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Geomagnetic Variability and Predictability
The Earth's magnetic field varies on time scales from seconds to millions of years. These variations can be measured directly by ground observatories and satellites, and indirectly through laboratories. They are from different electromagnetic processes in magnetosphere and ionosphere (external), ocean and crust (surface), and deep in the Earth's fluid outer core (internal). Of the measured magnetic signals, 95% is from the core, and is called the core field, or internal field. Variation of the core field, often called the geomagnetic secular variation (SV), is the manifestation of the magnetohydrodynamic processes in the core. Therefore, SV provides rich information on the core dynamical state that is then critical for understanding the geophysical mechanisms of the SV, the core-mantle interactions, and contribution of mass transport inside the core on Earth's gravity variation. Traditionally, the core state is probed via two independent methodologies: core flow inversion from the observed SV, and pure numerical dynamo simulation. The former is driven by observations, but does not include necessary interactions among physical variables; the latter is dynamically consistent, but is not constrained by any observation. Therefore, both are very limited in providing appropriate estimates of the core state. To avoid these limitations, a new approach, geomagnetic data assimilation, appears recently. In this approach, simulation results (model forecasts) are constantly corrected with observations, the corrected solutions (analysis), are then used as the initial conditions to make more accurate forecasts of future. Recent studies have demonstrated successfully that assimilation solutions are different from those of free running models. These new solutions are better estimates of the core state, and have been used to provide accurate prediction of SV for the period from 2010 to 2015. This prediction is part of the IGRF field model for international community applications.
Re-Evaluation of HSE DATA in Light of High P-T Partitioning Data: Late Chondritic Addition to Inner Solar System Bodies Not Always Required for HSE
Studies of terrestrial peridotite and martian and achondritic meteorites have led to the conclusion that addition of chondritic material to growing planets or planetesimals, after core formation, occurred on Earth, Moon, Mars, asteroid 4 Vesta, and the parent body of the angritic meteorites. One study even proposed that this was a common process in the final stages of growth. These conclusions are based al-most entirely on the 8 highly siderophile elements (HSE; Re, Au, Pt, Pd, Rh, Ru, Ir, Os), which have been used to argue for late accretion of chondritic material to the Earth after core formation was complete. This idea was originally proposed because the D(metal/silicate) values for the HSE are very high (greater than 10,000), yet their concentration in the terrestrial mantle is too high to be consistent with such high Ds. The HSE in the terrestrial mantle also are present in chondritic relative abundances and hence require similar Ds if this was the result of core-mantle equilibration. The conclusion that late chondritic additions are required for all five of these bodies is based on the chondritic relative abundances of the HSE, as well as their elevated concentrations in the samples. An easy solution is to call upon addition of chondritic material to the mantle of each body, just after core formation; however, in practice this means similar additions of chondritic materials to each body just after core formation which ranges from approximately 4-5 Ma after T(sub 0) for 4 Vesta and the angrites, to 10-25 Ma for Mars, to 35 to 60 Ma for Moon and perhaps the Earth. Since the work of there has been a realization that high PT conditions can lower the partition coefficients of many siderophile elements, indicating that high PT conditions (magma ocean stage) can potentially explain elevated siderophile element abundances. However, detailed high PT partitioning data have been lacking for many of the HSE to evaluate whether such ideas are viable for all four bodies. Re-cent partitioning studies have covered P, T, fO2, and compositional ranges that allow values to be predicted at conditions relevant to these five inner solar system bodies. Because the D(HSE) metal/silicate are lowered substantially at higher PT conditions and natural com-positions (FeNi metallic liquids and peridotites) it is natural to re-examine the role of core formation on the HSE patterns in a variety of inner solar system bodies. Here I will discuss other processes (including high PT core formation for Mars, Moon and Earth) that can produce the observed HSE patterns, and demonstrate that there are viable hypotheses other than the "one size fits all" hypothesis of late chondritic additions.
High pressure melt line of nickel using a generalized embedded atomic method potential
As the second most abundant metal in the Earth's core, nickel plays an important role in determining the structure and temperature of the Earth's core. Yet, the melt line of Ni at pressures corresponding to the Earth's core has not been explored in the literature. Many previous experimental and simulation efforts have reported the melting point of Ni at pressures below 100 GPa, but there exist large discrepancies, most of which have persisted due to various experimental and simulation bottlenecks in handling extreme pressure and temperature conditions. We adopted the generalized embedded atom method, which overcomes the limitations of existing interatomic potentials, to probe phase stability and phase boundaries of Ni at pressures between 50 and 500 GPa. Further, the potential was validated by comparing the cold curves, phonon dispersion curves, and enthalpies of fusion with ab initio density functional theory calculations. Our analysis shows that face centered cubic (FCC) is stable, and the hexagonal close packed (HCP) and body centered cubic (BCC) phases are metastable close to the melt line. Melting temperatures at different pressures were obtained from two-phase co-existence simulations and take the following functional form: $T$ m = $1969.23+19.15P-0.012P$ 2 . In contrast to iron, differences between the melting points of the stable and metastable phases of Ni are less than 250 K at 300 GPa, and the difference in melting points of the metastable BCC and HCP phases changes sign at 500 GPa, which implies that the phase transition mechanisms during solidification can be very complex.
The chemical composition of the cores of the terrestrial planets and the moon
Using models of the quasi-chemical theory of solutions, the activity coefficients of silicon are calculated in the melts Fe-Si, Ni-Si, and Fe-Ni-Si. The calculated free energies of solution of liquid nickel and silicon in liquid iron in the interval 0 to 1400 kbar and 1500 to 4000 K, shows that Fe-Ni-Si alloy is stable under the conditions of the outer core of the earth and the cores of the terrestrial planets. The oxidation-reduction conditions are studied, and the fugacity of oxygen in the mantles of the planets and at the core-mantle boundary are calculated. The mechanism of reduction of silicon is analyzed over a broad interval of p and T. The interaction between the matter of the core and mantle is studied, resulting in the extraction of silicon from the mantle and its solution in the material of the core. It is concluded that silicon can enter into the composition of the outer core of the earth and Venus, but probably does not enter into the composition of the cores of Mercury, Mars, and the moon, if in fact the latter possesses one.
Core Formation in the Earth: Constraints from Ni and Co
Due to their metal-loving nature, Ni and Co were strongly partitioned into the metallic core and were left depleted in the silicate mantle during core formation in the Earth. Based on experimental liquid metal- liquid silicate partition coefficients (D), studies have suggested that core formation in an early magma Ocean can explain the observed mantle depletions of Ni and Co [l-51. However, the conditions proposed by the magma ocean models have ranged from pressures of 24 to 59 GPa and temperatures of 2200 to < 4000 K. Furthermore, the proposed magma Ocean oxygen fugacities have differed by nearly two orders of magnitude.Chabot and Agee noted that the different models predicted contradictory behaviors for D(Ni) and D(Co) as a function of temperature. With the hope of resolving the discrepancies between the magma ocean models, we conducted a systematic experimental study to constrain the effects of temperature on D(Ni) and D(Co).
Effect of Pressure on the Activity Coefficients of Au and Other Siderophile Elements in Liquid Fe-Si Alloys
Light elements can alloy into the iron cores of terrestrial planetary bodies. It is estimated that the Earth’s core contains ~10% of a light element, most likely a combination of S, C, Si, and O with Si probably being the most abundant. Si dissolved into Fe metal liquids can have a significant influence on the activity coefficients of siderophile elements, and thus the partitioning behavior of those elements between the core and mantle. Many of these elements have been investigated extensively at ambient pressure, and studies up to 1 GPa are becoming more common, but few have been studied at pressures above this. The formation of the Earth’s core has been estimated to have formed at pressures between 40-60 GPa, so investigating the effect pressure has on Si’s influence on siderophile element partitioning is important for modeling core formation in the Earth and smaller planets. Pressure is well known to influence volumetric properties of metallic and silicate liquids, and oxygen fugacity (e.g., [10,11]), but less is known about its effect on activity coefficients (e.g., [12]). Some activity coefficients depend strongly upon the Si content of Fe liquids, and the concentration of siderophile elements such as P, Sb, and As in the terrestrial mantle is easily influenced by dissolved Si in the core. Thus, isolating the effect of pressure on activity coefficients in general is critical in quantitative analysis of core formation models. In this work, we investigate the effect variable Si content has on the partitioning of Au between Fe metal and silicate melt at 10 GPa and 2373 K, with the intention of comparing the behavior to that already investigated at lower pressures. In addition, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb were also measured and could thus be included in the assessment of potential pressure effects.
Partitioning of Phosphorus and Molybdenum between the Earth's Mantle and Core and the Conditions of Core Formation
There are several hypotheses on the specific processes that might have occurred during the formation of the Earth. One hypothesis that has been proposed is that early in the Earth's formation, there was a magma ocean present, and within this body, siderophile elements separated out of the silicate liquid to form the metal core. This study addresses this hypothesis. P and Mo are moderately siderophile elements that are present in both the mantle and the core. The concentrations of P and Mo in silicate vs. metal can be measured and in turn used to determine the temperatures, pressures, oxygen fugacity and melt composition required to achieve the same concentrations as observed in the mantle. The data here include eight experiments examining the partitioning of P and Mo between metallic liquid and silicate liquid. The purpose of the experiments has been to gain a greater understanding of core-mantle separation during the Earth formation process and examines temperature effect on P and Mo, which has not been systematically studied before.
Iron Bonding with Light Elements: Implications for Planetary Cores Beyond the Binary System
Light element alloying in iron is required to explain density deficit and seismic wave velocities in Earth’s core. However, the light element composition of the Earth’s core seems hard to constrain as nearly all light element alloying would reduce the density and sound velocity (elastic moduli). The alloying light elements include oxidizing elements like oxygen and sulfur and reducing elements like hydrogen and carbon, yet their chemical effects in the alloy system are less discussed. Moreover, Fe-X-ray Absorption Near Edge Structure (Fe-XANES) fingerprints have been studied for silicate materials with ferrous and ferric ions, while not many X-ray absorption spectroscopy (XAS) studies have focused on iron alloys, especially at high pressures. To investigate the bonding nature of iron alloys in planetary interiors, we presented X-ray absorption spectroscopy of iron–nitrogen and iron–carbon alloys at high pressures up to 50 GPa. Together with existing literature on iron–carbon, –hydrogen alloys, we analyzed their edge positions and found no significant difference in the degree of oxidation among these alloys. Pressure effects on edge positions were also found negligible. Our theoretical simulation of the valence state of iron, alloyed with S, C, O, N, and P also showed nearly unchanged behavior under pressures up to 300 GPa. This finding indicates that the high pressure bonding of iron alloyed with light elements closely resembles bonding at the ambient conditions. We suggest that the chemical properties of light elements constrain which ones can coexist within iron alloys.
Steady induction effects in geomagnetism. Part 1A: Steady motional induction of geomagnetic chaos
Geomagnetic effects of magnetic induction by hypothetically steady fluid motion and steady magnetic flux diffusion near the top of Earth's core are investigated using electromagnetic theory, simple magnetic earth models, and numerical experiments with geomagnetic field models. The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation indicated by broad-scale models of the observed geomagnetic field is examined and solved. In Part 1, the steady surficial core flow estimation problem is solved in the context of the source-free mantle/frozen-flux core model. In the first paper (IA), the theory underlying such estimates is reviewed and some consequences of various kinematic and dynamic flow hypotheses are derived. For a frozen-flux core, fluid downwelling is required to change the mean square normal magnetic flux density averaged over the core-mantle boundary. For surficially geostrophic flow, downwelling implies poleward flow. The solution of the forward steady motional induction problem at the surface of a frozen-flux core is derived and found to be a fine, easily visualized example of deterministic chaos. Geomagnetic effects of statistically steady core surface flow may well dominate secular variation over several decades. Indeed, effects of persistent, if not steady, surficially geostrophic core flow are described which may help explain certain features of the present broad-scale geomagnetic field and perhaps paleomagnetic secular variation.
Late Chondritic Additions and Planet and Planetesimal Growth: Evaluation of Physical and Chemical Mechanisms
Studies of terrestrial peridotite and martian and achondritic meteorites have led to the conclusion that addition of chondritic material to growing planets or planetesimals, after core formation, occurred on Earth, Mars, asteroid 4 Vesta, and the parent body of the angritic meteorites [1-4]. One study even proposed that this was a common process in the final stages of growth [5]. These conclusions are based almost entirely on the highly siderophile elements (HSE; Re, Au, Pt, Pd, Rh, Ru, Ir, Os). The HSE are a group of eight elements that have been used to argue for late accretion of chondritic material to the Earth after core formation was complete (e.g., [6]). This idea was originally proposed because the D(metal/silicate) values for the HSE are so high, yet their concentration in the mantle is too high to be consistent with such high Ds. The HSE also are present in chondritic relative abundances and hence require similar Ds if this is the result of core-mantle equilibration. Since the work of [6] there has been a realization that core formation at high PT conditions can explain the abundances of many siderophile elements in the mantle (e.g., [7]), but such detailed high PT partitioning data are lacking for many of the HSE to evaluate whether such ideas are viable for all four bodies. Consideration of other chemical parameters reveals larger problems that are difficult to overcome, but must be addressed in any scenario which calls on the addition of chondritic material to a reduced mantle. Yet these problems are rarely discussed or emphasized, making the late chondritic (or late veneer) addition hypothesis suspect.
Geochemical Constraints on Core Formation in the Earth
New experimental data on the partitioning of siderophile and chalcophile elements among metallic and silicate phases may be used to constrain hypotheses of core formation in the Earth. Three current hypotheses can explain gross features of mantle geochemistry, but none predicts siderophile and chalcophile element abundances to within a factor of two of observed values. Either our understanding of metal-silicate interactions and/or our understanding of the early Earth requires revision.
Modelling the core magnetic field of the earth
It is suggested that radial off-center dipoles located within the core of the earth be used instead of spherical harmonics of the magnetic potential in modeling the core magnetic field. The off-center dipoles, in addition to more realistically modeling the physical current systems within the core, are if located deep within the core more effective at removing long wavelength signals of either potential or field. Their disadvantage is that their positions and strengths are more difficult to compute, and such effects as upward and downward continuation are more difficult to manipulate. It is nevertheless agreed with Cox (1975) and Alldredge and Hurwitz (1964) that physical realism in models is more important than mathematical convenience. A radial dipole model is presented which agrees with observations of secular variation and excursions.
Terrestrial magma ocean and core segregation in the earth
According to the recent theories of formation of the earth, the outer layer of the proto-earth was molten and the terrestrial magma ocean was formed when its radius exceeded 3000 km. Core formation should have started in this magma ocean stage, since segregation of metallic iron occurs effectively by melting of the proto-earth. Therefore, interactions between magma, mantle minerals, and metallic iron in the magma ocean stage controlled the geochemistry of the mantle and core. We have studied the partitioning behaviors of elements into the silicate melt, high pressure minerals, and metallic iron under the deep upper mantle and lower mantle conditions. We employed the multi-anvil apparatus for preparing the equilibrating samples in the ranges from 16 to 27 GPa and 1700-2400 C. Both the electron probe microanalyzer (EPMA) and the Secondary Ion Mass spectrometer (SIMS) were used for analyzing the run products. We obtained the partition coefficients of various trace elements between majorite, Mg-perovskite, and liquid, and magnesiowustite, Mg-perovskite, and metallic iron. The examples of the partition coefficients of some key elements are summarized in figures, together with the previous data. We may be able to assess the origin of the mantle abundances of the elements such as transition metals by using the partitioning data obtained above. The mantle abundances of some transition metals expected by the core-mantle equilibrium under the lower mantle conditions cannot explain the observed abundance of some elements such as Mn and Ge in the mantle. Estimations of the densities of the ultrabasic magma Mg-perovskite at high pressure suggest existence of a density crossover in the deep lower mantle; flotation of Mg-perovskite occurs in the deep magma ocean under the lower mantle conditions. The observed depletion of some transition metals such as V, Cr, Mn, Fe, Co, and Ni in the mantle may be explained by the two stage process, the core-mantle equilibrium under the lower mantle conditions in the first stage, and subsequent downwards separation of the ultrabasic liquid (and magnesiowustite) and flotation of Mg-perovskite in the lower mantle.
Forced nutations of the earth: Influence of inner core dynamics. I - Theory. II - Numerical results and comparisons. III - Very long interferometry data analysis
A treatment is presented of the nutation problem for an oceanless, elastic, spheroidally stratified earth, with the dynamical role of the inner core explicitly included in the formulation. Solving the enlarged system of equations shows that a new almost diurnal eigenfrequency emerges. A rough estimate places it not far from the prograde annual tidal excitation frequency, so that possible resonance effects on nutation amplitudes need careful consideration. Tables are provided that exhibit the sensitivities of various relevant quantities, the eigenfrequencies and the coefficients which appear in the resonance expansion, as well as the nutation amplitudes at important tidal frequencies, to possible errors in the earth parameters which enter the theory set forth. Finally, the analysis of 798 VLBI experiments performed between July 1980 and February 1989 and the determination from this analysis of corrections to selected coefficients in the International Astronomical Union 1980 theory of the nutations of the earth are discussed.
Formation, history and energetics of cores in the terrestrial planets
The size, evolution and energetics of the earth's core and the probable central, metalic cores of Mercury, Venus, the moon and Mars are discussed. The cores of Mercury, Mars and the earth are considered likely to decrease in relative mass and volume with distance from the sun; the moon does not fit this sequence and data from Venus are insufficient. Core formation is concluded to have occurred early (prior to four billion years ago) on the earth and Mercury, while that on the moon would have occurred over a longer interval and the core of Mars would have formed much later. Of the possible energy sources in planetary cores able to maintain a molten state and drive magnetic dynamos, the energy of core formation was probably spent too early in planetary history to provide much present power, and the energy gained from freezing an inner core in the earth and Mercury are considered at best marginally able to match conductive heat loss. Future measurements proposed to improve the quantitative understanding of core properties include a better documentation of the magnetic fields of Venus and Mars and the seismometry of Mars.
The Topographic Torque on a Bounding Surface of a Rotating Gravitating Fluid and the Excitation by Core Motions of Decadal Fluctuations in the Earth's Rotation
General expressions (with potential applications in several areas of geophysical fluid dynamics) are derived for all three components of the contribution made by the geostrophic part of the pressure field associated with flow in a rotating gravitating fluid to the topographic torque exerted by the fluid on a rigid impermeable bounding surface of any shape. When applied to the Earth's liquid metallic core, which is bounded by nearly spherical surfaces and can be divided into two main regions, the "torosphere" and "polosphere," the expressions reduce to formulae given previously by the author, thereby providing further support for his work and that of others on the role of topographic coupling at the core-mantle boundary in the excitation by core motions of Earth rotation fluctuations on decadal time scales. They also show that recent criticisms of that work are vitiated by mathematical and physical errors. Contrary to these criticisms, the author's scheme for exploiting Earth rotation and other geophysical data (either real or simulated in computer models) in quantitative studies of the topography of the core-mantle boundary (CMB) by intercomparing various models of (a) motions in the core based on geomagnetic secular variation data and (b) CMB topography based on seismological and gravity data has a sound theoretical basis. The practical scope of the scheme is of course limited by the accuracy of real data, but this is a matter for investigation, not a priori assessment.
Prospect of Using Numerical Dynamo Model for Prediction of Geomagnetic Secular Variation
Modeling of the Earth's core has reached a level of maturity to where the incorporation of observations into the simulations through data assimilation has become feasible. Data assimilation is a method by which observations of a system are combined with a model output (or forecast) to obtain a best guess of the state of the system, called the analysis. The analysis is then used as an initial condition for the next forecast. By doing assimilation, not only we shall be able to predict partially secular variation of the core field, we could also use observations to further our understanding of dynamical states in the Earth's core. One of the first steps in the development of an assimilation system is a comparison between the observations and the model solution. The highly turbulent nature of core dynamics, along with the absence of any regular external forcing and constraint (which occurs in atmospheric dynamics, for example) means that short time comparisons (approx. 1000 years) cannot be made between model and observations. In order to make sensible comparisons, a direct insertion assimilation method has been implemented. In this approach, magnetic field observations at the Earth's surface have been substituted into the numerical model, such that the ratio of the multiple components and the dipole component from observation is adjusted at the core-mantle boundary and extended to the interior of the core, while the total magnetic energy remains unchanged. This adjusted magnetic field is then used as the initial field for a new simulation. In this way, a time tugged simulation is created which can then be compared directly with observations. We present numerical solutions with and without data insertion and discuss their implications for the development of a more rigorous assimilation system.