Geomagnetic polarity reversals in a turbulent core

The behavior of the main magnetic field components during a polarity transition is investigated using the α²-dynamo model for magnetic field generation in a turbulent core. It is shown that rapid reversals of the dipole field occur when the helicity, a measure of correlation between turbulent velocity and vorticity, changes sign. Two classes of polarity transitions are possible. Within the first class, termed component reversals, the dipole field reverses but the toroidal field does not. Within the second class, termed full reversals, both dipole and toroidal fields reverse. Component reversals result from long term fluctuations in core helicity; full reversals result from short term fluctuations. A set of time-evolution equations are derived which govern the dipole field behavior during an idealized transition. Solutions to these equations exhibit transitions in which the dipole remains axial while its intensity decays rapidly toward zero, and is regenerated with reversed polarity. Assuming an electrical conductivity of 3 × 10⁵ mho m^?1 for the fluid core, the time interval required to complete the reversal process can be as short as 7500 years. This time scale is consistent with paleomagnetic observations of the duration of reversals. A possible explanation of the cause of reversals is proposed, in which the core's net helicity fluctuates in response to fluctuations in the level of turbulence produced by two competing energy sources—thermal convection and segregation of the inner core. Symmetry considerations indicate that, in each hemisphere, helicity generated by heat loss at the core-mantle boundary may have the opposite sign of helicity generated by energy release at the inner core boundary. Random variations in rates of energy release can cause the net helicity and the α-effect to change sign occasionally, provoking a field reversal. In this model, energy release by inner core formation tends to destabilize stationary dynamo action, causing polarity reversals.     

Inner-core conductivity in numerical dynamo simulations

Speculation about its possible super-rotation has drawn the attention of many geophysical researchers to the Earth’s inner core. An issue of special interest for geodynamo modelling is the influence of the inner-core conductivity. It has been suggested that the finite magnetic diffusivity of the inner core prevents more frequent reversals of the Earth’s magnetic field. We explore the possible influence of the inner-core conductivity by comparing convection-driven 3D dynamo simulations with insulating or conducting inner cores (CIC) at various parameters. The influence on the field structure in the outer core is only marginal. The time behaviour of dipole-dominated non-reversing dynamos is also little affected. Concerning reversing dynamos, the inner-core conductivity reduces the number of short dipole-polarity intervals with a typical length of a few thousand years. Reversals are always correlated with low dipole strength and these short intervals are found in periods where the dipole moment stays low. Polarity intervals longer than about 10,000 years, where the dipole moment has time recover in strength, are equally likely in insulating and CIC models. Since these latter intervals are of more geophysical relevance, we conclude that the influence of the inner-core conductivity on Earth-like reversal sequences is insignificant for the dynamo model employed here.     

Magnetic variation generated by a tangential magnetic dipole located in the Earth's core

Summary The harmonically variable magnetic field, generated by a tangential magnetic dipole (TMD), located eccentrically at the surface of the Earth's core, is investigated for various periods of time variations and for a three-layer conductivity model of the Earth. Numerical computations have shown that the field is inductively damped for variation periods of less than 500 years as compared to the field of a static TMD. It is proved that the field appropriate to the TMD, has a more complicated distribution of the Earth's surface than the field of a radial magnetic dipole. Comparison with maps of the non-dipole part of the geomagnetic field shows that the TMD is not as suitable for interpreting the observed non-dipole field and its variations as the eccentric radial magnetic dipole.     

Theory of the evolution of the earth and the earth's crust

Summary The paleomagnetic field (declination and inclination) in different geological epochs is represented through the field of the so-called magnetic dipole. The optimal dipole coordinates so obtained show that during older geological times the optimal dipole lay outside the earth's centre and moved towards and around the earth centre. It is supposed that the optimal dipole trajectory in the earth coincides with earth core trajectory. This core motion brought about a motion of the masses of the mantle in a direction opposite to the motion of the core. This in turn brought about the break-down of Pangea and the separation of the continents. The drift of the continents, the relative changing of the earth's rotational axis and many other geological and geophysical phenomena may be explained through such a motion, that is through the motion of an eccentrical core towards the earth centre.     

Magnetohydrodynamic disturbances in the earth's core,III

Summary It is in the hope of establishing a theorem contributing to the origin of the Secular Variation of the geomagnetic field that this third paper under the same heading, is written, —In this paper it is supposed that amagnetic dipole is suddenly introduced in the earth's core to act as a source of disturbance to the exciting field taken as a poloidal one. The dipole axis is placed parallel to the original field and perpendicular to the mantle. Mathematical solutions have been obtained for the resulting fluid motion in the core as well as for the generated magnetohydrodynamic perturbations in the earth's core and in the mantle. It can be seen from the mathematical results obtained that although the disturbances in the core are so complicated, yet they are much less complicated in the mantle and specially at the plane boundary separating core and mantle.     

Motion of the north magnetic pole within the scope of the dynamic model of the main geomagnetic field sources

The dipole model of the main geomagnetic field sources has been developed by the authors for several years. At present, the model includes 13 sources that existed and continuously developed during the 20th century. It has been assumed that the main dipole motion can be related to the motion of the Earth’s axis of inertia. At the same time, the known sharp changes in the direction of this motion, the so-called “wanderings” of the axis of inertia coincide in time with a change in the coordinates of the exit point of the main dipole magnetic moment vector on the Earth’s surface, dependent mostly on changes in the vector inclination. The motion of the north magnetic pole has been studied based on the model. It has been obtained that the dynamics of the main dipole parameters and, mainly, a stable variation in the inclination of the magnetic moment vector are responsible for the westward pole motion. At the same time, the observed rapid northward motion of the pole is related to the time variations in the parameters of 12 sources approximating the so-called nondipole part of the main field.     

有限导电内核的驱动方式对发电机模型的影响

本文以两种绝缘内核的发电机为基准,设置内核电导率与外核相同,选择了以固定速度超速旋转和在外核驱动下发生旋转的两种内核旋转模式,比较分析不同模型间的能量差异、磁场强度、磁雷诺数、磁极翻转频率和四个类地发电机参数.结果表明:对于弱偶极子发电机模型,有限导电内核的引入会对其偶极子强度的相对变化量造成较大影响,最高达103.00%;由外核驱动旋转的有限导电内核模型对于本文其他目标研究量所带来的影响比较小,均小于5%;而固定旋转速度的有限导电内核的模型对磁极翻转频率、赤道对称性和纬向性均存在较明显影响,最大变化量达124.62%.综合本文所选用的发电机模型的特征和数值分析结果,可以发现虽然由外核驱动旋转的有限导电内核模型其转速不可控且存在较大波动,但各物理量变化量与实际内核与外核的能量比更为接近,因此可以推断其驱动机制较自驱动模式更为合理可靠.     

Evolution of the dipole geomagnetic field. Observations and models

The works on paleomagnetic observations of the dipole geomagnetic field, its variations, and reversals in the last 3.5 billion years have been reviewed. It was noted that characteristic field variations are related to the evolution of the convection processes in the liquid core due to the effect of magnetic convection and solid core growth. Works on the geochemistry and energy budget of the Earth’s core, the effect of the solid core on convection and the generation of the magnetic field, dynamo models are also considered. We consider how core growth affects the magnetic dipole generation and variations, as well as the possibility of magnetic field generation up to the appearance of the solid core. We also pay attention to the fact that not only the magnetic field but also its configuration and time variations, which are caused by the convection evolution in the core on geological timescales, are important factors for the biosphere.     

1690～2000年地磁场能量的三维分布及其长期变化

利用Bloxham & Jackson 地磁场模型和国际参考地磁场模型(IGRF),研究了1690～2000年地磁总能量及其北向、东向和垂直向分量的能量以及非偶极子磁场的能量在地球内部的分布及长期变化.结果表明,地表和地核以外地磁场总能量及其北向和垂直向的能量是持续衰减的,垂直向的磁场能量占总能量的64％以上,对总能量的贡献起主要作用;东向分量的能量随时间的变化以增加为主.地磁场的能量变化率存在56年的周期,主要是由偶极子磁场产生的.地表以外的非偶极子磁能从减小到增大转折出现在1770年,比地核以外滞后40年.地球内部磁能随时间的变化显示,偶极子磁能逐渐减小,非偶极子磁能增加,越靠近核幔边界增加越快;偶极子和非偶极子磁能的变化量相等的分界面在距地心3780km处.从核幔边界到地表,磁能变化的衰减非偶极子比偶极子快,表明偶极子磁场比非偶极子磁场有更深的场源.     

Linear Magnetoconvection in Rotating Fluid Spheres Permeated by a Uniform Axial Magnetic Field

A linear analysis of thermally driven magnetoconvection is carried out with emphasis on its application to convection in the Earth's core. We consider a rotating and self-gravitating fluid sphere (or spherical shell) permeated by a uniform magnetic field parallel to the spin axis. In rapidly rotating cases, we find that five different convective modes appear as the uniform field is increased; namely, geostrophic, polar convective, magneto-geostrophic, fast magnetostrophic and slow magnetostrophic modes. The polar convective (P) and magneto-geostrophic (E) modes seem to be of geophysical interest. The P mode is characterized by such an axisymmetric meridional circulation that the fluid penetrates the equatorial plane, suggesting that generation of quadrapole from dipole fields could be explained by a linear process. The E mode is characterized by a few axially aligned columnar rolls which are almost two-dimensional due to a modified Proudman-Taylor theorem.     

Cenozoic latitudinal shift of the Hawaiian hotspot and its implications for true polar wander

Pacific plate equatorial sediment facies provide estimates of the northward motion of the Pacific plate that are independent of paleomagnetic data and hotspot tracks. Analyses of equatorial sediment facies consistently indicate less northward motion than analyses of the dated volcanic edifices of the Hawaiian-Emperor chain. The discrepancy is largest 60–70 Ma B.P.; the 60- to 70-Ma equatorial sediment facies data agree with recent paleomagnetic results from deep-sea drilling on Suiko seamount [1] and from a northern Pacific piston core [2]. Equatorial sediment facies data and paleomagnetic data, combined with K-Ar age dates along the Emperor chain [3], indicate a position of the spin axis at 65 Ma B.P. of 82°N, 205°E in the reference frame in which the Pacific Ocean hotspots are fixed. This pole agrees well with the position of the spin axis in the reference frame in which the Atlantic Ocean hotspots and the Indian Ocean hotspots are fixed [4,5], supporting the joint hypotheses that (1) the Pacific Ocean hotspots are fixed with respect to the hotspots in other oceans, (2) the hotspots have shifted coherently with respect to the spin axis, and (3) the time average of the earth's magnetic field 65 Ma B.P. was an axial geocentric dipole. Global Neogene paleomagnetic data suggest that a shift of the mantle relative to the spin axis has been occurring during the Neogene in the same direction as the shift between 65 Ma B.P. and the present. All data are consistent with a model in which the hotspots (and by inference the mantle) have shifted with respect to the spin axis about a fixed Euler pole at a constant rate of rotation for the last 65 Ma.     

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.     

地球外核的电荷密度

为计算地球磁极处的磁感应强度,建立地球的磁场是由带电的地球外核的旋转产生的模型.先根据毕奥-萨伐尔定律计算球形模型绕自转轴旋转时在自转轴直径上产生的磁感应强度;再利用已知的地球外核的内外半径及地球半径和磁极处的磁感应强度值,计算出地球外核的电荷体密度及面密度.结果表明:若外核的电荷呈均匀的体密度分布,则其电荷体密度为3.5507 C/m³;若外核的电荷均匀分布在外核的外表面,则其面密度为2.4581×10⁶ C/m².通过地球表面的磁感应强度信息利用物理规律和地球物理数据推测地球内部难以直接进行探测的相关信息,具有实际意义.根据地震学方法对地球外核厚度、转向等变化的最新研究数据按该文模型可推测地球磁场强度、极性等的变化.而地球磁场的变化对地球上的人类生活颇有影响.     

二十世纪的地球偶极子磁场

1900~2000年的IGRF(国际地磁参考场)资料使研究20世纪中地磁场的变化规律成为可能,在20世纪中,即使从19世纪起,地球偶极子磁场发生了较大的变化,偶极矩一直保持衰减的势头,地心轴的所有3个分量都是减小的.地磁南极的位置变化在1930年左右发生大的转折,1960年起向西和向南快速移动,偶极子轴在纬度方面变化只有1°左右,经度变化在3°左右,离磁极倒转的条件差得远.     

The late Pleistocene geomagnetic field as recorded by sediments from Fargher Lake,Washington, U.S.A.

Measurement of the remanent magnetization of a 6.88-m oriented core of soft sediments and tephras from Fargher Lake near Mount St. Helens in southwestern Washington State shows that no significant geomagnetic reversals were recorded in the sediments of the lake. Radiocarbon and palynological dating of the tephra layers from the lake bed indicates deposition during the interval 17, 000–34, 000 years B.P. although geochemical correlation of a prominent tephra layer in the core with tephra set C of Mount St. Helens could mean that the maximum age of the sediments may be at least 36, 000 years B.P. The core was divided into specimens 0.02 m long, each representing approximately 55 years of deposition assuming a constant rate of sedimentation. Pilot alternating field demagnetization studies of every tenth specimen indicated a strong, stable remanence with median destructive field of 15 mT, and the remaining specimens were subsequently demagnetized in fields of this strength. The mean inclination for all specimens exclusive of the unstably magnetized muck and peat from near the surface is 56.1° which is 8° shallower than the present axial dipole field at this site, perhaps because of inclination error in the detrital remanent magnetization of the sediments, although because of the variability in the data, this departure from the axial dipole field may not be significant. The ranges of inclination and declination are comparable to those of normal secular variation at northern latitudes. Although three isolated specimens have remanence with negative inclination, these anomalous directions are due to sampling and depositional effects. Measurement of a second core of 6.86 m length also revealed only normal magnetic polarity, but this result is of little stratigraphic value as this core failed to penetrate the distinctive tephra found near the base of the former core.Studies of a concentrate of the magnetic minerals in the sediments by optical microscopy and X-ray diffraction indicate that the primary magnetic constituent is an essentially pure magnetite of detrital origin. The magnetite occurs in a wide range of grain sizes with much of it of sub-multidomain size (< 15 μm).As a whole, this study provides substantial evidence against the existence of large-scale worldwide geomagnetic reversals during the time interval of Fargher Lake sedimentation, a segment of geological time for which many excursions and reversals have been reported elsewhere.     

On the role of magnetostrophic waves in geodynamo

It is shown that magnetostrophic waves which are generated in the equatorial plane of the Earth’s core due to the instability of the equatorial jet and which propagate almost transversely to the rotational axis off the tangent cylinder, have a negative helicity in the northern hemisphere and positive helicity in the southern hemisphere. When the wave trains propagate through the regions with a constant azimuthal magnetic field caused by the Ω-effect, this helicity distribution induces an electromotive force (emf) (due to the α-effect), which may lead to the maintenance of the initial dipole field by the scenario of the α-Ω dynamo.     

Evolution of Dimensionless Numbers in Geodynamo Models

The evolution of the dimensionless Ekman, Rossby, and Rayleigh numbers in the model of composite convection in the Earth’s, which that determine the force balance and magnetic field evolution, is considered on the basis of known estimates of the rate of solid core growth and variations in the day length. Various scenarios of this evolution, both in the past and future, are presented over time intervals comparable with the age of the core. It is shown, in particular, that the current intensity of convection in the fluid core continues to increase. This fact corresponds to the increase in the frequency of geomagnetic field inversions and the transition from a dipole field to a multipole one. A decrease in the volume of the liquid core leads to a decrease in the magnetic field strength.     

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.     

Energy geodynamo parameters compatible with analytical,numerical, paleomagnetic models and observations

A hydromagnetic dynamo is only possible at a sufficiently powerful convection. In the Earth’s core, it is probably the nonthermal convection very much in excess of its critical level with the molecular transporr coefficients. However, in the case of medium- or large-scale fields, the critical energy level caused by the turbulent tranport coefficients is likely to be slightly below the actual level. This probably explains both the 22-year success of this type of simplified geodynamo models and the energy scaling laws for hydromagnetic fields, which generalize these models. Also the review of energy-dependent analytical and observational estimates of vortex fields, hydromagnetic scale sizes, and velocities in the core is presented. These typical parameters are partly in a new way linked to the observed and more ancient magnetic variations. New, albeit, simplified and self-evident, substantiation is given to the paleomagnetic hypothesis about the predominance of the axial dipole under a certain time averaging. In (Pozzo et al., 2012) and more recent works, it is shown that the adiabatic heat flow and electrical conductivity in the Earth’s core are severalfold higher than the generally accepted estimates. Here, the dynamo supporting Braginsky’s convection (Braginsky, 1963) (under the crystallization of the heavy fraction of a liquid onto the solid core) started less than 1 Ga ago, whereas the more ancient geodynamo was supported by the compositional convection of another type. The known mechanisms implementing this convection, which differ by the scenarios of magnetic evolution, are reviewed. This may help identify the sought mechanism through the most ancient paleomagnetic estimates of the field’s intensity and through the numerical models. The probable mechanisms of generation and their absence for the primordial and recent magnetic field of the studied terrestrial planets are discussed.     

Harmonic sources of the main geomagnetic field in the Earth’s core

The large-scale harmonic magnetic-convective sources of the main geomagnetic field in the Earth’s core have been determined for the first time. The determination is based on a complete system of eigenfunctions of the magnetic diffusion equation in a homogeneously conducting sphere, which is surrounded by an insulator. The sources of the main geomagnetic field observed, which is responsible for the distribution of the electric currents generating this field in the core, are expressed in terms of large-scale eigenfunctions. In this case, the dipole sources are directly related to the observed geomagnetic dipole, whereas the quadrupole sources are related to the quadrupole, etc. The time variations in the obtained sources are responsible for individual spatiotemporal features in the generation or suppression of each Gaussian component of the observed geomagnetic field. When the commonly accepted observational international geomagnetic reference field (IGRF) models were used to partially reveal these time variations, it became possible to specify the estimate of the Earth’s core conductivity and determine the minimum period that can separate us from the commencement of further inversion or excursion.