A thermal model of the earth

A thermal model, consistent as far as possible with the parameterised earth model of Dziewonski et al. and with thermodynamic principles and relevant equations of state, is tabulated. This is made more secure by two recent developments, an experimental study of the FeS eutectic to 100 kbar by Usselman and a calculation by Bukowinski which reveals an electronic phase collapse of potassium in the 200–300 kbar range and explains the core heat source. Use is made of the Vashchenko-Zubarev formulation of the Grüneisen ratio, and Lindemann's melting law, both of which have been shown recently to have particular relevance at very high pressures. Values of electronic specific heat and the Grüneisen ratio, which contribute significantly to core properties are calculated from the electron equation of state of Zharkov and Kalinin.     

Theory of the evolution of the earth and the earth's crust

Summary The paleomagnetic field (declination and inclination) in different geological epochs is represented through the field of the so-called magnetic dipole. The optimal dipole coordinates so obtained show that during older geological times the optimal dipole lay outside the earth's centre and moved towards and around the earth centre. It is supposed that the optimal dipole trajectory in the earth coincides with earth core trajectory. This core motion brought about a motion of the masses of the mantle in a direction opposite to the motion of the core. This in turn brought about the break-down of Pangea and the separation of the continents. The drift of the continents, the relative changing of the earth's rotational axis and many other geological and geophysical phenomena may be explained through such a motion, that is through the motion of an eccentrical core towards the earth centre.     

On the expanding earth hypothesis

Summary The hypothesis of an expanding Earth is discussed on the basis of lunar laser ranging It is provcd that the given data do not indicate a secular increase in the principal moment of the Earth's inertia which would have to occur if the Earth were really expanding.

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On free oscillations of the earth

This survey concerns mostly the theory of free oscillations, with a section on experimental work included at the end. Developments over the last 15 years are examined. The general theory of free oscillations is reviewed, and the effect on free oscillations of such factors as heterogeneity, the Earth's rotation and non-sphericity, and the source of the oscillations are discussed. Earth models, which have been obtained from oscillation data, are reviewed, and their use in forming theoretical seismograms is described.See note at p. 426.Note     

A thermal tool for direct investigation of the interior of the earth

Summary Direct access to the crust and the upper portion of the mantle may be achieved by letting a high temperature (>1100°C) reactor core melt the rock in which it is placed and fall through the resulting magma. Data gathering and retrieval seem feasible. A schematic design of the proposed instrument is given.There are many problems concerning the composition and conditions of the interior of the earth which will not be solved upon completion of the projectedMohole Project. Comparison of the continental crust with the oceanic crust, relative distribution of radioactivity under continents and oceans, and the investigation of the mantle itself require access to greater depths than the present drilling techniques permit. To achieve these aims, it is recommended that a dense, heatgenerating object (such as a nuclear reactor core) be placed in the top of a salt dome. The hot object would melt the salt and fall downward through the moten salt. The sinking object would pass out of the source salt bed into rock at such a depth, say 35 000 feet, that if a few percent of H₂O is present at that depth, then a granitic rock would melt at about 700°C. However, encounter with SiO₂ containing no water would require a much higher temperature of about 1700°C. The type of rock that actually exists immediately below the source salt bed is unknown, but it is probably not a granitic rock.Thermal considerations indicate that the hole will freeze shut after downward passage of the tool, leaving the tool inside a liquid bubble. If the tool can generate heat long enough to melt its way up, as well as down, it may be possible to obtain magma samples. Instrumentation for control and telemetry purposes appears extremely difficult. Initial emphasis is placed on attaining the depth of interest.     

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.     

Modeling the thermal evolution of an active geothermal system

Temperature inversions at shallow to moderate depths have been observed commonly in boreholes drilled in geothermal areas. The inversions result from thermal disequilibria generated by steam and/or hydrothermal fluids invading shallow horizontal, or sub-horizontal fractures, or permeable horizons, from a deep vertical, or sub-vertical feeder-fracture.Subsurface distribution of temperatures in Momotombo geothermal area of Nicaragua, Central America, indicates that the anomaly is generated by steam and water, convecting in a narrow feeder-fracture-zone located at the western edge of the field. The north-trending zone of the feeder-fracture is bound on the west by the area of massive, impermeable andesitic rocks, and is capped by an impermeable, approximately 300 m. thick silica-cap, which seals if from the ground surface. The thermal fluids penetrate a system of horizontal, or sub-horizontal fractures, extending east of the feeder-fracture beneath the silica cap. The flow of thermal fluids eastward through the system of the horizontal, or sub-horizontal fractures is generating a plume-like geothermal anomaly, which is expressed by the temperature inversion zone pervasive in the boreholes to the east of the feeder-fracture.A time-dependant model for a semi-infinite half-space (z > 0) in contact with a hot, well stirred, isotropic fluid flowing through an aquifer overlain by a finite space of constant thickness is solved for the data collected from the Momotombo geothermal boreholes. Curve fitting between the simulated and observed temperature/depth profiles suggests that the thermo-tectonic events which caused the present-day Momotombo hydrothermal system occurred approximately 5,500 years ago, following development of vertical, or subvertical fractures along a N5°E trending faultline. Hot fluids emerging from these fractures move eastward through a system of horizontal, or sub-horizontal fractures, with a velocity of 11 to 20 m/yr.     

Chemical heterogeneity of the Archaean mantle,composition of the earth and mantle evolution

New rare earth element (REE) data for Archaean basalts and spinifex-textured peridotites (STP) show a range of La/Sm ratios (chondrite-normalized) from 0.36 to 3.5, with the bulk of the data in the range 0.7–1.3. This supports the hypothesis, based on Sr isotope initial ratios, that the Archaean mantle was chemically heterogeneous. We suggest that the bulk mantle source for Archaean basaltic magmas was close to an undepleted earth material. An average chemical composition of the Archaean mantle is estimated using chemical regularities observed in Archaean STP and high-magnesian basalts. TiO₂ and MgO data show an inverse correlation which intersects the MgO axis at about 50% MgO (Fo₉₂). TiO₂ abundance in the mantle source is measured on this plot by assigning anMgO= 38% for the mantle. Concentrations of other elements are also estimated and these data are then used to obtain a composition for the bulk earth. We suggest an earth model with about 1.35 times ordinary chondrite abundances of refractory lithophile elements and about 0.2 times carbonaceous type 1 chondrite abundances of moderately volatile elements (such as Na, Rb, K, Mn). P shows severe depletion in the model earth relative to carbonaceous chondrites, a feature either due to volatilization or core formation (preferred). Our data support the hypothesis of Ringwood that the source material for the earth is a carbonaceous chondrite-like material.The generation of mid-ocean ridge basalts (MORB) is examined in the light of the model earth composition and Al₂O₃/TiO₂, CaO/TiO₂ ratios. It is suggested that for primitive basalts, these values can be used to predict the residual phases in their source. Comparison of chemical characteristics of inferred sources for 2.7-b.y. Archaean basalts and modern “normal” MORB indicates that the MORB source is severely depleted in highly incompatible elements such as Cs, Ba, Rb, U, Th, K, La and Nb, but has comparable abundances of less incompatible elements such as Ti, Zr, Y, Yb. The cause of the depletion in the MORB source is examined in terms of crust formation and extraction of silica-undersaturated melts. The latter seems to be a more likely explanation, since the degree of enrichment of highly incompatible elements in the crust only accounts for up to 40% of their abundances in the bulk earth and cannot match the depletion pattern in normal MORB. A large volume of material, less depleted than the source for normal MORB must therefore exist in the mantle and can serve as the source for the ocean island basalts and “normal” MORB.Three different mantle evolution models are examined and each suggests that the mantle is stratified with respect to abundances of incompatible trace elements. We suggest that no satisfactory model is available to fully explain the spectrum of geochemical and geophysical data. In particular the Pb and Sr isotope data on oceanic basalts, the depletion patterns of MORB and the balance between lithophile abundances in the crust and mantle, are important geochemical constraints to mantle models. Further modelling of the mantle evolution will be dependent on firmer information on the role of subduction, mantle convection pattern, and basalt production through geologic time together with a better understanding of the nature of Archaean crustal genesis.     

Origin and thermal evolution of icy satellites

The paper reviews the problem of formation and evolution of the so-called regular satellites of the giant planets, and it consists of two parts: the first describes the possible origin of the satellites, the second studies their evolution, attempting to stress the relations of the present status of the satellites with their evolutionary history.The formation of regular satellite systems around giant planets is probably related to the formation of the central planet. Some characteristics of regular satellite systems are quite similar, and suggest a common origin in a disk present around the central body. This disk can originate through different mechanisms which we will describe, paying attention to the so-called accretion disk model, in which the satellite-forming material is captured. The disk phase links the formation of the primary body with the formation of satellites. The subsequent stages of the disk's evolution can lead first to the formation of intermediate size bodies, and through the collisional evolution of these bodies, to the birth of satellite embryos able to gravitationally capture smaller bodies.Given the scenario in which icy satellites may be formed by homogeneous accretion of planetesimals made of a mixtures of ice and silicates, if no melting occurs during accretion, the satellites have a homogeneous ice-rock composition. For the smaller satellites this homogeneous structure should not be substantially modified; only sporadic local events, such as large impacts, can modify the surface structure of the smaller satellites. For the larger satellites, if some degree of melting appears during accretion, a differentiation of the silicate part occurs, the amount of differentiation and hence the core size depending on the fraction of gravitational potential energy retained during the accumulation process. Melting and differentiation soon after the accretion, for the larger satellites, could also depend on the convective evolution in presence of phase transitions and generate an intermediate rock layer, considerably denser than the underlying, still homogeneous core, and unstable to overturning on a geologic time scale. Moreover the liquid water mantle could be a transient feature because the mantle would freeze over several hundred million years. For these large bodies the stable configuration is expected to be one consisting of a silicate core and a mantle of mixed rock and ice.     

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.     

金星非单调冷却热演化历史分析

金星表层年龄和构造活动特点表明其岩石层在最近的地质历史时期经历过广泛的更新.这种全球性的表层改造与其内部热演化历史进程密切相关.如果金星存在相变形成的上、下地幔,依据现今所了解的金星物理性质和参量化的热对流理论,并且考虑金星地幔相变边界层状态对对流的控制作用,我们计算了金星热演化历史.结果表明,金星的热演化历史是一种非单调的冷却过程,在这种非单调的热演化历史进程中,金星地幔会出现大体等周期的翻转.由于参数选取的不同,翻转时金星上、下地幔的温差随时间可能出现稳定变化、逐渐加强、逐渐减弱三种不同演化模式,目前尚不能确定实际金星热演化历史究竟是哪一种模式.金星地幔相变边界层的穿透对流可能是推动其表层岩石层全球性更新的关键,导致其表层火山活动和地表构造以大致500 Ma时间间隔更新和重造.     

Coexisting bronzite and clinobronzite and the thermal evolution of the Steinbach meteorite

Steinbach is a stony-iron meteorite with approximately equal amounts of silicate and metal that shows Widmanstätten structure. The silicate portion contains tridymite, orthobronzite, and clinobronzite that formed by inversion from high-temperature protobronzite. The assemblage orthobronzite-protobronzite-tridymite-metallic iron indicates an equilibrium temperature of 1200°C and an ?o₂ of 10^?12 under a total pressure of less than 2 kbar. Preservation of the high-temperature phase relations implies much more rapid cooling in the 1200-700°C range than the rates that have been deduced for the development of Widmanstätten structure in the 700-500°C range.     

Ultrahigh-pressure metamorphic rocks and the thermal evolution of continent collision belts

Abstract Coesite-bearing eclogites exposed in the Alpine, Qinling-Dabie (China), Caledonian, and Ural orogenic belts provide insight into the time-dependent thermal structure of continent collision belts. Coesite-bearing eclogites record peak metamorphic temperatures of 550-900°C at pressures ≥ 2.5 GPa reflecting anomalously cool conditions at depths of 90 km or more. The low temperatures recorded by coesite-bearing eclogites strongly suggest formation in a convergent plate margin where the downward advection of cool lithosphere depresses isotherms on a regional scale. Subduction zone pressure-temperature (P-T) paths calculated using a two-dimensional finite-difference model predict steady-state temperatures of 450-650°C at 100 km depth at the slab-mantle interface for convergence rates of 10 to 100 mm/yr. Coesite-bearing eclogites record peak temperatures ~100-250°C higher, possibly reflecting (i) formation during the early stages of convergence prior to the achievement of thermal steady state; (ii) attainment of peak metamorphic temperatures during decompression (exhumation); (iii) formation during slow, <10 mm/yr, convergence; or (iv) uncertainties in the modeling parameters. Retrograde P-T paths determined for coesite-bearing eclogites from the western Alps and China indicate cooling during decompression from depths of ~100 km. Cooling of eclogite terrains during exhumation requires loss of heat downward into lithosphere that continues to subduct beneath the eclogites, loss of heat upward into the cooler hanging wall of a large-scale normal fault/shear zone, or a combination of the two scenarios.     

On the free oscillations of a laterally heterogeneous earth model

Summary The equations of motion for the free oscillations of a heterogeneous spherical earth model are derived. It is found that the lateral variations of density and elastic moduli couple the odd(even) harmonics of the spheroidal oscillations with themselves as well as with the even (odd) harmonics of the torsional oscillations.List of symbols r, , Spherical coordinates;r is the radial distance from earth's center, is the co-latitude, and is the east longitude - r Space vector denoting a point with coordinatesr, , and - Gradient operator - ² Laplacian operator - _ij Kronecker's delta function - I Identity matrix - i      

Rare earth element chemistry indicates chemical alteration of zircons during the evolution of weathering profile

Although rare earth elements(REEs)in magmatic zircons have been widely used to identify the type and compositional evolution of host rocks,REE distribution patterns during the chemical alteration of zircons need clarification.We investigated REE characteristics in zircons with different degrees of chemical weathering through systematic observation of a granodiorite-weathering profile in southeast China.Despite the relatively stable provenance of the studied profile(zircon U–Pb ages are95.2±4.8 Ma),the zircon REEs exhibited systematic differences in abundance and fractionation patterns from the bedrock to upper layers,e.g.∑PREE,(LREE/HREE)_(CN),and Ce/Ce*.This evidence suggests chemical alteration of zircons during intensive chemical weathering and an expected influence on REE variability in the weathered products due to the presence of REE-bearing minerals.     

On the nearly axially-symmetrical model of the hydromagnetic dynamo of the earth

A short review of the present state of the nearly axially-symmetrical dynamo model is given. A simplified theory for hydromagnetic dynamos taking into account the forces acting in the Earth's core is considered. The role of weak core-mantle friction is discussed and a form of solution is suggested which is characterized by a large geostrophic velocity in the core and by a boundary layer of a new type. The consequences of such a model (called model Z) for the Earth's dynamo are discussed.     

Equations of thermal convection for a viscous compressible mantle of the earth including phase transitions

A system of equations for the calculation of thermal convection in a compressible mantle with variable parameters and phase transitions is derived from the general laws of mass, momentum, and energy conservation and thermodynamic relations. Mantle convection is successively calculated in the anelastic liquid, truncated anelastic liquid, mean density, expanded Boussinesq, and Boussinesq approximations. Phase transitions are automatically taken into account with the help of effective thermodynamic parameters determined from general thermodynamic relations.     

On the triaxiality of the earth on the basis of satellite data

Summary The evolution of the opinions as to the problem of the triaxiality of the Earth in the period prior to satellite geodesy can be seen, e.g., in[1–18]. Recently the opinion has been voiced that triaxiality is a result of the mathematical treatment of data rather than reality[19–21], especially since this is a comparatively small parameter. This opinion is not in contradiction with the results of satellite observations[22–28], but the non-zero values of the harmonic coefficients of the second degree and second order are a reality, they yield a value of the equatorial flattening of about1/90 000, and the representation of the equatorial section by an ellipse is justified even if the harmonics n=3, k=1 and n=3, k=3 have amplitudes only about half as small, and some other parameters might occur with just as much justification besides triaxiality.