Models of the earth's magnetic field
Earth geomagnetic core field model construction from land and ocean magnetometer data
MAGNETOMETER↗
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A model for core formation in the early Earth
Two basic types exogenous models were proposed to account for siderophile and chalcophile element abundances in the Earth's upper mantle. The first model requires that the Earth be depleted in volatiles and that, after a core formation event which extracted the most siderophile elements into the core, additional noble siderophile elements (Pt, Ir, Au) were added as a late veneer and mixed into the mantle. The second model postulates a reduced Earth with approximately CI elemental abundances in which a primary core forming event depleted all siderophile elements in the mantle. The plausibility of models which require fine scale mixing of chondritic material into the upper mantle is analyzed. Mixing in liquids is more efficient, but large degrees of silicate partial melting will facilitate the separation of magma from residual solids. Any external events affecting the upper mantle of the Earth should also be evident in the Moon; but siderophile and chalcophile element abundance patterns inferred for the mantles of the Earth and Moon differ. There appear to be significant physical difficulties associated with chondritic veneer models.
Jones, J. H.↗
Core-Mantle Fractionation of Carbon in Earth and Mars: the Effects of Sulfur
Constraining carbon (C) fractionation between silicate magma ocean (MO) and core-forming alloy liquid during early differentiation is essential to understand the origin and early distribution of C between reservoirs such as the crust-atmosphere, mantle, and core of Earth and other terrestrial planets. Yet experimental data at high pressure (P)-temperature (T) on the effect of other light elements such as sulfur (S) in alloy liquid on alloy-silicate partitioning of C and C solubility in Fe-alloy compositions relevant for core formation is lacking. Here we have performed multi-anvil experiments at 6–13 GPa and 1800–2000 °C to examine the effects of S and Ni on the solubility limit of C in Fe-rich alloy liquid as well as partitioning behavior of C between alloy liquid and silicate melt (𝐷𝐷(sub C)(sup alloy/silicate)). The results show that C solubility in the alloy liquid as well as 𝐷𝐷(sub C)(sup alloy/silicate) decreases with increasing in S content in the alloy liquid. Empirical regression on C solubility in alloy liquid using our new experimental data and previous experiments demonstrates that C solubility significantly increases with increasing temperature, whereas unlike in S-poor or S-free alloy compositions, there is no discernible effect of Ni on C solubility in S-rich alloy liquid. Our modelling results confirm previous findings that in order to satisfy the C budget of BSE, the bulk Earth C undergoing alloy-silicate fractionation needs to be as high as those of CI-type carbonaceous chondrite, i.e., not leaving any room for volatility-induced loss of carbon during accretion. For Mars, on the other hand, an average single-stage core formation at relatively oxidized conditions (1.0 log unit below IW buffer) with 10-16 wt.% S in the core could yield a Martian mantle with a C budget similar to that of Earth’s BSE for a bulk C content of ~0.25-0.9 wt.%. For the scenario where C was delivered to the proto-Earth by a S-rich differentiated impactor at a later stage, our model calculations predict that bulk C content in the impactor can be as low as ~0.5 wt.% for an impactor mass that lies between 9-20% of present day Earth’s mass. This value is much higher than 0.05-0.1 wt.% bulk C in the impactor predicted by Li et al. (2016) because C-solubility limit of 0.3 wt.% in a S-rich alloy predicted by their models is significantly lower than the experimentally derived C-solubility of ~1.6 wt. % for the relevant S-content in the core of the impactor.
Carbon↗
An excitation mechanism for the free 'core nutation'
The earth is believed to possess a free nutational mode due to its rotating, elliptical, fluid core, with an eigenfrequency of approximately (1 + 1/460) cycle per sidereal day as seen from the sidereally rotating earth. This free 'core nutation' has not yet been undisputably observed. Furthermore, there has been considerable doubt that any known mechanism could excite this mode to an observable level. It is shown here that diurnal atmospheric and oceanic loading of the earth's surface provides an efficient excitation mechanism which depends critically on the physical damping of the mode. Possible effects of the mode on geodetic measurements are discussed. The effects of 'wobble' and 'nutation' on astrometric observations are also considered.
Sasao, T.↗
Comments on the earth's figure.
Core convection consequences with regard to earth figure and continental drift, indicating no changes in magnitude of magnetization
Paddack, S. J.↗
Elementary Theoretical Forms for the Spatial Power Spectrum of Earth's Crustal Magnetic Field
The magnetic field produced by magnetization in Earth's crust and lithosphere can be distinguished from the field produced by electric currents in Earth's core because the spatial magnetic power spectrum of the crustal field differs from that of the core field. Theoretical forms for the spectrum of the crustal field are derived by treating each magnetic domain in the crust as the point source of a dipole field. The geologic null-hypothesis that such moments are uncorrelated is used to obtain the magnetic spectrum expected from a randomly magnetized, or unstructured, spherical crust of negligible thickness. This simplest spectral form is modified to allow for uniform crustal thickness, ellipsoidality, and the polarization of domains by an periodically reversing, geocentric axial dipole field from Earth's core. Such spectra are intended to describe the background crustal field. Magnetic anomalies due to correlated magnetization within coherent geologic structures may well be superimposed upon this background; yet representing each such anomaly with a single point dipole may lead to similar spectral forms. Results from attempts to fit these forms to observational spectra, determined via spherical harmonic analysis of MAGSAT data, are summarized in terms of amplitude, source depth, and misfit. Each theoretical spectrum reduces to a source factor multiplied by the usual exponential function of spherical harmonic degree n due to geometric attenuation with attitude above the source layer. The source factors always vary with n and are approximately proportional to n(exp 3) for degrees 12 through 120. The theoretical spectra are therefore not directly proportional to an exponential function of spherical harmonic degree n. There is no radius at which these spectra are flat, level, or otherwise independent of n.
Voorhies, C.↗
The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves
Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics of thermal Rossby waves in a cylindrical annulus with azimuthally modulated height.
Abarzhi, S. I.↗
Hydrogen storage in Earth's mantle and core
Two different approaches to explaining how hydrogen might be stored in the mantle are illustrated by a number of papers published over the past 25-30 years, but there has been little attempt to provide objective comparisons of the two. One approach invokes the presence in the mantle of dense hydrous magnesium silicates (DHMS) stable at elevated pressures and temperatures. The other involves nominally anhydrous minerals (NAM) that contain hydrogen as a minor constituent on the ppm level. Experimental studies on DHMS indicate these phases may be stable to pressures and temperatures as high at 16 GPa and 1200 C. This temperature is lower than that indicated by a mantle geotherm at 16 GPa, but may be reasonable for a subducting slab. It is possible that other DHMS could be stable to even higher pressures, but little is known about maximum temperature limits. For NAM, small amounts of hydrogen (up to several hundred ppm) have been detected in olivine, orthopyroxene, clinopyroxene, and garnet recovered from xenoliths in kimberlites, eclogites, and alkali basalts; it has been demonstrated that synthetic wadsleyite and perovskite can accommodate significant amounts of hydrogen. A number of problems are associated with each possibility. For NAM originating in the mantle, one would like to assume that the hydrogen measured in samples recovered on Earth's surface was incorporated when the phase-crystallized at high temperatures and pressures, but it could have been introduced during transport to the surface. Major problems for the DHMS proponents are that none of these phases have been found as minerals and little is yet known about their stabilities in systems containing other cations such as Fe, Al, and Ca.
Prewitt, Charles T.↗
Possible detection of the earth's free-core nutation
The 5.5 years of VLBI observations primarily collected under project IRIS are used to search for evidence of the free-core nutation (FCN). The observations are consistent with an irregular excitation process, and a model which assumes a step excitation in the FCN amplitude to about 2.0 milliseconds of arc in late 1985 fits the data well. Theoretical analysis appears to rule out the strong Mexican earthquake of September 19, 1985, as a cause of the excitation.
Robertson, D. S.↗
Partitioning of Pd Between Fe-S-C and Mantle Liquids at High Pressure and Temperature: Implications for Core Formation
One of the most elusive geochemical aspects of the early Earth has been explaining the near chondritic relative abundances of the highly siderophile elements (HSE; Au, Re and the platinum group elements) in Earth's primitive upper mantle (PUM). Perhaps they were delivered to the Earth after core formation, by late addition of carbonaceous chondrite material. However, the recognition that many moderately siderophile elements can be explained by high pressure and temperature (PT) metal-silicate equilibrium, leads to the question whether high PT equilibrium can also explain the HSE concentrations. Answers to this question have been slowed by experimental difficulties (nugget effect and very low solubilities). But two different perspectives have emerged from recent studies. One perspective is that D(M/S) for HSE at high PT are not low enough to explain terrestrial mantle depletions of these elements (for Pd and Pt). A second perspective is D(M/S) are reduced substantially at high PT and even low enough to explain terrestrial mantle depletions (for Au and Pt). Issues complicating interpretation of all experiments include use of MgO- and FeO-free silicate melts, and S-free and FeNi metal-free systems. In addition, conclusions for Pt rest on an interpretation that the tiny metallic nuggets plaguing many such experiments, were formed upon quench. There is not agreement on this issue, and the general question of HSE solubility at high PT remains unresolved
Righter, K.↗
Mass Redistribution in the Core and Time-varying Gravity at the Earth's Surface
The Earth's liquid outer core is in convection, as suggested by the existence of the geomagnetic field in much of the Earth's history. One consequence of the convection is the redistribution of mass resulting from relative motion among fluid parcels with slightly different densities. This time dependent mass redistribution inside the core produces a small perturbation on the gravity field of the Earth. With our numerical dynamo solutions, we find that the mass redistribution (and the resultant gravity field) symmetric about the equator is much stronger than that anti-symmetric about the equator. In particular, J(sub 2) component is the strongest. In addition, the gravity field variation increases with the Rayleigh number that measures the driving force for the geodynamo in the core. With reasonable scaling from the current dynamo solutions, we could expect that at the surface of the Earth, the J(sub 2) variation from the core is on the order of l0(exp -16)/year relative to the mean (i.e. spherically symmetric) gravity field of the Earth. The possible shielding effect due to core-mantle boundary pressure variation loading is likely much smaller and is therefore negligible. Our results suggest that time-varying gravity field perturbation due to core mass redistribution may be measured with modem space geodetic observations, which will result a new means of detecting dynamical processes in the Earth's deep interior.
Kuang, Wei-Jia↗
The melting curve of iron to 250 gigapascals - A constraint on the temperature at earth's center
The melting curve of iron, the primary constituent of earth's core, has been measured to pressures of 250 gigapascals with a combination of static and dynamic techniques. The melting temperature of iron at the pressure of the core-mantle boundary (136 GPa) is 4800 + or - 200 K, whereas at the inner core-outer core boundary (330 GPa), it is 7600 + or - 500 K. A melting temperature for iron-rich alloy of 6600 K at the inner core-outer core boundary and a maximum temperature of 6900 K at earth's center are inferred. This latter value is the first experimental upper bound on the temperature at earth's center, and these results imply that the temperature of the lower mantle is significantly less than that of the outer core.
Williams, Quentin↗
Report of the panel on earth rotation and reference frames, section 7
Objectives and requirements for Earth rotation and reference frame studies in the 1990s are discussed. The objectives are to observe and understand interactions of air and water with the rotational dynamics of the Earth, the effects of the Earth's crust and mantle on the dynamics and excitation of Earth rotation variations over time scales of hours to centuries, and the effects of the Earth's core on the rotational dynamics and the excitation of Earth rotation variations over time scales of a year or longer. Another objective is to establish, refine and maintain terrestrial and celestrial reference frames. Requirements include improvements in observations and analysis, improvements in celestial and terrestrial reference frames and reference frame connections, and improved observations of crustal motion and mass redistribution on the Earth.
Dickey, Jean O.↗
Accounting for crustal magnetization in models of the core magnetic field
The problem of determining the magnetic field originating in the earth's core in the presence of remanent and induced magnetization is considered. The effect of remanent magnetization in the crust on satellite measurements of the core magnetic field is investigated. The crust as a zero-mean stationary Gaussian random process is modelled using an idea proposed by Parker (1988). It is shown that the matrix of second-order statistics is proportional to the Gram matrix, which depends only on the inner-products of the appropriate Green's functions, and that at a typical satellite altitude of 400 km the data are correlated out to an angular separation of approximately 15 deg. Accurate and efficient means of calculating the matrix elements are given. It is shown that the variance of measurements of the radial component of a magnetic field due to the crust is expected to be approximately twice that in horizontal components.
Jackson, Andrew↗
Obliquity histories of Earth and Mars: Influence of inertial and dissipative core-mantle coupling
For both the Earth and Mars, secular variations in the angular separation of the spin axis from the orbit normal are suspected of driving major climatic changes. There is considerable interest in determining the amplitude and timing of these obliquity variations. If the orientation of the orbital plane were inertially fixed, and the planet were to act as a rigid body in it response to precessional torques, the spin axis would simply precess around the orbit at a fixed obliquity and at a uniform angular rate. The precession rate parameter depends on the principal moments of inertia and rotation rate of the perturbed body, and on the gravitational masses and semiminor axes of the perturbing bodies. For Mars, the precession rate is not well known, but probably lies in the interval 8 to 10 arcsec/year. Gravitational interactions between the planets lead to secular motions of the orbit planes. In the rigid body case, the spin axis still attempts to precess about the instantaneous orbit normal, but now the obliquity varies. The hydrostatic figure of a planet represents a compromise between gravitation, which attempts to attain spherical symmetry, and rotation, which prefers cylindrical symmetry. Due to their higher mean densities the cores of the Earth and Mars will be more nearly spherical than the outer layers of these planets. On short time scales it is appropriate to consider the core to be an inviscid fluid constrained to move with the ellipsoidal region bounded by the rigid mantle. The inertial coupling provided by this mechanism is effective whenever the ellipticicy of the container exceeds the ratio of precessional to rotational rates. If the mantle were actually rigid, this would be an extremely effective type of coupling. However, on sufficiently long time scales, the mantle will deform viscously and can accommodate the motions of the core fluid. A fundamentally different type of coupling is provided by electromagnetic or viscous torques. This type of coupling is likely to be most important on longer time scales. In each case, the mantle exerts an equal and opposite torque on the core.
Bills, Bruce G.↗
Core-mantle equilibrium - Comments on a paper by R. Brett
Critique of paper on earth core-mantle chemical equilibrium, considering upper mantle element abundance, oxidation state and volatiles nature
Ringwood, A. E.↗
Magnetic reversal spurts: Rain gauges for comet showers
Abrupt increases in the rate of magnetic reversals (magnetic reversal spurts) were first studied by many others. They hypothesized that spurts result from increased turbulence in the earth's core dynamo during episodes of intense bolide bombardment of the earth. Mechanisms for creating episodes of intense bombardment of the earth involve gravitational perturbation of the Oort cloud of comets, either by a hidden planet, a solar companion, or massive matter in the galactic plane. Herein, the time variation in reversal rate is analyzed using methods of statistical density estimation. A smooth, continuous estimate of reversal rate is obtained using an adaptive kernel method, in which the kernel width is adjusted as a function of reversal rate. The estimates near the ends of the data series (at 165 my ago and the present) are obtained by extending the data by reflection. The results show that the reversal spurts are not associated demonstrably with extinctions or well-dated impacts. If the spurts do record episodes of intense bombardment of the earth, then the mass extinctions do not, in general, occur at times of impacts. Furthermore, the large impact craters seen are not obviously related to the spurts, suggesting that the craters may have been caused by bolides of a different nature and with a different temporal pattern. However, the most simple explanation seems to be that the spurts do not record comet showers, either because the recording mechanism suggested by Muller and Morris is not effective or because comet showers are not triggered in the ways considered by Hut et al.
Lutz, T. M.↗
A New Approach to Isolating External Magnetic Field Components in Spacecraft Measurements of the Earth's Magnetic Field Using Global Positioning System observables
We review the problem of separating components of the magnetic field arising from sources in the Earth's core and lithosphere, from those contributions arising external to the Earth, namely ionospheric and magnetospheric fields, in spacecraft measurements of the Earth's magnetic field.
magnetic field components ionospheric and magnetos↗