Thermal regime in the earth's core and lower mantle

Current views favour the presence of sulphur in the core, giving a composition of Fe + FeS. It is argued that the core composition is close to the eutectic and that this eutectic composition is Fe₂S. The consequences for the thermal regime in the core are examined in terms of the most likely properties of the Fe₂S eutectic. This leads to much lower temperatures than would be expected for an iron or FeSi core.Consideration of the thermal regime in the mantle and the probable thermal properties of lower-mantle assemblages leads to a similar low temperature for the core-mantle boundary. These temperatures require a temperature gradient near the adiabatic in the mantle, implying a convective thermal history.     

Oceanic island Pb: Two-stage histories and mantle evolution

Leads in basaltic suites from seven oceanic islands form linear arrays on²⁰⁶Pb/²⁰⁴Pb versus²⁰⁷Pb/²⁰⁴Pb diagrams. These arrays are more reasonably interpreted as secondary isochrons than as mixing lines, because of their systematic relationship. Separate two-stage histories calculated for the leads from each island indicate that the source materials for the magmas were derived from a single primary reservoir with present²³⁸U/²⁰⁴Pb of 7.91 ± 0.04 by secondary enrichment in U/Pb at different times from 2.5 to 1 Ga ago. This is confirmed by a plot of isochron slope versus intercept, on which the points describing each island's Pb-Pb array all lie very near a single straight line. The isochrons for the Canary Islands and Hawaii, at least, are significantly different. The²⁰⁸Pb/²⁰⁴Pb versus²⁰⁶Pb/²⁰⁴Pb relationships are less coherent. The lead isotopic characteristics are consistent with a model in which lead in the oceanic island magmas is derived from ancient subducted oceanic crust. In particular, this explains the close relationship between lead in mid-ocean ridge and oceanic island basalts without invoking mixing.     

Homogeneity and constitution of the earth''s lower mantle and outer core

The lower mantle and outer core of the recent “parametric earth model” (PEM), in which the velocity and density distributions in these regions are both smooth and consistent with the Adams-Williamson equation, are extrapolated to zero pressure using fourth-order finite-strain relations, and the results are compared with recent experimental data on relevant materials. The fourth-order term is found to significantly improve the fits to the model. The lower-mantle velocities are found to be significantly higher than those expected for mixtures of MgO, FeO and SiO₂ of olivine or pyroxene compositions. It is concluded that a slightly denser phase assemblage, with a low FeO content (roughly 5 mole%) is required to explain these results. This Fe content is not significantly different from that in the upper mantle. These results imply that no compositional or thermal constraints on whole-mantle convection can be resolved. The extrapolation of the outer core is well-determined, and the results are consistent with a mixture of Fe and a small proportion of a lighter element.     

Equation of state fits to the lower mantle and outer core

The lower mantle and outer core are subjected to tests for homogeneity and adiabaticity. An earth model is used which is based on the inversion of body waves and Q-corrected normal-mode data. Homogeneous regions are found at radii between 5125 and 4825 km, 4600 and 3850 km, and 3200 and 2200 km. The lower mantle and outer core are inhomogeneous on the whole and are only homogeneous in the above local regions.Finite-strain and atomistic equations of state are fit to the homogeneous regions. The apparent convergence of the finite-strain relations is examined to judge their applicability to a given region. In some cases the observed pressure derivatives of the elastic moduli are used as additional constraints. The effect of minor deviations from adiabaticity on the extrapolations is also considered. An ensemble of zero-pressure values of the density and seismic velocities are found for these regions. The range of extrapolated values from these several approaches provides a measure of uncertainties involved.     

Thermal regime of the Earth's outer core

Summary First an introduction into the dynamo problem and the core paradox is given. A novel theory of the volume dependence of Grüneisen's parameter is used for calculating the adiabatic temperatures on the assumption that the melting temperature of the material is reached at the boundary between the inner and outer cores of the Earth (IOB). On this condition, thermal convectionthroughout the outer core is impossible according to the melting-point curves ofKennedy andHiggins (1973) andLiu (1975), whereas it is permitted by that ofLeppaluoto (1972),Boschi (1975), andStacey (1977). Various possibilities of solving the core paradox are described.Mitt. d. ZIPE Nr. 682.     

Global P-wave tomography: On the effect of various mantle and core phases

In this work, many global tomographic inversions and resolution tests are carried out to investigate the influence of various mantle and core phase data from the International Seismological Center (ISC) data set on the determination of 3D velocity structure of the Earth's interior. Our results show that, when only the direct P data are used, the resolution is good for most of the mantle except for the oceanic regions down to about 1000 km depth and for most of the D″ layer, and PP rays can provide a better constraint on the structure down to the middle mantle, in particular for the upper mantle under the oceans. PcP can enhance the ray sampling of the middle and lower mantle around the Pacific rim and Europe, while Pdiff can help improve the spatial resolution in the lowermost mantle. The outer core phases (PKP, PKiKP and PKKP) can improve the resolution in the lowermost mantle of the southern hemisphere and under oceanic regions. When finer blocks or grid nodes are adopted to determine a high-resolution model, pP data are very useful for improving the upper mantle structure. The resulting model inferred from all phases not only displays the general features contained in the previous global tomographic models, but also reveals some new features. For example, the image of the Hawaiian mantle plume is improved notably over the previous studies. It is imaged as a continuous low velocity anomaly beneath the Hawaiian hotspot from the core-mantle boundary (CMB) to the surface, implying that the Hawaiian mantle plume indeed originates from the CMB. Low-velocity anomalies along some mid-oceanic ridges extend down to about 600 km depth. Our results suggested that later seismic phases are of great importance in better understanding the structure and dynamics of the Earth's interior.     

Lead isotope systematics and the evolution of the core,mantle, crust and atmosphere

A new analysis of the isotope systematics of sulphide common leads can be made on the basis of examining the deriations of the data from a simple single-stage evolution. Δt, the age discrepancy between the single-stage lead model age and the geologic age, increases systematically from 3.8 Ga to the present. This trend appears to reflect an increase in the μ of the primitive mantle due to incorporation of a large portion of the earth's lead into the core, early in the earth's evolution. Leads associated with shale-hosted lead-zinc deposits show a rapid increase in Δt beginning at 2.5 to 2.0 Ga. This deviation of shale-hosted leads from the general trend is interpreted as a response to concentration of uranium in organic-rich shales subsequent to the evolution of an oxidizing atmosphere. Comparison of common leads in alkali feldspars with the volcanogenic sulphide data suggests that they have a similar evolution of Δt with time. Numerical simulations reveal that even substantial increases in real μ over the last 2.0 Ga are not reflected in significant increases in the single-stage model μs.     

Thermal field and electric conductors in the crust and upper mantle of Ukraine

The paper presents data on the distribution of the deep heat flow in Ukraine, thermal models of the tectonosphere, and electric conductors in the crust and mantle that are mostly related to partial melting and dehydration of rocks.     

The electric field produced in the mantle by the dynamo in the core

A rigorous singular perturbation theory is developed to estimate the electric field E produced in the mantle M by the core dynamo when the electrical conductivity σ in M depends only on radius r, and when |r?_rln σ| ? 1 in most of M. It is assumed that σ has only one local minimum in M, either (a) at the Earth's surface ?V, or (b) at a radius b inside the mantle, or (c) at the core-mantle boundary ?K. In all three cases, the region where σ is no more than e times its minimum value constitutes a thin critical layer; in case (a), the radial electric field E_r ≈ 0 there, while in cases (b) and (c), E_r is very large there. Outside the critical layer, E_r ≈ 0 in all three cases. In no case is the tangential electric field E_S small, nearly toroidal, or nearly calculable from the magnetic vector potential A as ??_tA_S. The defects in Muth's (1979) argument which led him to contrary conclusions are identified. Benton (1979) cited Muth's work to argue that the core-fluid velocity u just below ?K can be estimated from measurements on ?V of the magnetic field B and its time derivative $\text{?}{}_{\mathrm{t}}\text{B}$. A simple model for westward drift is discussed which shows that Benton's conclusion is also wrong.In case (a), it is shown that knowledge of σ in M is unnecessary for estimating E_S on ?K with a relative error |r?_r 1nσ|^?1from measurements of E_S on ?V and knowledge of ?_tB in M (calculable from ?_tB on ?V if σ is small). Then, in case (a), u just below ?K can be estimated as $\text{?}\text{r}\text{×}\text{E}{}_{\mathrm{S}}\text{/B}{}_{\mathrm{r}}$. The method is impractical unless the contribution to E_S on ?V from ocean currents can be removed.The perturbation theory appropriate when σ in M is small is considered briefly; smallness of σ and of |r?_r ln σ|^?1 a independent questions. It is found that as σ → 0, B approaches the vacuum field in M but E does not; the explanation lies in the hydromagnetic approximation, which is certainly valid in M but fails as σ → 0. It is also found that the singular perturbation theory for |r?_r ln σ|^?1 is a useful tool in the perturbation calculations for σ when both σ and |r?_r ln σ|^?1 are small.     

On the effect of oceanic tides on the inertial coupling between the liquid core and the mantle

The amplitudes and phases of forced nutation and diurnal earth tides depend significantly on the moment of forces between the liquid core and mantle of the Earth, resulting from the differential rotation of the core. The solution to the dynamic problem of rotation of an imperfectly elastic mantle with an imperfectly liquid core and an ocean indicates that the predominant role is played by the so-called core-mantle inertial coupling (related to the effect of hydrodynamic pressure in the liquid core on the ellipsoidal core-mantle boundary). The magnitude of this coupling depends significantly not only on the dynamic flattening of the liquid core but also on the elastic and inelastic properties of the mantle, as well as on the amplitudes and phases of oceanic tides. In this paper, the effects of oceanic tides on the magnitude of inertial coupling between the liquid core and the mantle and on the period and damping decrement of free nearly diurnal nutation are estimated.     

On the diffusion of the perturbing toroidal magnetic field from the core to the mantle

Zusammenfassung Es werden die Wurzeln einer charakteristischen Gleichung für die Randbedingung der Diffusion des toroidalen magnetischen Störungsfeldes berechnet, das in dünner Schicht unterhalb der Grenze Kern — Mantel, als eine Folge von Störung der Winkelgeschwindigkeit dieser Schicht in Anwesenheit des magnetischen Dipolfeldes induziert wird. Die Wurzeln werden für verschiedene Werte des Verhältnisses der Leitfähigkeit des Erdmantels und Erdkerns ausgerechnet. Es wird gezeigt, dass das aus dem Milieu mit der elektrischen Leitfähigkeit in das Milieu mit elektrischer Leitfähigkeit _m diffundierende toroidale magnetische Störungsfeld vom Werte _m/<10^–2 an von dem Verhältnis elektrischer Leitfähigkeiten beider Milieus unabhänging bleibt.     

Thermal regime of the Earth's core

The outer core is assumed to consist of iron and sulfur, with a small amount of potassium that generates heat by radioactive decay of sim||pre|40 K. Two cases are considered, corresponding respectively to a high rate of heat production (Q = 2 · 10¹² cal./sec, about 0.1% K), and to a low rate (Q = 2 · 10¹¹ cal./sec). The temperature at a depth of 2800 km in the mantle is taken to be 3300°K (Wang, 1972). The temperature T_c at the core-mantle boundary depends on whether or not a density gradient in the lowermost layer D″ of the mantle prevents convection in that layer. In the first case, and for high Q, T_c = 4500–5000°K. In the second case, or for low Q, T_c ≈ 3500°K.The heat-conduction equation is used to calculate the temperature T_i at the inner-core boundary in the absence of convection. For high Q, T_i ? T_c ≈ 1600°K; for low Q, T_i ? T_c ≈ 160°K. Corresponding temperature gradients at r = r_c and r = r_i are listed in Table I.The adiabatic gradient at the top of the core is calculated by the method of Stewart (1970). It strongly depends on the parameters (ρ₀, c₀, γ₀, etc.) that characterize core material at low pressure. Stewart has drawn graphs that allow the selection of sets of parameters that are consistent with seismic velocities and a given density distribution in the core. Some acceptable sets of parameters are listed in Table II. Many sets yield temperatures T_c in the range 3500–5000°K; some give an adiabatic gradient steeper than the conductive gradient and are compatible with convection; others do not. Since properties of FeS melts remain unknown, there is at present no way of selecting any set in preference to another.Properties of the FeS system at low pressure suggest the possible appearance of immiscibility at high temperature in liquids of low sulfur content; accordingly, the inner-core boundary is thought to represent equilibrium between a solid (FeNi) inner core and a liquid layer containing only a small amount of sulfur; layer F in turn is in equilibrium with another liquid (forming layer E) containing more sulfur, and slightly less dense, than F. The temperature T_i at the inner-core boundary is about 6000–6500°K for high Q and T_c ≈ 4500–5000°K. It is consistent with Alder's (1966) and Leppaluoto's (1972) estimates of the melting point of iron at 3.3 Mbar, but not with that of Higgins and Kennedy (1971).     

Thermal structure and rheology of upper mantle beneath Zhejiang Province, China

The paleogeotherm derived from spinel and garnet lherzolites xenoliths for the upper mantle beneath Zhejiang Province, China is higher than the oceanic geotherm but is similar to the geotherm for the upper mantle beneath eastern China constructed by Xu et al. and the upper mantle geotherm of southeastern Australia. The crust-mantle boundary defined by this geotherm is about 34 km, while the lithosphere-asthenosphere boundary is about 75 km. This result coincides well with geophysical data. The study of rheological features of the xenoliths has revealed that at least two periods of deformation events occurred in the upper mantle beneath this region. The first event might be related to upper mantle diapir occurring in this region before or during late Tertiary, and the second might be related to the occurrence of small-scale shear zones in the upper mantle. Project supported by the National Natural Science Foundation of China (Grant No. 49472105).     

硅酸盐熔体和液态铁的两相模拟与核幔间的氧交换

地球早期经历了很多撞击事件, 其中与地月系统形成相关的大撞击甚至造成深达核幔边界的全球规模的岩浆洋, 在此过程中的核幔分异基本确定了地幔与地核的物质组成, 也决定了地球随后的演化路径.我们采用基于量子力学理论的第一性原理方法和机器学习技术, 实现了硅酸盐熔体和液态铁的超大体系两相分子动力学模拟, 获得了核幔边界条件下的两相平衡数据, 为超深岩浆洋中的核幔分异过程提供了重要约束.基于本研究模拟结果和现有的高温高压实验数据, 我们还建立了能够准确预测核幔间元素交换的平衡模型, 利用该模型深入探讨了核幔间的氧交换问题, 并分析了其与地球生长、大撞击和岩浆洋事件、地球早期磁场等争议问题之间的关系.

     

Observations of multiple core reflections of the PnKP and SnKP type and regional variations at the base of the mantle

Seismological results interpreted as evidence for large inhomogeneities near the base of the Earth's mantle below Hawaii have recently been published. It is possible to place constraints on the magnitude of such heterogeneities by identifying seismic phases multiply reflected within the Earth's core. The value of such a simple technique is illustrated by using array recordings of P and S5KP waves that have traversed the bottom of the mantle beneath Hawaii to show that there is no clear evidence for the unusual physical properties attributed to this region of the Earth. Identification of the phase S7KP is also reported.     

Excitation of hide waves in the core due to transient-spatially periodic stress in the lower mantle

Summary Forced hydromagnetic oscillations in the outer core due to stress at its top are studied by means of a simple linear theoretical model originally proposed byHide [1] for the free oscillation studies. Both the magnetic and the inertial modes are excited. The expressions for the velocity, magnetic and vorticity fields are presented for a variety of stresses. They depend upon the wave number and frequency. In a numerical example wherein the stress varies periodically both in the space and the time, the amplitude of the induced magnetic field is found to be significant for reasonable values of various parameters.     

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/cm3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.     

Core formation and chemical equilibrium in the Earth—II: Chemical consequences for the mantle and core

We present here a new model of core formation which is based on the current understanding of planetary accretion and discuss its implications for the chemistry of the Earth's mantle and core. Formation of the Earth by hierarchical accretion of progressively larger bodies on a time scale much longer than that of solid body differentiation in the nebula indicates that a significant fraction of metal in the core could be inherited from preterrestrially differentiated planetesimals. An analysis of the segregation of this iron to form the core suggests that most of the metal settles to the core without interaction with silicates; only a small fraction of the metal chemically equilibrates at high temperatures and pressures with the silicates. The siderophile element abundances in the mantle are considered to be a consequence of a two-step equilibration with iron, once preterrestrially in the planetesimals at low temperatures and pressures, and later in the Earth at high temperatures and pressures. The highly siderophile elements such as Re, Au and the platinum group elements in the mantle are essentially excluded from silicates from the preterrestrial equilibration. We attribute the abundances of these elements in the mantle to the later equilibration in the Earth at substantially reduced metal-silicate partition coefficients (D^met/sil), for which there is a considerable experimental evidence now. Mass balance considerations constrain the fraction of core metal involved in such an equilibration at approximately 0.3 – 0.5%. The model accounts for the levels and the near-chondritic ratios of the highly siderophile elements in the mantle. The mantle abundances of the less siderophile elements are largely determined by preterrestrial metal-silicate equilibrium and are not significantly affected by the second equilibration. The extreme depletion of sulfur and the lack of silicate melt-sulfide signature in the noble metal abundances in the mantle are natural consequences of this mode of core formation. Sulfur was added to the magma ocean during the high-T, high-P equilibration in the Earth, not extracted from it by sulfide segregation to the core. Except for Ni and Co, the overall siderophile abundances of the mantle can be well matched in this two-step equilibration model.

The mantle characteristics of Ni and Co are unique to the Earth and hence suggest a terrestrial process as the likely cause. One such process is the flotation and addition of olivine to the primitive upper mantle. In our model of core formation, neither the elemental and isotopic data of Re---Os, nor the low sulfur content of the mantle remains as an objection to the existence of a magma ocean and olivine flotation.

The small fraction of core metal that equilibrates with silicates at high T and P suggests that the light elements O, Si or H are unimportant in the core, leaving S (and possibly C) as prime candidates. Sulfur, as FeS associated with incoming iron metal, is directly sequestered to the core along with the bulk of the iron metal. It appears unlikely that other light elements can be added to the core after its formation. U and Th are excluded from the core but the model allows for entry of some K; however, the extent to which K serves as a heat source in the core remains uncertain.

The model is testable in two ways. One is by investigation of the metal-silicate partitioning at high temperatures and pressures under magma ocean conditions to determine if the (D^met/sil) values are lowered to the levels required in the model. The other is by experiments to determine if a solvus closure between metal and silicate liquids occurs at high temperatures relevant to a magma ocean.     

A conceptual model for kimberlite emplacement by solitary interfacial mega-waves on the core mantle boundary

If convection in the Earth's liquid outer core is disrupted, degrades to turbulence and begins to behave in a chaotic manner, it will destabilize the Earth's magnetic field and provide the seeds for kimberlite melts via turbulent jets of silicate rich core material which invade the lower mantle. These (proto-) melts may then be captured by extreme amplitude solitary nonlinear waves generated through interaction of the outer core surface with the base of the mantle. A pressure differential behind the wave front then provides a mechanism for the captured melt to ascend to the upper mantle and crust so quickly that emplacement may indirectly promote a type of impact fracture cone within the relatively brittle crust. These waves are very rare but of finite probability. The assumption of turbulence transmission between layers is justified using a simple three-layer liquid model. The core derived melts eventually become frozen in place as localised topographic highs in the Mohorovicic discontinuity (Moho), or as deep rooted intrusive events. The intrusion's final composition is a function of melt contamination by two separate sources: the core contaminated mantle base and subducted Archean crust. The mega-wave hypothesis offers a plausible vehicle for early stage emplacement of kimberlite pipes and explains the age association of diamondiferous kimberlites with magnetic reversals and tectonic plate rearrangements.