Constraints on the composition of the Earth's core from ab initio calculations

Knowledge of the composition of the Earth's core is important for understanding its melting point and therefore the temperature at the inner-core boundary and the temperature profile of the core and mantle. In addition, the partitioning of light elements between solid and liquid, as the outer core freezes at the inner-core boundary, is believed to drive compositional convection, which in turn generates the Earth's magnetic field. It is generally accepted that the liquid outer core and the solid inner core consist mainly of iron. The outer core, however, is also thought to contain a significant fraction of light elements, because its density--as deduced from seismological data and other measurements--is 6-10 per cent less than that estimated for pure liquid iron. Similar evidence indicates a smaller but still appreciable fraction of light elements in the inner core. The leading candidates for the light elements present in the core are sulphur, oxygen and silicon. Here we obtain a constraint on core composition derived from ab initio calculation of the chemical potentials of light elements dissolved in solid and liquid iron. We present results for the case of sulphur, which provide strong evidence against the proposal that the outer core is close to being a binary iron-sulphur mixture.     

Melting of the Earth's inner core

The Earth's magnetic field is generated by a dynamo in the liquid iron core, which convects in response to cooling of the overlying rocky mantle. The core freezes from the innermost surface outward, growing the solid inner core and releasing light elements that drive compositional convection. Mantle convection extracts heat from the core at a rate that has enormous lateral variations. Here we use geodynamo simulations to show that these variations are transferred to the inner-core boundary and can be large enough to cause heat to flow into the inner core. If this were to occur in the Earth, it would cause localized melting. Melting releases heavy liquid that could form the variable-composition layer suggested by an anomaly in seismic velocity in the 150 kilometres immediately above the inner-core boundary. This provides a very simple explanation of the existence of this layer, which otherwise requires additional assumptions such as locking of the inner core to the mantle, translation from its geopotential centre or convection with temperature equal to the solidus but with composition varying from the outer to the inner core. The predominantly narrow downwellings associated with freezing and broad upwellings associated with melting mean that the area of melting could be quite large despite the average dominance of freezing necessary to keep the dynamo going. Localized melting and freezing also provides a strong mechanism for creating seismic anomalies in the inner core itself, much stronger than the effects of variations in heat flow so far considered.     

Outer-core compositional stratification from observed core wave speed profiles

Light elements must be present in the nearly pure iron core of the Earth to match the remotely observed properties of the outer and inner cores. Crystallization of the inner core excludes light elements from the solid, concentrating them in liquid near the inner-core boundary that potentially rises and collects at the top of the core, and this may have a seismically observable signal. Here we present array-based observations of seismic waves sensitive to this part of the core whose wave speeds require there to be radial compositional variation in the topmost 300?km of the outer core. The velocity profile significantly departs from that of compression of a homogeneous liquid. Total light-element enrichment is up to five weight per cent at the top of the core if modelled in the Fe-O-S system. The stratification suggests the existence of a subadiabatic temperature gradient at the top of the outer core.     

Inner-core shear-wave anisotropy and texture from an observation of PKJKP waves

Since the discovery of the Earth's core a century ago, and the subsequent discovery of a solid inner core (postulated to have formed by the freezing of iron) seismologists have striven to understand this most remote part of the deep Earth. The most direct evidence for a solid inner core would be the observation of shear-mode body waves that traverse it, but these phases are extremely difficult to observe. Two reported observations in short-period data have proved controversial. Arguably more successful have been studies of longer-period data, but such averaging limits the usefulness of the observations to reported sightings. We present two observations of an inner-core shear-wave phase at higher frequencies in stacked data from the Japanese High-Sensitivity Array, Hi-Net. From an analysis of timing, amplitude and waveform of the 'PKJKP' phase we derive constraints on inner-core compressional-wave velocity and shear attenuation at about 0.3 Hz which differ from standard isotropic core models. We can explain waveform features and can partially reconcile the otherwise large differences between core wavespeed and attenuation models that our observations apparently suggest if we invoke shear-wave anisotropy in the inner core. A simple model of an inner core composed of hexagonal close-packed iron with its c axis aligned perpendicular to the rotation axis yields anisotropy that is compatible with both the shear-wave anisotropy that we observe and the well-established 3 per cent compressional-wave anisotropy.     

Thermal and electrical conductivity of iron at Earth's core conditions

The Earth acts as a gigantic heat engine driven by the decay of radiogenic isotopes and slow cooling, which gives rise to plate tectonics, volcanoes and mountain building. Another key product is the geomagnetic field, generated in the liquid iron core by a dynamo running on heat released by cooling and freezing (as the solid inner core grows), and on chemical convection (due to light elements expelled from the liquid on freezing). The power supplied to the geodynamo, measured by the heat flux across the core-mantle boundary (CMB), places constraints on Earth's evolution. Estimates of CMB heat flux depend on properties of iron mixtures under the extreme pressure and temperature conditions in the core, most critically on the thermal and electrical conductivities. These quantities remain poorly known because of inherent experimental and theoretical difficulties. Here we use density functional theory to compute these conductivities in liquid iron mixtures at core conditions from first principles--unlike previous estimates, which relied on extrapolations. The mixtures of iron, oxygen, sulphur and silicon are taken from earlier work and fit the seismologically determined core density and inner-core boundary density jump. We find both conductivities to be two to three times higher than estimates in current use. The changes are so large that core thermal histories and power requirements need to be reassessed. New estimates indicate that the adiabatic heat flux is 15 to 16 terawatts at the CMB, higher than present estimates of CMB heat flux based on mantle convection; the top of the core must be thermally stratified and any convection in the upper core must be driven by chemical convection against the adverse thermal buoyancy or lateral variations in CMB heat flow. Power for the geodynamo is greatly restricted, and future models of mantle evolution will need to incorporate a high CMB heat flux and explain the recent formation of the inner core.     

Evidence for an oxygen-depleted liquid outer core of the Earth

On the basis of geophysical observations, cosmochemical constraints, and high-pressure experimental data, the Earth's liquid outer core consists of mainly liquid iron alloyed with about ten per cent (by weight) of light elements. Although the concentrations of the light elements are small, they nevertheless affect the Earth's core: its rate of cooling, the growth of the inner core, the dynamics of core convection, and the evolution of the geodynamo. Several light elements-including sulphur, oxygen, silicon, carbon and hydrogen-have been suggested, but the precise identity of the light elements in the Earth's core is still unclear. Oxygen has been proposed as a major light element in the core on the basis of cosmochemical arguments and chemical reactions during accretion. Its presence in the core has direct implications for Earth accretion conditions of oxidation state, pressure and temperature. Here we report new shockwave data in the Fe-S-O system that are directly applicable to the outer core. The data include both density and sound velocity measurements, which we compare with the observed density and velocity profiles of the liquid outer core. The results show that we can rule out oxygen as a major light element in the liquid outer core because adding oxygen into liquid iron would not reproduce simultaneously the observed density and sound velocity profiles of the outer core. An oxygen-depleted core would imply a more reduced environment during early Earth accretion.     

Fine-scale heterogeneity in the Earth's inner core

The seismological properties of the Earth's inner core have become of particular interest as we understand more about its composition and thermal state. Observations of anisotropy and velocity heterogeneity in the inner core are beginning to reveal how it has grown and whether it convects. The attenuation of seismic waves in the inner core is strong, and studies of seismic body waves have found that this high attenuation is consistent with either scattering or intrinsic attenuation. The outermost portion of the inner core has been inferred to possess layering and to be less anisotropic than at greater depths. Here we present observations of seismic waves scattered in the inner core which follow the expected arrival time of the body-wave reflection from the inner-core boundary. The amplitude of these scattered waves can be explained by stiffness variations of 1.2% with a scale length of 2 kilometres across the outermost 300 km of the inner core. These variations might be caused by variations in composition, by pods of partial melt in a mostly solid matrix or by variations in the orientation or strength of seismic anisotropy.     

Slow differential rotation of the Earth's inner core indicated by temporal changes in scattering

The finding that the Earth's inner core might be rotating faster than the mantle has important implications for our understanding of core processes, including the generation of the Earth's magnetic field. But the reported signal is subtle--a change of about 0.01 s per year in the separation of two seismic waves with differing paths through the core. Subsequent studies of such data have generally supported the conclusion that differential rotation exists, but the difficulty of accurately locating historic earthquakes and possible biases induced by strong lateral variations in structure near the core-mantle boundary have raised doubt regarding the proposed inner-core motion. Also, a study of free oscillations constrained the motion to be relatively small compared to previous estimates and it has been proposed that the interaction of inner-core boundary topography and mantle heterogeneity might lock the inner core to the mantle. The recent detection of seismic waves scattered in the inner core suggests a simple test of inner-core motion. Here we compare scattered waves recorded in Montana, USA, from two closely located nuclear tests at Novaya Zemlya, USSR, in 1971 and 1974. The data show small but coherent changes in scattering which point toward an inner-core differential rotation rate of 0.15 degrees per year--consistent with constraints imposed by the free-oscillation data.     

Mars' core and magnetism.

The detection of strongly magnetized ancient crust on Mars is one of the most surprising outcomes of recent Mars exploration, and provides important insight about the history and nature of the martian core. The iron-rich core probably formed during the hot accretion of Mars approximately 4.5 billion years ago and subsequently cooled at a rate dictated by the overlying mantle. A core dynamo operated much like Earth's current dynamo, but was probably limited in duration to several hundred million years. The early demise of the dynamo could have arisen through a change in the cooling rate of the mantle, or even a switch in convective style that led to mantle heating. Presently, Mars probably has a liquid, conductive outer core and might have a solid inner core like Earth.     

Hemispherical variations in seismic velocity at the top of the Earth's inner core

Knowledge of the seismic velocity structure at the top of the Earth's inner core is important for deciphering the physical processes responsible for inner-core growth. Previous global seismic studies have focused on structures found 100 km or deeper within the inner core, with results for the uppermost 100 km available for only isolated regions. Here we present constraints on seismic velocity variations just beneath the inner-core boundary, determined from the difference in travel time between waves reflected at the inner-core boundary and those transmitted through the inner core. We found that these travel-time residuals-observed on both global seismograph stations and several regional seismic networks-are systematically larger, by about 0.8 s, for waves that sample the 'eastern hemisphere' of the inner core (40 degrees E to 180 degrees E) compared to those that sample the 'western hemisphere' (180 degrees W to 40 degrees E). These residuals show no correlation with the angle at which the waves traverse the inner core; this indicates that seismic anisotropy is not strong in this region and that the isotropic seismic velocity of the eastern hemisphere is about 0.8% higher than that of the western hemisphere.     

A doubling of the post-perovskite phase boundary and structure of the Earth's lowermost mantle

The thermal structure of the Earth's lowermost mantle--the D' layer spanning depths of approximately 2,600-2,900 kilometres--is key to understanding the dynamical state and history of our planet. Earth's temperature profile (the geotherm) is mostly constrained by phase transitions, such as freezing at the inner-core boundary or changes in crystal structure within the solid mantle, that are detected as discontinuities in seismic wave speed and for which the pressure and temperature conditions can be constrained by experiment and theory. A recently discovered phase transition at pressures of the D' layer is ideally situated to reveal the thermal structure of the lowermost mantle, where no phase transitions were previously known to exist. Here we show that a pair of seismic discontinuities observed in some regions of D' can be explained by the same phase transition as the result of a double-crossing of the phase boundary by the geotherm at two different depths. This simple model can also explain why a seismic discontinuity is not observed in some other regions, and provides new constraints for the magnitude of temperature variations within D'.     

Accretion of the Earth and segregation of its core

The Earth took 30-40 million years to accrete from smaller 'planetesimals'. Many of these planetesimals had metallic iron cores and during growth of the Earth this metal re-equilibrated with the Earth's silicate mantle, extracting siderophile ('iron-loving') elements into the Earth's iron-rich core. The current composition of the mantle indicates that much of the re-equilibration took place in a deep (> 400 km) molten silicate layer, or 'magma ocean', and that conditions became more oxidizing with time as the Earth grew. The high-pressure nature of the core-forming process led to the Earth's core being richer in low-atomic-number elements, notably silicon and possibly oxygen, than the cores of the smaller planetesimal building blocks.     

Elasticity of iron at the temperature of the Earth's inner core.

Seismological body-wave and free-oscillation studies of the Earth's solid inner core have revealed that compressional waves traverse the inner core faster along near-polar paths than in the equatorial plane. Studies have also documented local deviations from this first-order pattern of anisotropy on length scales ranging from 1 to 1,000 km (refs 3, 4). These observations, together with reports of the differential rotation of the inner core, have generated considerable interest in the physical state and dynamics of the inner core, and in the structure and elasticity of its main constituent, iron, at appropriate conditions of pressure and temperature. Here we report first-principles calculations of the structure and elasticity of dense hexagonal close-packed (h.c.p.) iron at high temperatures. We find that the axial ratio c/a of h.c.p. iron increases substantially with increasing temperature, reaching a value of nearly 1.7 at a temperature of 5,700 K, where aggregate bulk and shear moduli match those of the inner core. As a consequence of the increasing c/a ratio, we have found that the single-crystal longitudinal anisotropy of h.c.p. iron at high temperature has the opposite sense from that at low temperature. By combining our results with a simple model of polycrystalline texture in the inner core, in which basal planes are partially aligned with the rotation axis, we can account for seismological observations of inner-core anisotropy.     

The plastic deformation of iron at pressures of the Earth's inner core

Soon after the discovery of seismic anisotropy in the Earth's inner core, it was suggested that crystal alignment attained during deformation might be responsible. Since then, several other mechanisms have been proposed to account for the observed anisotropy, but the lack of deformation experiments performed at the extreme pressure conditions corresponding to the solid inner core has limited our ability to determine which deformation mechanism applies to this region of the Earth. Here we determine directly the elastic and plastic deformation mechanism of iron at pressures of the Earth's core, from synchrotron X-ray diffraction measurements of iron, under imposed axial stress, in diamond-anvil cells. The epsilon-iron (hexagonally close packed) crystals display strong preferred orientation, with c-axes parallel to the axis of the diamond-anvil cell. Polycrystal plasticity theory predicts an alignment of c-axes parallel to the compression direction as a result of basal slip, if basal slip is either the primary or a secondary slip system. The experiments provide direct observations of deformation mechanisms that occur in the Earth's inner core, and introduce a method for investigating, within the laboratory, the rheology of materials at extreme pressures.     

The influence of a chemical boundary layer on the fixity,spacing and lifetime of mantle plumes

Seismological observations provide evidence that the lowermost mantle contains superposed thermal and compositional boundary layers that are laterally heterogeneous. Whereas the thermal boundary layer forms as a consequence of the heat flux from the Earth's outer core, the origin of an (intrinsically dense) chemical boundary layer remains uncertain. Observed zones of 'ultra-low' seismic velocity suggest that this dense layer may contain metals or partial melt, and thus it is reasonable to expect the dense layer to have a relatively low viscosity. Also, it is thought that instabilities in the thermal boundary layer could lead to the intermittent formation and rise of mantle plumes. Flow into ascending plumes can deform the dense layer, leading, in turn, to its gradual entrainment. Here we use analogue experiments to show that the presence of a dense layer at the bottom of the mantle induces lateral variations in temperature and viscosity that, in turn, determine the location and dynamics of mantle plumes. A dense layer causes mantle plumes to become spatially fixed, and the entrainment of low-viscosity fluid enables plumes to persist within the Earth for hundreds of millions of years.     

Tidal dissipation and the strength of the Earth's internal magnetic field

Magnetic fields at the Earth's surface represent only a fraction of the field inside the core. The strength and structure of the internal field are poorly known, yet the details are important for our understanding of the geodynamo. Here I obtain an indirect estimate for the field strength from measurements of tidal dissipation. Tidally driven flow in the Earth's liquid core develops internal shear layers, which distort the internal magnetic field and generate electric currents. Ohmic losses damp the tidal motions and produce detectable signatures in the Earth's nutations. Previously reported evidence of anomalous dissipation in nutations can be explained with a core-averaged field of 2.5?mT, eliminating the need for high fluid viscosity or a stronger magnetic field at the inner-core boundary. Estimates for the internal field constrain the power required for the geodynamo.     

Power requirement of the geodynamo from ohmic losses in numerical and laboratory dynamos

In the Earth's fluid outer core, a dynamo process converts thermal and gravitational energy into magnetic energy. The power needed to sustain the geomagnetic field is set by the ohmic losses (dissipation due to electrical resistance). Recent estimates of ohmic losses cover a wide range, from 0.1 to 3.5 TW, or roughly 0.3-10% of the Earth's surface heat flow. The energy requirement of the dynamo puts constraints on the thermal budget and evolution of the core through Earth's history. Here we use a set of numerical dynamo models to derive scaling relations between the core's characteristic dissipation time and the core's magnetic and hydrodynamic Reynolds numbers--dimensionless numbers that measure the ratio of advective transport to magnetic and viscous diffusion, respectively. The ohmic dissipation of the Karlsruhe dynamo experiment supports a simple dependence on the magnetic Reynolds number alone, indicating that flow turbulence in the experiment and in the Earth's core has little influence on its characteristic dissipation time. We use these results to predict moderate ohmic dissipation in the range of 0.2-0.5 TW, which removes the need for strong radioactive heating in the core and allows the age of the solid inner core to exceed 2.5 billion years.     

Thermochemical flows couple the Earth's inner core growth to mantle heterogeneity

Seismic waves sampling the top 100 km of the Earth's inner core reveal that the eastern hemisphere (40 degrees E-180 degrees E) is seismically faster, more isotropic and more attenuating than the western hemisphere. The origin of this hemispherical dichotomy is a challenging problem for our understanding of the Earth as a system of dynamically coupled layers. Previously, laboratory experiments have established that thermal control from the lower mantle can drastically affect fluid flow in the outer core, which in turn can induce textural heterogeneity on the inner core solidification front. The resulting texture should be consistent with other expected manifestations of thermal mantle control on the geodynamo, specifically magnetic flux concentrations in the time-average palaeomagnetic field over the past 5 Myr, and preferred eddy locations in flows imaged below the core-mantle boundary by the analysis of historical geomagnetic secular variation. Here we show that a single model of thermochemical convection and dynamo action can account for all these effects by producing a large-scale, long-term outer core flow that couples the heterogeneity of the inner core with that of the lower mantle. The main feature of this thermochemical 'wind' is a cyclonic circulation below Asia, which concentrates magnetic field on the core-mantle boundary at the observed location and locally agrees with core flow images. This wind also causes anomalously high rates of light element release in the eastern hemisphere of the inner core boundary, suggesting that lateral seismic anomalies at the top of the inner core result from mantle-induced variations in its freezing rate.     

A crystallizing dense magma ocean at the base of the Earth's mantle

The distribution of geochemical species in the Earth's interior is largely controlled by fractional melting and crystallization processes that are intimately linked to the thermal state and evolution of the mantle. The existence of patches of dense partial melt at the base of the Earth's mantle, together with estimates of melting temperatures for deep mantle phases and the amount of cooling of the underlying core required to maintain a geodynamo throughout much of the Earth's history, suggest that more extensive deep melting occurred in the past. Here we show that a stable layer of dense melt formed at the base of the mantle early in the Earth's history would have undergone slow fractional crystallization, and would be an ideal candidate for an unsampled geochemical reservoir hosting a variety of incompatible species (most notably the missing budget of heat-producing elements) for an initial basal magma ocean thickness of about 1,000 km. Differences in 142Nd/144Nd ratios between chondrites and terrestrial rocks can be explained by fractional crystallization with a decay timescale of the order of 1 Gyr. These combined constraints yield thermal evolution models in which radiogenic heat production and latent heat exchange prevent early cooling of the core and possibly delay the onset of the geodynamo to 3.4-4 Gyr ago.     

地球内核的动力学理论及章动效应

 地球固体内核与其其余部分之间的引力和压力的耦合作用将引起一内力矩,内核通过这一力矩影响岩石圈相对惯性空间的定向.讨论了一个弹性无海洋、球形分层的内核地球章动理论,将内核的作用明确地反映在公式中.并依据Mathews et al的内核地球动力学理论,讨论了归一化章动振幅的Mathews形式和Wahr形式的应用;通过PREM地球模型检测了内核对章动振幅的影响,由此发现本文的结果与Mathews et al的结果存在一定的差异,但都在亚毫角秒量级上影响主要的圆章动项.