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.     

Upwelling flow in Earth's mantle and sea-floor spreading

Upwelling flows in the Earth's mantle are accompanied by mass, momentum and energy transports from deep to upper layers. Those flows beneath the mid-ocean ridges give rise to sea-floor spreading. Mantle plumes, on the other hand, cause hot spots to be formed on the Earth's surface. Using the basic equations of fluid dynamics, temperature and velocity distributions in two-dimensional upwelling and cylindrical plumes can be obtained by an integral-relation method. Then the mass, momentum and energy transported to the lithosphere by these upwelling flows can readily be calculated. Based on those results we can more thoroughly discuss problems of plate dynamics, such as the driving mechanism of plate motion, the causes of formation of rift valleys over mid-ocean ridges, and the effect of mantle plumes on sea-floor spreading.     

Stability of waste spoils in an area strip mine—geological and geotechnical considerations

Results of investigations into the stability of coal mine spoil consisting of thick clay, saturated sand, and shale overburden in an areal strip mine are presented. Atterberg limits, particle size distributions, and compaction tests were performed to provide index characteristics of the materials. Unconsolidated undrained and consolidated undrained triaxial compression test results on 10·2 cm diameter samples of compacted shale and shale-soil mixtures were used to investigate the short-term and the long-term conditions respectively of the spoil slope. There is evidence that the failure envelope of mine spoil made up of shale or shale-soil mixture is curved. However, stability analyses reveal that the use of strength parameters defined by a linear Mohr-Coulomb envelope yields results that are comparable with those obtained when the non-linear failure envelope is used, provided that such strength parameters are defined at the operating normal stress level on the failure surface. The study illustrates a very good case of spoil instability resulting from very thick overburden soils of low strength and high water content. Results show that the key to achieving stability in such areas lies in an almost total segregation of the soils from the rocks.     

The distribution of thermal diffusivity in the Earth's crust

Data in the literature and additional measurements on the thermal diffusivities of granites, granulites and ultrabasic rocks at temperatures up to 1000 K and pressures to 2 GPa, have been used to propose a new model for thermal diffusivity distribution in the crust and upper mantle.The laboratory measurements were made using a pulse method or the Angstroem method with cylindrical heat flow. After making particular assumptions about the pressure and temperature distribution within the top 60 km the pressure and temperature dependencies of diffusivity were transformed into a depth dependence.The model is characterised by a continuous decrease of diffusivity to a depth of ～30 km where there is a small but rapid increase to a nearly constant value of 7.3 × 10^?3 cm² s^?1.     

Experimental frost and salt weathering of chalk—I

To try to resolve the conflicts surrounding the influence of salts on frost weathering, chalk cubes were immersed, separately, in solutions of sodium chloride, sodium sulphate, and magnesium sulphate at concentrations of 5·5 per cent and 12·5 per cent, in a mixed solution of sodium chloride and sodium sulphate, and in distilled water. The cubes were subjected to six freeze-thaw cycles with temperatures ranging from either +15 to — 10°C or + 15 to — 30°C. The results confirm that frost weathering can be enhanced by the presence of certain salts, but the degree of enhancement depends both on the concentration and type of salt and on the intensity of the freeze-thaw regime. Some, but not all, of the results can be explained by the phase changes that occur during the freezing of the salt solutions.     

Dissipation of the rare gases contained in the primordial Earth's atmosphere

If the Earth was formed by accumulation of rocky bodies in the presence of the gases of the primordial solar nebula, the Earth at this formation stage was surrounded by a massive primordial atmosphere (of about 1 × 10²⁶ g) composed mainly of H₂ and He. We suppose that the H₂ and He escaped from the Earth, owing to the effects of strong solar wind and EUV radiation, in stages after the solar nebula itself dissipated into the outer space.The primordial atmosphere also contained the rare gases Ne, Ar, Kr and Xe whose amounts were much greater than those contained in the present Earth's atmosphere. Thus, we have studied in this paper the dissipation of these rare gases due to the drag effect of outflowing hydrogen molecules. By means of the two-component gas kinetic theory and under the assumption of spherically symmetric flow, we have found that the outflow velocity of each rare gas relative to that of hydrogen is expressed in terms of only two parameters — the rate of hydrogen mass flow across the spherical surface under consideration and the temperature at this surface. According to this result, the rare gases were dissipated below the levels of their contents in the present atmosphere, when the mass loss rate of hydrogen was much greater than 1 × 10¹⁷ g/yr throughout the stages where the atmospheric mass decreased from 1 × 10²⁶ g to 4 × 10¹⁹ g.     

How strong is the magnetic field in the Earth's liquid core?

A crucial step in the investigation of the energetics of motions in the Earth's core and the generation of the geomagnetic field by the hydromagnetic dynamo process is the estimation of the average strength $\text{B}$ of the magnetic field B = B_p + B_T in the core. Owing to the probability that the toroidal field B_T in the core, which has no radial component, is a good deal stronger than the poloidal field B_p, direct downward extrapolation of the surface field to the core-mantle interface gives no more than an extreme lower limit to $\text{B}$. This paper outlines the indirect methods by which $\text{B}$ can be estimated, arguing that $\text{B}$ is probably about 10^?2 T (100 Γ) but might be as low as 10^?3 T (10 Γ) or as high as 5 × 10^?2 T (500 Γ).     

Evidence for long-term asymmetries in the Earth's magnetic field and possible implications for dynamo theories

Paleomagnetic data indicate that there is a north-south asymmetry in the time-averaged magnetic field and that there are small but significant differences between the normal and reverse polarity states. The geographical variation is most likely due to spatial variation in the boundary conditions at the core-mantle interface. The difference in the magnetic fields of the reverse and normal polarity states can be modeled in terms of a “standing field”. The paleomagnetic data are insufficient to determine whether or not this “standing field” is of core origin. However, consideration of mechanisms, including thermoelectric currents, indicates that there probably are important differences in core processes between the two polarity states. At first glance this interpretation is difficult to reconcile with the fact that the magnetic induction equation is antisymmetric with respect to the magnetic field. A way around this problem is the possibility that only certain transitions are allowed between acceptable eigenstates in dynamo models of the Earth's magnetic field.     

On the activation volume for creep and its variation with depth in the Earth's lower mantle

This activation volume ΔV for creep may be derived from Keyes's elastic strain energy model or from Weertman's empirical relationship between viscosity and the melting temperature. These formulations are shown to be equivalent if the anharmonic Grüneisen parameters γ of all acoustic modes are equal and if the pressure dependence of the melting temperature follows Lindemann's law, both of which assumptions are valid for the close-packed mineral structure of the lower mantle. The pressure derivative of ΔV depends only on the bulk modulus and the acoustic γ, both of which are directly available from seismic models. Using the data of Brown and Shankland, we show that ΔV decreases by almost 50% between the top and the bottom of the lower mantle, which makes it easier to maintain a constant viscosity in this region. The isoviscous temperature profile can be adiabatic in the deep lower mantle only below 1700 km depth; it is super-adiabatic in the top 1000 km of the lower mantle.     

Heat transport by variable viscosity convection and implications for the Earth's thermal evolution

The case is presented that the efficiency of variable viscosity convection in the Earth's mantle to remove heat may depend only very weakly on the internal viscosity or temperature. An extensive numerical study of the heat transport by 2-D steady state convection with free boundaries and temperature dependent viscosity was carried out. The range of Rayleigh numbers (Ra) is 10⁴?10⁷ and the viscosity contrast goes up to 250000. Although an absolute or relative maximum of the Nusselt number (Nu) is obtained at long wavelength in a certain parameter range, at sufficiently high Rayleigh number optimal heat transport is achieved by an aspect ratio close to or below one. The results for convection in a square box are presented in several ways. With the viscosity ratio fixed and the Rayleigh number defined with the viscosity at the mean of top and bottom temperature the increase of Nu with Ra is characterized by a logarithmic gradient β = ?ln(Nu)/? ln(Ra) in the range of 0.23–0.36, similar to constant viscosity convection. More appropriate for a cooling planetary body is a parameterization where the Rayleigh number is defined with the viscosity at the actual average temperature and the surface viscosity is fixed rather than the viscosity ratio. Now the logarithmic gradient β falls below 0.10 when the viscosity ratio exceeds 250, and the velocity of the surface layer becomes almost independent of Ra. In an end-member model for the Earth's thermal evolution it is assumed that the Nusselt number becomes virtually constant at high Rayleigh number. In the context of whole mantle convection this would imply that the present thermal state is still affected by the initial temperature, that only 25–50% of the present-day heat loss is balanced by radiogenic heat production, and the plate velocities were about the same during most of the Earth's history.     

Site effects at Euroseistest—I. Determination of the valley structure and confrontation of observations with 1D analysis

This paper describes the process of construction of the 2D model of Volvi's geological structure and results of empirical and theoretical approaches to the evaluation of site response at Euroseistest. The construction of the 2D model is based on a re-interpretation of the available geophysical and geotechnical data in an effort to improve the definition of the subsoil structure at Euroseistest in terms of the most important parameters needed to model site response. The results of this re-interpretation are compared with a previous published 2D model of the same alluvial valley. Different analysis of the measurements and different criteria in the synthesis of data have led to a different model, even if both studies had access to the same field measurements. This underscores the fact that a model results of an interpretation and is not uniquely determined by the data, no matter how detailed they are. The well known subsoil structure opened the possibility to correlate the geometry and the dynamic properties of the 2D model with the results of site response determined from a detailed analysis of two events in frequency and time domains and 1D numerical modeling. The study of site response shows the important effect of the lateral variations on the ground motion and suggests that the contribution of locally generated surface waves to the resonant peak may be important. In the case of Volvi's graben, the limitations of the 1D approximation to simulate ground motion under complex soil conditions in both frequency and time domains are also shown. This paper lays the ground for a companion article dealing with 2D site effects in this basin.     

Hafnium/rare earth element fractionation in the sedimentary system and crustal recycling into the Earth's mantle

Among long-lived radioactive parent-daughter element pairs, the ratio Lu/Hf is strongly fractionated relative to constant Sm/Nd in the Earth's sedimentary system. This is caused by high resistance to chemical weathering of the mineral zircon (Zr,Hf)SiO₄. Zircon-bearing sandy sediments on and near continents have very low Lu/Hf, while deep-sea clays have up to three times the chondritic Lu/Hf ratio. Turbidity currents mechanically carry the low-Lu/Hf sandy material onto the ocean floor. The results are important for the crust-to-mantle recycling discussion, where most recycled materials would be subducted oceanic sediments. Such sediment should be capable of explaining the HfNd mantle isotopic variation by mixing with peridotite, but in fact any average pelagic sediment has Nd/Hf and Lu/Hf too high to allow mixing curves to pass through the Hf/Nd isotopic array. The array could only be reproduced by subduction of turbidite sandstone with pelagic sediment in the approximate ratio 1.2 to 1, and by maintaining a good mixture between the two components. At least today, turbidites are available for subduction only at locations quite different and distant from those where pelagic sediments may be recycled; furthermore, mantle isotopic variation shows that the mantle often cannot mix itself well enough to homogenize these widely-separated sedimentary components to the degree required. The Lu/Hf fractionations place a severe restriction on the ability of recycled sediments to explain mantle isotopic patterns.     

Arsenic — a Review. Part I: Occurrence,Toxicity, Speciation,Mobility

In natural waters arsenic concentrations up to a few milligrams per litre were measured. The natural content of arsenic found in soils varies between 0.01 mg/kg and a few hundred milligrams per kilogram. Anthropogenic sources of arsenic in the environment are the smelting of ores, the burning of coal, and the use of arsenic compounds in many products and production processes in the past. A lot of arsenic compounds are toxic and cause acute and chronic poisoning. In aqueous environment the inorganic arsenic species arsenite (As(III)) and arsenate (As(V)) are the most abundant species. The mobility of these species is influenced by the pH value, the redox potential, and the presence of adsorbents such as oxides and hydroxides of Fe(III), Al(III), Mn(III/IV), humic substances, and clay minerals.     

Physical parameters governing the formation of Pele's hair and tears

The physical parameters that affect the formation of Pele's hair and Pele's tears during lava fountaining are discussed. Experiments on ink jets produced from a nozzle under different Weber number (We) and Reynolds number (Re) show the following results: if (Re) is relatively large compared with (We), an ink droplet is produced. However, if (Re) is relatively small and (We) is large, the spurting ink becomes thread-like. I define the Pele number (Pe) as (We)/(Re), which is expressed as v/₀, where v is the spuring velocity from an erupting vent, and are viscosity and interfacial tension of the erupting magma, and and ₀ are density of air and magma. The experimental results from ink jets suggest that Pele's hair will be produced for larger (Pe), while Pele's tears are very likely produced for relatively small (Pe). I conclude that Pele's hair could be produced when the spurting velocity of erupting magmas is high, and Pele's tears when it is relatively low. As an additional point of interest, the similarity of SEM photographs of the characteristic shape of Pele's hair to those of the failed products of commercial glass fibre are shown.     

Poisson's ratio behaviour in various crystalline rocks: application to the study of the Earth's interior

The study of Poisson's ratio (σ) behaviour in various crystalline rocks under different temperatures and pressures shows this parameter to depend upon the rock composition rather than upon P-T conditions. The results of this study are presented in the form of a comparison of σ(z) distributions within the consolidated crust and continental upper mantle and the specific variations of σ in crust and mantle rocks underlying the Voronezh crystalline massif (VCM). These investigations, which are based upon seismic and seismological data as well as high pressure experiments, should clarify in particular the composition and petrology of the Earth's interior.     

Evaluating equilibrium and non‐equilibrium transport of ammonium in a loam soil column

Release of nitrogen compounds into groundwater, particularly those compounds from excessive agricultural fertilization, is a major concern in an aquifer recharge. Among the nitrogen compounds, ammonium ( ) is a common one. In order to assess the risk of agricultural fertilizer contamination to an aquifer through infiltration, adsorption onto a loamy agricultural soil profile (0–0.60 m depth) was studied using a soil column experiment and modelling simulation. The soil used in the experiment was drawn from an agricultural field in Xinzhen, Fangshan district, Beijing, China, and reconstituted in laboratory soil columns. Column experiments were conducted using bromide (conservative tracer) and ‐bearing aqueous solutions. The ammonium concentrations in the soil water samples were measured, and their values were plotted as the breakthrough curves. The chemical's soil–water distribution coefficients (K_d) were calculated using breakthrough curves. Then the retardation factor (R) in saturated soil was calculated. For the ‐bearing aqueous solutions, the strongest adsorption occurred at the soil depth of 0.30–0.45 m. The convection–dispersion equation model and chemical non‐equilibrium model in Hydrus‐1D were used to simulate transport in the loamy soil. The two‐site chemical non‐equilibrium model in Hydrus‐1D was best to simulate transport through the soil column. Parameter sensitivity study was conducted to investigate the influences of solute transport by K_d, the fraction of exchange sites assuming to be in equilibrium with the solution phase (f), the longitudinal dispersivity (λ), and the first‐order rate coefficients (ω). The sensitivity analysis results indicate K_d is the most critical parameter.     

An asymptotic solution of hydrodynamic equations at the mid-plane of a plume in the Earth's mantle

From the partial differential equations of hydrodynamics governing the movements in the Earth's mantle of a Newtonian fluid with a pressure- and temperature-dependent viscosity, considering the bilateral symmetry of velocity and temperature distributions at the mid-plane of the plume, an analytical solution of the governing equations near the mid-plane of the plume was found by the method of asymptotic analysis. The vertical distribution of the upward velocity, viscosity and temperature at the mid-plane, and the temperature excess at the centre of the plume above the ambient mantle temperature were then calculated for two sets of Newtonian rheological parameters. The results obtained show that the temperature at the mid-plane and the temperature excess are nearly independent of the rheological parameters. The upward velocity at the mid-plane, however, is strongly dependent on the rheological parameters.