辑, 即“真”的问题; 二是人地关系或地学的价值理念, 即“善”的问题; 三是地球演化的平衡或人与地球的和谐, 即“美”的问题.文化视角下的地球科学是由“真”、“善”、“美”三者构成的统一体系.      

Formation of the Moon and the Earth from a common supraplanetary gas-dust cloud (lecture presented at the XIX all-Russia symposium on isotope geochemistry on November 16, 2010)

A hypothesis is proposed on the formation of the Earth and the Moon from a large-scale gas-dust cloud, the size of which is limited by the Hill radius, i.e., approximately one million kilometers. The compression of the supraplanetary gas-dust cloud resulted in an adiabatic temperature increase in its interior parts and evaporation of volatiles, including iron, from the surface of particles. At a certain stage, within 50–70 Ma after solar system formation, the supraplanetary gas-dust disk was fragmented, the Moon was separated, and the Earth embryo was formed. The remaining part of the gas-dust material was accreted mainly to the Earth. During this process, the gas dominated by primordial hydrogen was squeezed out of the disk. Vapor was removed together with hydrogen from the interparticle space. The hydrodynamic lifting resulted in the loss of volatiles, including Rb, Xe, and Pb, which is reflected in the Rb-Sr, Xe-I-Pu, and U-Pb isotopic systems. The gas-dust accretion was accomplished within 110–130 Ma (most likely, ∼120 Ma) after the beginning of solar system formation. Since then, the hydrodynamic lifting and volatile loss have ceased, and the history of the Earth as a condensed body has started.