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.     

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.     

Structural superplastic creep and linear viscosity in the earth's mantle

The rheology of dry polycrystalline olivine is examined by adopting a hyperbolic sine flow law (which reduces to a power law below 3 kbars) for high stress behavior, and a model for diffusion accommodated, coherent, grain boundary sliding (structural superplastic creep) for low stress behavior. The model for superplastic creep gives a linear relation between stress and strain rate and is consistent with the behavior of polycrystalline olivine during ductile faulting experiments (Post, 1973). For any given stable grain size, linear superplastic creep is promoted by relatively low stress and temperature. For a 1 -cm grain size and a homologous temperature between 0.6 and 0.8, superplastic creep dominates below transition stresses between 402 and 25 bars, respectively. Transition stresses are higher for smaller grain size and lower temperature. If grain size is stress dependent, superplastic creep is non-linear and dominates above a stress of 300 bars. Below that stress, relatively lower temperatures promote superplastic creep. Grain size may be stabilized by either physical or kinetic inhibition of grain growth, thereby allowing linear superplastic creep in the mantle. Results suggest that superplastic creep can dominate in most of the upper mantle except possibly for the asthenosphere where homologous temperatures are maximal and hyperbolic sine law creep can dominate. Mantle diapirism is at least in part accomplished by superplastic flow above and along the margins of the rising diapir.     

Some geophysical constraints on the chemical composition of the earth's lower mantle

The physical properties(?, K, K′) of the adiabatically decompressed lower mantle are interpreted in terms of an (Mg,Fe)SiO₃ perovskite + magnesiowüstite mineralogy. The approach employed in this paper involves the removal of the relatively better characterised magnesiowüstite component from the two-phase mixture in order to highlight the physical properties required of the perovskite phase for consistency between the seismological data and any proposed compositional model. It is concluded that a wide tradeoff (emphasized by Davies [1]) between composition, temperature and the physical properties (especially thermal expansion) of the perovskite phase accommodates most recently proposed compositional models including Ringwood's [2] pyrolite and the more silicic models of Burdick and Anderson [3], Anderson [4], Sawamoto [5], Butler and Anderson [6], Liu [7,8] and Watt and Ahrens [9].     

The system enstatite-pyrope at high pressures and temperatures and the mineralogy of the earth's mantle

In a diamond-anvil pressure cell coupled with laser heating, the system enstatite (MgSiO₃)-pyrope (3 MgSiO₃ · Al₂O₃) has been studied in the pressure region between about 100 and 300 kbar at about 1000°C using glass starting materials. The high-pressure phase behavior of the intermediate compositions of the system contrasts greatly with that of the two end-members. Differences between MgSiO₃ and 95% MgSiO₃ · 5% Al₂O₃ are especially remarkable. The phase assemblages β-Mg₂SiO₄ + stishovite and γ-Mg₂SiO₄ (spinel) + stishovite displayed by MgSiO₃ were not observed in 95% MgSiO₃ · 5% Al₂O₃, and the garnet phase, which was observed in 95% MgSiO₃ · 5% Al₂O₃ at high pressure, was not detected in MgSiO₃. These results suggest that the high-pressure phase transformations found in pure MgSiO₃ would be inhibited under mantle conditions by the presence even of small amounts of Al₂O₃ (?4% by weight). On the other hand, pyrope displays a wide stability field, finally transforming at 240–250 kbar directly to an ilmenite-type modification of the same stoichiometry. The two-phase region, within which orthopyroxene and garnet solid solutions coexist, is very broad. The structure of the earth's mantle is discussed in terms of the phase transformations to be expected in a simple mixture of 90% MgSiO₃ · 10% Al₂O₃ and Mg₂SiO₄. The seismic discontinuity at a depth of 400 km in the earth's mantle is probably due entirely to the olivine → β-phase transition in Mg₂SiO₄, with the progressive solution of pyroxene in garnet (displayed in 90% MgSiO₃ · 10% Al₂O₃) occurring at shallower depths. The inferred discontinuity at 650 km is due to the combination of the phase changes spinel → perovskite + rocksalt in Mg₂SiO₄ and garnet → ilmenite in 90% MgSiO₃ · 10% Al₂O₃. The 650-km discontinuity is thus characterized by an increase in the primary coordination of silicon from 4 to 6. A further discontinuity in the density and seismic wave velocities at greater depth associated with the ilmenite-perovskite phase transformation in 90% MgSiO₃ · 10% Al₂O₃ is expected.     

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.     

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.     

Latent-heat driven convection in the earth's core: Numerical results

The paper presents a numerical model of a slowly cooling Earth's core. On the boundary conditions selected, cooling alone is too slow to effect convection. Convective motions arise only by the additional release of latent heat of crystallization owing to the growth of the inner core. A fundamental feature of the model is the choice of a subadiabatic initial temperature distribution.This is the reason why the outer core acts as a heat reservoir, that slows down the growing rate of the inner core on an acceptable size. For the whole time convection covers only the lower part of the outer core, the upper part remains stably stratified.     

P-wave velocities in the earth's core: An interim report

Recent observations of core phases made at conventional stations and seismograph arrays are summarized and evaluated to produce a series of conclusions concerning the P-wave velocity structure of the earth's core. Limits are suggested for allowable variations in P velocity in various parts of the core. The prime conclusion is that observations that previously demanded velocity discontinuities in the lower part of the outer core may now be explained adequately on a scattering hypothesis, and that in models where parametric simplicity is desired, the earth's core may be approximated by a two-layered model, with the P-wave velocity varying continuously in each layer.     

DC resistivity methods for determining resistivity in the earth's crust

The use of Schlumberger and dipole arrays for crustal-scale resistivity soundings is considered. Advantages and disadvantages of the two methods are described. The depth to which resistivity may be determined from field measurements is discussed as well as the determination from the sounding curves of various parameters associated with layered structure. The interpretation of experimental data using reference curves as well as two approaches used in computer assisted interpretation are discussed.     

Oceanic area's influence on the range of multi-annual variations of the earth's magnetic field in France

The pluri-annual variations of the earth's magnetic field in France increase their range of influence from East to West. This leads to presume a discontinuity of electric conductivities at the transition from the continental to the oceanic area.     

The mechanical and electrical properties of earth's asthenosphere

An adequate theory of continental drift can be based on heat transfer theory, but it does demand the acceptance of a large downward revision of traditional estimates of average upper mantle temperatures and a consistent understanding of lithosphere and asthenosphere in terms of a difference in rheological behaviour under prolonged non-hydrostatic stress. The recognition that an extremely viscous average state of the upper mantle is self regulating both requires and permits an explanation of magma generation at a strictly limited rate (when averaged for the whole planet over a few years) in terms of unsteady and local deformational heating.The activity of water as a reducer of silicate creep resistance is used to develop the hypothesis that water produced by an amphibole dehydration has been effectively trapped in the Earth and is the underlying cause of a low seismic Q ～ 50 and an electrical conductivity 10^?2 ?10^?1 ohm^?1 m^?1, at depths of ～ 100 km. At the predicted low horizontally-avera temperatures, the conductivity contrast of rock and aqueous solutions is very large, and mantle electrical conductivity studies now look best-suited to explore this trapping process, and the distinctly recognisable possibility that the uptake of ocean water in the subduction process exceeds the rate of loss that can be explained purely through magmatic activity.     

Early Archaean rocks and geochemical evolution of the earth's crust

Remnants of Early Archaean rocks (>FX3000 m.y. old) are reported from most continents. A critical review of the radiometric data shows that few of these are well authenticated and most are very limited in extent. The oldest are predominantly plutonic gneisses of tonalitic-to-granitic composition (e.g., the basement gneisses of West Greenland, Labrador, Rhodesia and South Africa). In all cases there are inclusions of meta-volcanic and sedimentary rocks with greenstone belt affinities which probably represent crust into which the igneous parents of the gneisses were intruded.The trace element chemistry of these very old rocks is reviewed in an attempt to establish the mechanism of formation of early crust and place constraints on the chemical evolution of the earth's mantle. “Mantle-type” Sr isotope compositions show that the sialic members of both early gneisses and greenstone belts were not derived from much older crustal differentiates, either at 3800 or at 2800 m.y. ago. However, trace element ratios such as K/Rb and Sr/Ba, and rare earth element abundances, are not consistent with direct derivation of the plutonic suite from the upper mantle and also rule out a common parentage for the tonalites and granites. An origin by partial melting of metamorphosed juvenile crust with a composition range equivalent to that represented by the greenstone belts is preferred. Tonalites resulted from high-pressure melting of mafic garnet-amphibolite and at least some of the granites from low-pressure melting of more felsic (possibly even sedimentary) material.The trace element chemistry of the greenstone belt volcanics is thought to characterize the composition of early mantle melts, although the best preserved and best documented cases are about 500–1000 m.y. younger than the oldest known gneisses. The dominant type is tholeiite with low incompatible element contents and light-depleted or essentially flat rare earth patterns, features even more marked in the ultramafic komatiites which represent large degrees of melting. More evolved calc-alkaline rocks with relative incompatible and light rare earth element enrichment are also important. With the exception of the ultramafic lavas, all these types can be matched by the chemistry of present-day oceanic volcanism.It is concluded that the range of trace element variations in the earth's mantle was comparable in early Archaean times to that at the present. This is supported by mass balance calculations for the lithophile elements which have been preferentially extracted into the crust. Thus the isotope and trace element evidence of the oldest rocks argues against primary differentiation of the crust either during accretion of the earth or during its first 500 m.y. as a solid body. Crust formation has probably occurred continuously, although worldwide evidence for magmatism at around 2800 m.y. ago probably marks a particularly active period.     

Pressure dependence of the thermal Grüneisen parameter,with application to the earth's lower mantle and outer core

By considering high-temperature (classical) thermal oscillations of atoms in certain simple crystal structures with purely central interatomic forces, the treatment of anharmonic oscillations is generalised to random three-dimensional motion, yielding the Vashchenko and Zubarev relationship for the Grüneisen ratio γ at any pressure. If one-dimensional atomic oscillations only are considered the equation reduces to the Dugdale-MacDonald expression. To account for non-central forces additional terms must be introduced, giving:

$\text{γ=}\text{1}\text{2}\text{d}\text{K}\text{d}\text{P}\text{?}\text{5}\text{6}\text{+}\text{2}\text{9}\text{P}\text{K}\text{?}\text{f}\text{18K}\text{+}\text{1}\text{6}\text{d}\text{f}\text{d}\text{P}\text{1?}\text{4}\text{3}\text{P}\text{K}\text{+}\text{f}\text{3K}$

where f = 0 for purely central forces. Calculations of f in terms of the Poisson ratio for different crystal structures have not been made, but for many materials the central-force approximation suffices. This is believed to be true both for the outer core $\text{(}\text{γ}\text{≈1.4)}$ and for the close-packed structures of the lower mantle $\text{(}\text{γ}\text{≈1.0)}$. For the upper mantle non-central atomic forces are important and we have no estimate of ($\text{γ}$ independently of laboratory values for plausible minerals which suggest γ ≈ 0.8.     

Noble gas abundance patterns in deep-sea basalts — Primordial gases from the mantle

Rapidly cooled portions of eleven samples of mid-ocean ridge tholeiitic basalt pillows have noble gas abundance patterns which resemble the solar rare gas pattern rather than the noble gas pattern of the terrestrial atmosphere. We conclude that these samples contain primordial noble gases. In contrast, holocrystalline samples and a sample from the interior of a basalt pillow have noble gas abundance patterns which resemble the sea water pattern. Whereas the quenched glossy margins of basalt pillows record a non-atmospheric gas reservoir, these slowly cooled samples apparently have undergone exchange of their noble gases with those dissolved in sea water.     

Gas-mineral equilibria and a possible geochemical model of the earth's interior

The study of the thermodynamic regime of metamorphism and magmatism has been based on mineralogical thermometry and barometry and calculations of the oxidation-reduction, hydration-dehydration and carbonatization-decarbonatization reactions. The origin of the fluids is considered in connection with the hydride-carbide-oxide structure of the earth's interior.     

Behaviour of the earth's magnetic field as recorded in the sediment of Loch Lomond

A palaeomagnetic record of geomagnetic secular variation during the last 7000 years has been obtained from the sediments of Loch Lomond, Scotland. The magnetic direction fluctuations repeat well between cores and show greater detail, especially over the last 5000 years, than other European records. A time scale has been derived from¹⁴C analyses on the Lomond sediment and comparison with other¹⁴C-dated sediments. Investigation of relative palaeointensity determination methods has shown that the widely used normalization parameter of partial ARM is insensitive to even small sediment grain size fluctuations.The new high-fidelity direction record and improved time scale show that geomagnetic field changes have not followed a simple oscillatory pattern during the last 7000 years. The record enhances the application of palaeomagnetism to dating recent sediments, as the main declination swings are now characterized by fine detail, and paired inclination data are also available. The problem of mismatching swings when correlating with other paired directional records is thus reduced.The palaeomagnetic record agrees well with some archaeomagnetic results. It confirms the period of anticlockwise motion of the geomagnetic field vector, between 1000 and 600 years B.P., which was first documented by English archaeomagnetic investigations. Clockwise motion is shown to predominate during the remainder of the last 5500 years. The VGP path does not correlate with that of Japanese archaeomagnetic results nor North American sediment data from 2000 to 0 years B.P. This suggests that the secular changes are dominated by local non-dipole sources rather than wobbling of the main geomagnetic dipole.     

Noble gas state of the ancient mantle as deduced from noble gases in coated diamonds

Cores and coats of five coated diamonds, one from Botswana and four from Zaire, were separately analyzed for their noble gases. Noble gases in the diamonds are essentially of a trapped origin, including radio- and nucleogenic components such as⁴He, ⁴⁰Ar, ²¹Ne_excess and excesses in Xe isotopes (129, 131–136). The fairly precise elemental and isotopic abundances allow us to infer the noble gas state in the ancient mantle. ²⁰Ne/²²Ne ratios are fairly constant (11.8 ± 0.4), and very close to that of SEP (solar energetic particle)-Ne, but distinctly different from the atmospheric ratio. ²¹Ne/²²Ne ratios range from 0.028 to 0.06, which is attributed to nucleogenic ²¹Ne from ¹⁸O(α, n)²¹Ne and ²⁴Mg(n, α)²¹Ne reactions. The difference in ²⁰Ne/²²Ne between atmosphere and mantle can be attributed to the hydrodynamic escape of hydrogen from the primitive atmosphere during the very early stage in the Earth's history. ³⁸Ar/³⁶Ar and Kr isotopic ratios are identical to the atmospheric values within 1%. After correction for ²³⁸U- or ²⁴⁴Pu-fission Xe, the ^131–136Xe abundance ratios are indistinguishable from atmospheric ratios. Lighter Xe isotopes (^124–128Xe) are also likely to be atmospheric, but a final conclusion must wait until better data are obtained.In a ¹³⁶Xe/¹³⁰Xe−¹²⁹Xe/¹³⁰Xe diagram, diamond data lie on the same line as defined for MORB. The observed identical correlation for both diamonds and MORB's appears to suggest that the progenitor of the excess^131–136Xe is ²⁴⁴Pu, but not²³⁸U, though the direct Xe isotopic measurements was not precies enough to decide unanimously the progenitor.     

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.