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.     

Dissolution of the primordial rare gases into the molten Earth's material

We have shown in a previous paper that, if the primordial solar nebula existed when the Earth was formed, the Earth was once surrounded by a dense and massive primordial atmosphere, whose temperature and pressure were about 4000 K and 900 atm, respectively, at the bottom. We suppose that this hydrogen-rich atmosphere escaped from the Earth after the solar nebula itself disappeared, both phenomena probably being due to the effect of strong solar wind and radiation.Using the results of our previous and new calculations on the structure of the primordial atmosphere, we have investigated the amount of dissolution of the rare gases, which were contained in the primordial atmosphere, into the molten Earth's material.The amount of the dissolved rare gases is found to be strongly dependent on the grain opacity of the atmosphere, i.e., on the amount of fine grains. However, their isotopic ratios and relative abundance are independent of the opacity and approximately equal to those in the primordial solar nebula, that is, to the present solar values. Especially, the dissolved neon is expected to have remained in the present mantle. Therefore, if a considerable amount of neon with nearly the solar isotopic ratio is discovered in present mantle material, this offers direct evidence for the proposition that the proto-Earth was once surrounded by the primordial atmosphere.     

Electromagnetic evidence for lateral inhomogeneities within the Earth's upper mantle

The composition of the upper mantle is of great significance to our understanding of plate tectonics and global evolution. Information about the physical properties of the Earth at upper mantle depths, including lateral variations in electrical conductivity, can be deduced from measurements of the electric and magnetic fields at the Earth's surface. Electromagnetic methods appear to give poorer resolution than do some other methods, for example seismics, but as they are sensitive to quite different properties of a medium they provide a different and complementary class of information.The basic theory of electromagnetic sounding methods is briefly reviewed below, and evidence regarding lateral conductivity inhomogeneities in the Earth's upper mantle is examined. While lateral electrical conductivity inhomogeneities appear to be the rule rather than the exception, the interpretation of electromagnetic data still presents difficulties and the results from many regions are not as yet unambiguous. Where the data are of sufficient resolution, a rapid increase in electrical conductivity can usually be identified within the upper mantle. The depth to this highly conductive zone is different in different tectonic environments, but is broadly consistent between analogous but widely separated tectonic environments. A comparatively shallow conducting region is found beneath the ocean lithosphere. The depth of this region is dependent on lithospheric age. Many of the more shallow conducting regions in both continental and oceanic environments are associated with high heat flow values and seismic low velocity zones. These highly conducting regions may be zones of partial melt.     

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.     

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.     

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).     

Earth's magnetic field modelling and earth's structure and evolution

The advantages of the approximation of the Earth's magnetic field by means of the field of the so-called natural magnetic sources are discussed. The shifting of these natural magnetic sources, determined for different epochs, is used to forecast the Earth's magnetic field and to draw conclusions about the motion of the corresponding part of the Earth. On the basis of the representation of the Earth's magnetic field from several past geological epochs as a field of one optimum dipole a new theory about the Earth's evolution is proposed.     

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.     

Coupled Os–Os enrichments in the Earth’s mantle – core–mantle interaction or recycling of ferromanganese crusts and nodules?

¹⁸⁶Os enrichments in volcanic rocks and peridotite-derived iridosmine grains have been attributed to contributions from Earth’s outer core to the mantle, and apparently constrain the scale of mantle convection and an early timing for inner–outer core segregation more than 3.5 Gyr ago. Here, we highlight that marine ferromanganese crusts and nodules are characterised by high Pt/Os ratios and Pt–Os contents that develop much larger ¹⁸⁶Os excesses over geological time (≥0.2%/Gyr) than those hypothesised for Earth’s outer core (<0.005–0.01%/Gyr). ¹⁸⁷Os/¹⁸⁸Os ratios in ferromanganese crusts are radiogenic due to sequestering of continental Os from seawater. Similarly, ancient ferromanganese materials may have had ¹⁸⁶Os excesses (>0.1%) as a result of high Pt/Os ratios in continental crust, even prior to in-growth of ¹⁸⁶Os after formation due to their high Pt/Os ratios. Past recycling of small amounts of these materials into the Earth’s mantle will produce coupled ¹⁸⁷Os–¹⁸⁶Os excesses and little change in Re and platinum-group-element concentrations, as observed in Hawaiian picrites, and in contrast to the predicted result of outer core addition to the mantle. ¹⁸⁷Os and ¹⁸⁶Os enrichments in the Hawaiian mantle source are potentially consistent with it comprising recycled oceanic lithosphere, pelagic sediments and ferromanganese materials, and questions the notion that Os isotopes can be used to uniquely identify core–mantle interactions and the depth at which mantle sources for volcanism originate.     

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.     

Noble gases in the earth's mantle

The abundances and isotopic compositions of noble gases in two samples from ultramafic xenoliths in alkali basalt, a young kaersutitic amphibole separated from a peridotite xenolith from Dish Hill, California and an ancient whole-rock lherzolite xenolith from Baja California, are reported and compared with the results of analyses on other mantle samples. In addition to previously recognized excesses of ³He and ¹²⁹Xe, our results indicate that ambient gases in the mantle show a general enrichment of the lighter-mass nonradiogenic isotopes of Ar, Kr and Xe, and Ar with ⁴⁰Ar/³⁶Ar = 3 · 10².     

Applications of liquid state physics to the Earth's core

By use of the modern theory of liquids and some guidance from the hard-sphere model of liquid structure, the following new results have been derived for application to the Earth's outer core. (1) dK/$\text{d}\text{P ? 5 ? 5. 6P}$/K, where K is the incompressibility and P the pressure. This is valid for a high-pressure liquid near its melting point, provided that the pressure is derived primarily from a strongly repulsive pair potential φ. This result is consistent with seismic data, except possibly in the lowermost region of the outer core, and demonstrates the approximate universality of dK/dP proposed by Birch (1939) and Bullen (1949). (2) dlnT_M/dlnρ = (γC_V ? 1)/($\text{C}{}_{\mathrm{<mtext>V</mtext>}}\text{?}\text{3}\text{2}\text{),}\text{where}\text{T}{}_{\mathrm{<mtext>M</mtext>}}$ is the melting point, ρ the density, γ the atomic thermodynamic Grüneisen parameter and C_V the atomic contribution to the specific heat in units of Boltzmann's constant per atom. This reduces to Lindemann's law for C_V = 3 and provides further support for the approximate validity of this law. (3) It follows that the “core paradox” of Higgins and Kennedy can only occur if $\text{γ <}\text{2}\text{3}$. However, it is shown that $\text{γ <}\text{2}\text{3}\text{? ∫}{}^{\mathrm{\infty }}{}_0\text{(?g/?T)}{}_{\mathrm{\rho }}\text{r(}\text{d}\text{/}\text{d}\text{r)(r}{}^2\text{φ)}\text{d}\text{r > 0}$, which cannot be achieved for any strongly repulsive pair potential φ and the corresponding pair distribution function g. It is concluded that $\text{γ >}\text{2}\text{3}$ and that the core paradox is almost certainly impossible for any conceivable core composition. Approximate calculations suggest that γ ～ 1.3–1.5 in the core. Further work on the thermodynamics of the liquid core must await development of a physically realistic pair potential, since existing pair potentials may be unsatisfactory.     

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.     

The influence of extrinsic pressure changes on the Earth's dynamo

Reversals of the Earth's magnetic field have been claimed to correlate with ice ages, tectonic events and falls of tectites. A physical mechanism is needed to relate reversals with the other events before these correlations can be taken seriously. One possible connection lies through changes in pressure in the core. If events high up in the mantle were to lead to changes in core pressure, this would affect the rate of freezing of the liquid core and modify the power supplied to the dynamo. A sufficiently large modification could set off a reversal or perhaps change the mode of operation of the dynamo from a non-reversing to a reversing state.The model of Gubbins et al., allows a quantitative calculation to be made for the effect of a pressure change on the energy release. Any sufficiently sudden pressure change would change the power, but it seems unrealistic to consider less than a 1000 year time scale. Relaxation of shear forces in the mantle, overturning of core fluid, and changes in magnetic fields all take place on about this time scale. According to the model, a pressure change of 0.1 bar over a 1000 years could change the power supply drastically.A continuous process of mantle differentiation leading to the formation of the upper mantle from an initially homogeneous mantle can only provide 10% of the required pressure change, but the effect cannot be ruled out as a power source for the dynamo because uncertainties in the calculations can amount to at least an order of magnitude. The other effects produce changes of up to 1% in the power supply, which may be sufficient to alter the characteristics of the dynamo and produce reversals or a change in reversal behaviour. Further speculation must await a better understanding of the dynamics of reversals, and of mantle processes.     

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.     

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).     

A note on convection in the earth's mantle

In the present note a boundary-layer model of thermal convection throughout the mantle is outlined. It is shown that recent criticisms of mantle-wide convection by A.E. Ringwood do not apply to this model. The phase transitions discussed by Ringwood are consistent with the model, and in fact provide an additional driving force for the convective motion. It is further noted that the model offers explanations of the core-mantle coupling hypothesized by R. Hide from consideration of correlations between the earth's magnetic and gravity fields, and of the appearance in several parts of the world of pairs of trenches separated by distances of the order of 2000 km.     

Noble gas systematics of the Réunion mantle plume source and the origin of primordial noble gases in Earth’s mantle

New noble gas data of ultramafic xenoliths from Réunion Island, Indian Ocean, further constrain the characteristics of primordial and radiogenic noble gases in Earth’s mantle plume reservoirs. The mantle source excess of nucleogenic ²¹Ne is significantly higher than for the Hawaiian and Icelandic plume reservoirs, similar to excess of radiogenic ⁴He. ⁴⁰Ar/³⁶Ar of the Réunion mantle source can be constrained to range between 8000 and 12 000, significant ¹²⁹Xe and fission Xe excess are present. Regarding the relative contribution of primordial and radiogenic rare gas nuclides, the Réunion mantle source is intermediate between Loihi- and MORB-type reservoirs. This confirms the compositional diversity of plume sources recognized in other radioisotope systematics. Another major result of this study is the identification of the same basic primordial component previously found for the Hawaiian and Icelandic mantle plumes and the MORB reservoir. It is a hybrid of solar-type He and Ne, and ‘atmosphere-like’ or ‘planetary’ Ar, Kr, Xe (Science 288 (2000) 1036). ²⁰Ne/²²Ne ratios extend to maximum values close to 12.5 (Ne-B), which is the typical signature of solar neon implanted as solar corpuscular radiation. This suggests that Earth’s solar-type noble gas inventory was acquired by small (less than km-sized) precursor planetesimals that were irradiated by an active early sun in the accretion disk after nebular gas dissipation, or, alternatively, that planetesimals incorporated constituents irradiated in transparent regions of the solar nebula. Previously, such an early irradiation scenario was suggested for carbonaceous chondrites which follow common volatile depletion trends in the sequence CI–CM–CV–Earth. In turn, CV chondrites closely match Earth’s mantle composition in ²⁰Ne/²²Ne, ³⁶Ar/²²Ne and ³⁶Ar/³⁸Ar. This indicates that mantle Ar could well be a planetary component inherited from precursor planetesimals. However, a corresponding conclusion for mantle Kr and Xe is less convincing yet, but this may be just due to the lack of appropriate ‘meteoritic’ building blocks matching terrestrial composition. Alternatively, heavy noble gases in Earth’s mantle could be due to admixing of severely fractionated air, but this effect must have affected all mantle sources to a very similar extent, e.g. by global subduction before the last homogenization of the mantle reservoirs.