Core-mantle interactions

Several aspects of core-mantle interactions were considered during a Royal Astronomical Society Discussion Meeting on 12th May 1989, including modelling the geomagnetic field at the core surface, the morphology of the field between 1600 and 1820 AD, dynamo theory, Taylor's constraint, fluid motions at the top of the core that reproduce the observed secular variation, pressure coupling between the core and mantle and its geophysical consequences, topographic core-mantle coupling, angular momentum transfer at the core-mantle interface, the detection and implications of core oscillations, particularly those with associated fluctuations in the Earth's rotation rate, and the seismological determination of the core-mantle boundary topography from lateral inhomogeneities in the mantle.     

Axial poloidal electromagnetic core-mantle coupling torque: A re-examination for different conductivity and satellite supported geomagnetic field models

We investigate the temporal behaviour of the axial component of the electromagnetic core-mantle coupling torque that is associated with the poloidal part of the geomagnetic field observable at the Earth surface. For its computation, we use different models of the geomagnetic field, expanded into spherical harmonics (Wardinski and Holme, 2006; Sabaka et al., 2004), and the mantle conductivity. The geomagnetic field, which we have to know at the core-mantle boundary for the associated computations, will be inferred from the field at the Earth surface by the non-harmonic field continuation through a conducting mantle shell. The aims of this investigation are (i) to check how sensitive is the computation of the torque with respect to the different geomagnetic field models, (ii) to check its dependence on the spherical harmonic degree n, and (iii) to determine the difference between the mechanical torque derived from the observed length-of-day variations (atmospheric influence subtracted) and the poloidal electromagnetic torque in dependence on the assumed conductivity. To use the non-harmonic field continuation for the torque calculation and to obtain an insight into the influence of the different geomagnetic field models on the EM torques are the major aspects of this paper. grm@gfz-potsdam.de     

Axial and equatorial rotations of the Earth's cores associated with the Quaternary ice age

The differential axial and equatorial rotations of both cores associated with the Quaternary glacial cycles were evaluated based on a realistic earth model in density and elastic structures. The rheological model is composed of compressible Maxwell viscoelastic mantle, inviscid outer core and incompressible Maxwell viscoelastic inner core. The present study is, however, preliminary because I assume a rigid rotation for the fluid outer core. In models with no frictional torques at the boundaries of the outer core, the maximum magnitude of the predicted axial rotations of the outer and inner cores amounts to ∼2° year⁻¹ and ∼1° year⁻¹, respectively, but that for the secular equatorial rotations of both cores is ∼0.0001° at most. However, oscillating parts with a period of ∼225 years are predicted in the equatorial rotations for both cores. Then, I evaluated the differential rotations by adopting a time-dependent electromagnetic (EM) torque as a possible coupling mechanism at the core-mantle boundary (CMB) and inner core boundary (ICB). In a realistic radial magnetic field at the CMB estimated from surface magnetic field, the axial and equatorial rotations couple through frictional torques at the CMB, although these rotations decouple for dipole magnetic field model. The differential rotations were evaluated for conductivity models with a conductance of 10⁸ S of the lowermost mantle inferred from studies of nutation and precession of the Earth and decadal variations of length of day (LOD). The secular parts of equatorial rotations are less sensitive to these parameters, but the magnitude for the axial rotations is much smaller than for frictionless model. These models, however, produce oscillating parts in the equatorial rotations of both cores and also in the axial rotations of the whole Earth and outer and inner cores. These oscillations are sensitive to both the magnitude of radial magnetic field at the CMB and the conductivity structure. No sharp isolated spectral peaks are predicted for models with a thin conductive layer (∼200 m) at the bottom of the mantle. In models with a conductive layer of ∼100 km thickness, however, sharp spectral peaks are predicted at periods of ∼225 and ∼25 years for equatorial and axial rotations, respectively, although these depend on the strength of radial magnetic field at the CMB. While the present study is preliminary in modelling the fluid outer core and coupling mechanism at the CMB, the predicted axial rotations of the whole Earth may be important in explaining the observed LOD through interaction between the equatorial and axial rotations.     

On the coherence between changes in biota and geomagnetic reversals in the Phanerozoic

The data on geomagnetic reversals, organic changes, and lower-mantle plume magmatism in the Phanerozoic are collected and correlated. No direct relationship is revealed between the geomagnetic reversals, plumes, and biozones. However, the frequency of geomagnetic reversals is found to correlate to the frequency of biozonal alterations. We relate this inconsistency to the coupling of the two processes, which are mutually independent, with the long-term changes in the Earth’s rotation. The plumes are formed at the core-mantle boundary and, thus, the reversals should have a different source. We hypothesize that the change in the geomagnetic polarity is due to the nonuniform rotation of the inner core relative to the mantle in combination with the changes in the axial tilt of the Earth’s rotation.     

The Boussinesq and anelastic liquid approximations for convection in the Earth’s core

Convection in the Earth’s core is usually studied in the Boussinesq approximation in which the compressibility of the liquid is ignored. The density of the Earth’s core varies from ICB to CMB by approximately 20%. The question of whether we need to take this variation into account in core convection and dynamo models is examined. We show that it is in the thermodynamic equations that differences between compressible and Boussinesq models become most apparent. The heat flux conducted down the adiabat is much smaller near the inner core boundary than it is near the core-mantle boundary. In consequence, the heat flux carried by convection is much larger nearer the inner core boundary than it is near the core-mantle boundary. This effect will have an important influence on dynamo models. Boussinesq models also assume implicitly that the rate of working of the gravitational and buoyancy forces, as well as the Ohmic and viscous dissipation, are small compared to the heat flux through the core. These terms are not negligible in the Earth’s core heat budget, and neglecting them makes it difficult to get a thermodynamically consistent picture of core convection. We show that the usual anelastic equations simplify considerably if the anelastic liquid approximation, valid if αT?1, where α is the coefficient of expansion and T a typical core temperature, is used. The resulting set of equations are not significantly more difficult to solve numerically than the usual Boussinesq equations. The relationship of our anelastic liquid equations to the Boussinesq equations is also examined.     

On topographic core-mantle coupling

Abstract

The purpose of this note is two-fold: to draw attention to a perplexing difficulty connected with topographic core-mantle coupling, and to suggest tentatively an explanation. The difficulty is an apparent conflict between the most comprehensive theory of the coupling so far attempted (Anufriev and Braginsky, 1975a, b, 1977a, b) and recent explicit calculations based on magnetic and seismic information (Speith et al., 1986). It is argued that asymmetric deviations from Anufriev and Braginsky's basically axisymmetric model of the underlying core flow are capable of resolving the difficulty.     

Secular variation in numerical geodynamo models with lateral variations of boundary heat flow

We study magnetic field variations in numerical models of the geodynamo, with convection driven by nonuniform heat flow imposed at the outer boundary. We concentrate on cases with a boundary heat flow pattern derived from seismic anomalies in the lower mantle. At a Rayleigh number of about 100 times critical with respect to the onset of convection, the magnetic field is dominated by the axial dipole component and has a similar spectral distribution as Earth’s historical magnetic field on the core-mantle boundary (CMB). The time scales of variation of the low-order Gauss coefficients in the model agree within a factor of two with observed values. We have determined the averaging time interval needed to delineate deviations from the axial dipole field caused by the boundary heterogeneity. An average over 2000 years (the archeomagnetic time scale) is barely sufficient to reveal the long-term nondipole field. The model shows reduced scatter in virtual geomagnetic pole positions (VGPs) in the central Pacific, consistent with the weak secular variation observed in the historical field. Longitudinal drift of magnetic field structures is episodic and differs between regions. Westward magnetic drift is most pronounced beneath the Atlantic in our model. Although frozen flux advection by the large-scale flow is generally insufficient to explain the magnetic drift rates, there are some exceptions. In particular, equatorial flux spot pairs produced by expulsion of toroidal magnetic field are rapidly advected westward in localized equatorial jets which we interpret as thermal winds.     

Detecting thermal boundary control in surface flows from numerical dynamos

The geomagnetic field and secular variation exhibit asymmetrical spatial features which are possibly originating from an heterogeneous thermal control of the Earth's lower mantle on the core. The identification of this control in magnetic data is subject to several difficulties, some of which can be alleviated by the use of core surface flow models. Using numerical dynamos driven by heterogeneous boundary heat flux, we confirm that within the parameter space accessible to simulations, time average surface flows obey a simple thermal wind equilibrium between the Coriolis and buoyancy forces, the Lorentz, inertial and viscous forces playing only a secondary role, even for Elsasser numbers significantly larger than 1. Furthermore, we average the models over the duration of three vortex turnovers, and correlate them with a longer time average which fully reveals the signature of boundary heterogeneity. This allows us to quantify the possibility of observing mantle control in core surface flows averaged over a short time period. A scaling analysis is performed in order to apply the results to the Earth's core. We find that three vortex turnovers could represent between 100 and 360 years of Earth time, and that the heat flux heterogeneity at the core-mantle boundary could be large enough to yield an observable signature of thermal mantle control in a time average core surface flow within reach of the available geomagnetic data.     

Core motions,electromagnetic core-mantle coupling and variations in the earth's rotation: New constraints from geomagnetic secular variation impulses

Recently observed secular acceleration impulses (SAI) of the geomagnetic field are interpreted in terms of organized motions of the outer core layers. Such motions have planetary dimensions (5000 km) and a large amplitude (3 × 10^?4 m s^?1) and are established in very short times (less than one year). The correlation of SAI observed in the Northern Hemisphere with minima in the Earth's rotation rate (around 1840, 1905 and 1970) is shown to be consistent with a simple model involving electromagnetic coupling of the weakly conducting (of the order of 100 ω^?1 m^?1) mantle, of a coherent outer core layer (thickness 100 to a few hundred kilometres) and of the rest of the core. The magnitude of the torque which acts suddenly on both parts of the core at the time of the impulses is estimated.     

核幔耦合对地球自由核章动的激发影响

地球自由核章动（FCN）是地幔与液核相互作用的重要动力学现象,其激发机制涉及地表流体层、地幔和地核等圈层之间的耦合,此前研究多利用地表流体层角动量数据单独研究其对FCN的激发,对核幔耦合的影响考虑不足.本文基于角动量守恒理论分析了核幔耦合对FCN周期及振幅的影响,并结合多个大气及海洋角动量函数时间序列首次估算了核幔耦合在FCN激发过程中的贡献.结果表明核幔耦合对FCN周期产生的固定和时变影响对FCN激发的作用均不可忽视,尤其时变影响可达几十个微角秒,对于进一步解释FCN时变特征非常重要;核幔耦合对FCN振幅的直接影响是地表流体层的激发与实测FCN不相符的主要原因,黏滞、电磁和地形等耗散耦合的存在对地表流体的激发振幅有67%左右的减弱效果.     

Core mantle boundary topography from short period PcP, PKP, and PKKP data

We use a total of 839,369 PcP, PKPab, PKPbc, PKPdf, PKKPab, and PKKPbc residual travel times from [Bull. Seism. Soc. Am. 88 (1998) 722] grouped in 29,837 summary rays to constrain lateral variation in the depth to the core-mantle boundary (CMB). We assumed a homogeneous outer core, and the data were corrected for mantle structure and inner-core anisotropy. Inversions of separate data sets yield amplitude variations of up to 5 km for PcP, PKPab, PKPbc, and PKKP and 13 km for PKPdf. This is larger than the CMB undulations inferred in geodetic studies and, moreover, the PcP results are not readily consistent with the inferences from PKP and PKKP. Although the source-receiver ambiguity for the core-refracted phases can explain some of it, this discrepancy suggest that the travel-time residuals cannot be explained by topography alone. The wavespeed perturbations in the tomographic model used for the mantle corrections might be too small to fully account for the trade off between volumetric heterogeneity and CMB topography. In a second experiment we therefore re-applied corrections for mantle structure outside a basal 290 km-thick layer and inverted all data jointly for both CMB topography and volumetric heterogeneity within this layer. The resultant CMB model can explain PcP, PKP, and PKKP residuals and has approximately 0.2 km excess core ellipticity, which is in good agreement with inferences from free core nutation observations. Joint inversion yields a peak-to-peak amplitude of CMB topography of about 3 km, and the inversion yields velocity variations of ±5% in the basal layer. The latter suggests a strong trade-off between topography and volumetric heterogeneity, but uncertainty analyses suggest that the variation in core radius can be resolved. The spherical averages of all inverted topographic models suggest that the data are best fit if the actual CMB radius is 1.5 km less than in the Earth reference model used (i.e. the average outer core radius would be 3478 km).     

Core-mantle coupling and viscoelastic deformations

Writing the angular momentum theorem for the Earth and for its fluid core, we show that there are couplings between the core and the mantle induced by viscomagnetic torque, by external active torque, by topographic torque acting at the core-mantle boundary (CMB) but also by viscoelastic deformations of the CMB which may perturb the axial rotations of the Earth and of the core. We compute these deformations at the CMB induced by the Pleistocenic deglaciation. The time-dependence of inertia tensor perturbations, i.e. the rheology of the mantle, is very important in the calculation of the coupling. Taking into account the passive viscomagnetic torque of tangential traction acting at the CMB, we investigate, for different values and various temporal evolutions of the topographic torque, the perturbations in the rotations of the Earth and of the core induced by the deglaciation, by the constant torque of tidal friction and by the 18.6 year tidal potential. We show that, for these excitation sources, the existence of a constant topographic torque involves the core oscillating with respect to the mantle and thus forbids any large drift of the core with respect to the mantle. However, it seems theoretically possible to have an excitation source with enough energy which involves a shift of the core with respect to the mantle. If the pressure within the fluid core varies with time, the motion of the core with respect to the mantle could be drastically different.     

行星尺度地磁异常的长期变化

为了综合反映地球表面行星尺度磁异常的展布面积、磁场极值以及磁场分布特征等多种因素及其与磁能的关系，本文用穿过各异常区的“无符号磁通量”为特征参数来表征磁异常区强度.用第八代国际参考地磁场模型(IGRF)，分析了1900年到2000年全球最大的5个磁异常区的长期变化，结果表明，在一百年中，南大西洋(SAT)、大洋洲(AUS)和非洲(AF)3个异常区的磁通量均增加了200MWb以上，欧亚异常(EA)磁通量增加幅度稍小(157MWb)，上述4个异常区磁通量增幅为30%-60%，而北美异常(NAM)的磁通量则减小了50MWb.各异常区面积虽有变化，但最大变化仅为%左右.对磁异常区的西向漂移研究表明，地球表面和核幔界面的西漂明显存在差异：地表磁场有持续而稳定的西向漂移，全球平均西漂速度为0.2°/a；但核幔界面磁场的西向漂移速度要小得多，最大不超过0.1°/a.形成这种差异的原因可能是组成地磁场的不同球谐分量有不同的漂移速度；地表磁场的西漂主要决定于占优势的低阶分量，而核幔界面的西漂则受到高阶分量的重大影响.本文指出，在把地表西漂值用作地核磁流体运动速度的典型值时必须十分谨慎.     

On the theory of core-mantle coupling

This article commences by surveying the basic dynamics of Earth's core and their impact on various mechanisms of core-mantle coupling. The physics governing core convection and magnetic field production in the Earth is briefly reviewed. Convection is taken to be a small perturbation from a hydrostatic, “adiabatic reference state” of uniform composition and specific entropy, in which thermodynamic variables depend only on the gravitational potential. The four principal processes coupling the rotation of the mantle to the rotations of the inner and outer cores are analyzed: viscosity, topography, gravity and magnetic field. The gravitational potential of density anomalies in the mantle and inner core creates density differences in the fluid core that greatly exceed those associated with convection. The implications of the resulting “adiabatic torques” on topographic and gravitational coupling are considered. A new approach to the gravitational interaction between the inner core and the mantle, and the associated gravitational oscillations, is presented. Magnetic coupling through torsional waves is studied. A fresh analysis of torsional waves identifies new terms previously overlooked. The magnetic boundary layer on the core-mantle boundary is studied and shown to attenuate the waves significantly. It also hosts relatively high speed flows that influence the angular momentum budget. The magnetic coupling of the solid core to fluid in the tangent cylinder is investigated. Four technical appendices derive, and present solutions of, the torsional wave equation, analyze the associated magnetic boundary layers at the top and bottom of the fluid core, and consider gravitational and magnetic coupling from a more general standpoint. A fifth presents a simple model of the adiabatic reference state.     

On the nearly axially-symmetrical model of the hydromagnetic dynamo of the earth

A short review of the present state of the nearly axially-symmetrical dynamo model is given. A simplified theory for hydromagnetic dynamos taking into account the forces acting in the Earth's core is considered. The role of weak core-mantle friction is discussed and a form of solution is suggested which is characterized by a large geostrophic velocity in the core and by a boundary layer of a new type. The consequences of such a model (called model Z) for the Earth's dynamo are discussed.     

Harmonic splines for geomagnetic modelling

Which features of a geomagnetic field model on the surface of the core are really necessary in order to fit, within observational error, the field observations at and above the Earth's surface? To approach this question, we define ‘roughness’ in various ways as a norm on an appropriate Hilbert space of field models which is small when the field is smooth on the core surface. Then, we calculate the model with least norm (the smoothest model) which fits the data, sources outside the core being treated as noise. Sample calculations illustrate the effects of noise, of the choice of norm and of an uneven distribution of observing stations.     

On core surface flows inferred from satellite magnetic data

Satellite-data allows the magnetic field produced by the dynamo within the Earth’s core to be imaged with much more accuracy than previously possible with only ground-based data. Changes in this magnetic field can in turn be used to make some inferences about the core surface flow responsible for them. In this paper, we investigate the improvement brought to core flow computation by new satellite-data based core magnetic field models. It is shown that the main limitation now encountered is no longer the (now high) accuracy of those models, but the “non-modelled secular variation” produced by interaction of the non-resolvable small scales of the core flow with the core field, and by interaction of the (partly) resolvable large scales of the core flow with the small scales of the core field unfortunately masked by the crustal field. We show how this non-modelled secular variation can be taken into account to recover the largest scales of the core flow in a consistent way. We also investigate the uncertainties this introduces in core flows computed with the help of the frozen-flux and tangentially geostrophic assumptions. It turns out that flows with much more medium and small scales than previously thought are needed to explain the satellite-data-based core magnetic field models. It also turns out that a significant fraction of this flow unfortunately happens to be non-recoverable (being either “non-resolvable” because too small-scale, or “invisible”, because in the kernel of the inverse method) even though it produces the detectable “non-modelled secular variation”. Applying this to the Magsat (1980) to Ørsted (2000) field changes leads us to conclude that a flow involving at least strong retrograde vortices below the Atlantic Hemisphere, some less-resolved prograde vortices below the Pacific Hemisphere, and some poorly resolved (and partly non-resolvable) polar vortices, is needed to explain the 1980-2000 satellite-era average secular variation. The characteristics of the fraction of the secular variation left unexplained by this flow are also discussed.     

Long-term variations in the second sectorial Stokes harmonics on the basis of TOPEX/POSEIDON altimetry between 1993 and 2000

The long-term variations in the second degree sectorial Stokes parameters of the geopotential have been determined from TOPEX-POSEIDON (T/P) satellite altimeter data, covering the period of January 1, 1993 to January 3, 2001 (T/P cycles 11-305). It is the first attempt to determine the variations in the second sectorial harmonics in the Earth’s inertia tensor due to the ocean dynamics. The variations amount to about 1 × 10⁻¹⁰ (J ₂ ⁽²⁾ ≈ 1.6 × 10⁻⁶ and S ₂ ⁽²⁾ ≈ −0.9 × 10⁻⁶). The variations are about 5% of the tidal effect. This corresponds to variations in the directions of the equatorial axes of the Earth’s inertia ellipsoid of up to 10 arc-seconds. Consequently, the annual and semi-annual variations of the Earth’s equatorial flattening is about 10⁻⁹; i.e. it corresponds to a change of 8 units of its denominator of 91 030. (The equatorial flattening ≈ 1/91 030). Since the coverage of the Earth’s ocean surface is not worldwide, and the inclination of T/P is i = 66°, it is only 58.2% (min. depth of the ocean 2 000 m) of the Earth’s surface which is processed, the torque, resulting from the seasonal transfer of masses within a sea surface layer, is not zero. It amounts up to 10¹⁶ kg m²s⁻², which is comparable to the total indirect tidal torque due to the Moon and the Sun, ∼ 3.9 × 10¹⁶ kg m²s⁻². However, the above estimate strongly depends on the adopted thickness of the sea surface layer, ΔR = 50 m. For a larger thickness of ΔR = 100 m, the seasonal torque amounts to about ∼ 2.3 × 10¹⁶ kg m²s⁻².     

Helical core flow from geomagnetic secular variation

Fluid flow below the core-mantle boundary is inferred from geomagnetic secular variation data, assuming frozen magnetic flux and a new physical assumption termed helical flow, in which the tangential divergence correlates with the radial vorticity. Helical flow introduces streamfunction diffusion and removes non-uniqueness in the inversion of the magnetic induction equation. We combine helical flow with tangential geostrophy and compare the following physical assumptions: tangential geostrophy, strong helicity, weak helicity and columnar flow, using geomagnetic field models from the 2000 Oersted and 1980 Magsat satellites. Our solutions contain some features found in previous core flow models, such as large mid-latitude vortices, westward drift in most of the southern hemisphere, and suggested polar vortices. However, our solutions contain significantly more flow along contours of the radial magnetic field than previous core flow models.     

Topographic heterogeneity of the core-mantle boundary in subduction zones and its effect on kinematics of main geomagnetic field sources

This work considers the kinematics of the source of the main geomagnetic field (MGF) near the core-mantle boundary under the Caribbean region. This source was selected because (i) its trajectory for the reviewed 110 years crosses this boundary, (ii) the region belongs to the so-called cemeteries of the tectonic plates, and (iii) numerous works have studied the structural heterogeneities of the lower mantle in this region with seismic tomography. Our study of the structural heterogeneities of the lower mantle and the trajectory of the MGF source indicates that the relics of the ancient tectonic plates in this region not only reach the coremantle boundary but could penetrate to the liquid core as well to the depth of 300 km. The “cemeteries” of the tectonic plates span significant areas in size. If the topographic heterogeneities of the core-mantle boundary, which are formed by the relics of the ancient tectonic plates, reach several hundreds of kilometers, then they can significantly affect the kinematics of individual structured flows in the liquid core and, consequently, change the spatial structure of secular MGF variations on the Earth’s surface.