Spatial and temporal spectra of the geomagnetic field and their scaling properties

Many natural phenomena show a relationship between their spatial and temporal Fourier spectra. This paper discusses such a connection for the geomagnetic field, when some assumptions are made about the (exponential or power-law) behaviour of the spatial power spectrum of the field itself and that of its time derivative (the spatial spectrum of the secular variation) as estimated from global geomagnetic field models. It is shown that, under either assumption, the temporal spectrum of the geomagnetic field computed at the core–mantle boundary (CMB) would have a power-law behaviour with a negative spectral exponent of about 0.5. At the Earth’s surface, although the temporal spectrum obtained from the power-law spatial model assumes a slightly more complicated form, it can be practically approximated with a power law with a negative exponent of about 3.6. Analysis of magnetic observatory data confirms these results and that the starting hypotheses are reasonable, especially in view of the possibly chaotic state of the dynamical processes underlying the generation and maintenance of the geomagnetic field.     

Crustal geomagnetic field: two-dimensional intermediate-wavelength spatial power spectra

Two-dimensional Fourier spatial power spectra of equivalent magnetization values are presented for a region that includes a large portion of the western United States. The magnetization values were determined by inversion of POGO satellite data, assuming a magnetic crust 40 km thick, and were located on an 11 × 10 array with 300 km grid spacing. The spectra appear to be in good agreement with values of the crustal geomagnetic field spatial power spectra given by McLeod and Coleman (1980) and with the crustal field model given by Serson and Hannaford (1957). The spectra show evidence of noise at low frequencies in the direction along the satellite orbital track (N-S), indicating that for this particular data set additional filtering would probably be desirable. These findings illustrate the value of two-dimensional spatial power spectra both for describing the geomagnetic field statistically and as a guide for diagnosing possible noise sources.     

Geomagnetic field mapping from a satellite: Spatial power spectra of the geomagnetic field at various satellite altitudes relative to natural noise sources and instrument noise

For a low-level geomagnetic satellite survey, for which the motion of the satellite converts spatial variation into temporal variation, the limit on accuracy may well be background temporal fluctuations. The sources of the temporal fluctuations are current systems external to the Earth and include currents induced in the Earth due to these sources. The internal sources consist primarily of two components, the main geomagnetic field with sources in the Earth's core and a crustal geomagnetic field.Power spectra of the vertical geomagnetic field internal component that would be observed by a spacecraft in circular orbit at various altitudes, due to satellite motion through the spatially varying geomagnetic field, are compared to power spectra of the natural temporal fluctuations of the geomagnetic field vertical component (natural noise) and to the power spectrum for typical fluxgate magnetometer instrument noise. The natural noise is shown to be greater than this typical instrument noise over the entire frequency range for which useful measurements of the geomagnetic field may be made, for all geomagnetic latitudes and all times. Thus there would be little benefit in reducing the instrument noise below the typical value of 10^?4 gamma² Hz^?1 plus a 1/f component of 10 milligamma rms decade^?1.For a given satellite altitude, there is a maximum frequency above which the natural noise is greater than the power spectrum of the crustal geomagnetic field vertical component. Below this maximum frequency, the situation is reversed. This maximum frequency depends on geomagnetic latitude (and to a lesser extent on time of day and season of year), being lower in the auroral zone than at lower latitudes. The maximum frequency is also lower at higher satellite altitudes. The maximum frequency determines the spatial resolution obtainable on a magnetic field map. The spatial resolution (for impulses) obtainable at low latitudes for a 100-km satellite altitude (possibly achievable by tethering a small satellite at this altitude to a space vehicle at a higher altitude) is 60 km, while at the auroral zone the obtainable spatial resolution is 100 km. At the higher satellite altitude of 300 km the obtainable spatial resolution is 230 km at low latitudes and 530 km at the auroral zone. At 500-km satellite altitude, the obtainable spatial resolution is 500 km at low latitudes, while maps cannot be made at all for the auroral zone unless the data are selected for “quiet” days.For the lower satellite altitudes, greater spatial resolution can be obtained than at higher altitudes. Furthermore since the crustal geomagnetic field power spectrum is larger at lower altitudes, the relative error due to the natural noise is less than for higher altitudes.     

Spatial features of the manifestation of the geomagnetic field westward drift

The specific features of the spatial structure and time dynamics of the main geomagnetic field during the 20th century, proceeding from the present-day concepts of geomagnetic jerks have been studied. The variations, caused by global dissipation of the geomagnetic field dipole part, have been separated from the regional variations, described by nondipole spatial harmonics of the spherical harmonic expansion series. It has been indicated that the geomagnetic field westward drift manifests itself in a limited region of the Earth’s surface, forming the known Brazil anomaly. However, the drift component in the variations in the geomagnetic field morphological structures is globally found out during the considered almost 100-year period along the narrow belt around the geomagnetic axis. However, this drift is northwestward in the Northern Hemisphere, and the structures drift southeastward in the Southern Hemisphere. The detected variations of the drift nature are reflected in the variations in the integral geomagnetic characteristic, when changes in the position of the Earth’s magnetic center are considered. The direct correlation between the global geomagnetic variations of the drift nature and the trend variations in the orientation of the vector of the Earth daily rotation velocity has been detected.     

不同卫星轨道高度对地壳磁场反演的影响研究

利用最新的波茨坦地磁场球谐模型（Potsdam Magnetic Model of the Earth,POMME）进行仿真实验,分别模拟出不同卫星轨道高度下的磁测数据.根据仿真的观测数据反演地壳磁场的高斯球谐系数,对反演结果进行对比和分析,总结出卫星轨道高度对反演结果的影响.针对CHAMP卫星实测数据进行地壳磁场反演,由不同轨道高度磁测数据反演得到的磁场（Magnetic Field,MF）系列模型,验证卫星轨道高度对反演的影响,从而为磁测卫星系统设计论证指标中的卫星轨道高度设计提供一定的参考和指导.

     

Spatial field structure and polarization of geomagnetic pulsations in conjugate areas

The ultra-low-frequency (ULF) geomagnetic pulsations observed at two nearly conjugate mid-latitude sites are examined to study their spatial structure and polarization, and learn about the role of ionospheric conductivity in forming their ground signatures. The data of 1999–2002 from Antarctica and New England (L of 2.4) are compared with the numerical results obtained in a simple plane model of ULF wave propagation through the ionosphere and atmosphere. The multi-layered model environment includes an anisotropic and parametrically time-dependent ionosphere, a uniform magnetosphere and a conducting Earth, all placed in a tilted geomagnetic field. The measured diurnal and seasonal variations in the orientation angle of the polarization ellipse are interpreted as effects of hydromagnetic wave propagation through the ionosphere and conversion to an electromagnetic field below. Essentially, the phase, amplitude and polarization of ULF waves observed at the ground are controlled by the wave's spatial structure in the magnetosphere and ionospheric transverse conductivities. The differences shown by the characteristics of simultaneous pulsations in conjugate areas arise mainly from different local ionospheric conditions, while the source waves of the pulsations are common to both sites.     

地磁正常场的选取与地磁异常场的计算

根据2003年中国地磁观测数据（包括135年地磁测点和35个地磁台）以及我国邻近地区38个IGRF计算点的地磁数据,计算中国地磁异常场的分布。选取两种地磁场模型作为地磁正常场,一是国际参考地磁场的球谐模型,二是中国地磁场泰勒多项式模型。根据各个测点的地磁异常值（观测值减去模型计算值）,用球冠谐分析方法计算地磁异常场的球冠谐模型,并绘制2003年中国地磁异常（△D,△I,△F,△X,△Y,△Z）。分析和讨论了中国地磁异常场。     

地球主磁场空间功率谱的变化特征

根据第8代IGRF模型，计算分析了1900－2000年地球磁场和分量X，Y，Z的空间功率谱的变化特征。结果表明1900－2000年主磁场的空间功率谱呈减小趋势，由功率谱随谐波阶次n的变化关系得出的非偶极子场的等效磁源位于核幔边界附近，而且其位置随时间变化，用n=1,2两阶谐波的谱得到的等效磁源位于地球内核边缘，1900年以来离开地心一直向外增大。     

地磁场水平梯度及高空地磁场的计算与分析

本文以2000.0年中国地区的实测数据为例,首先利用5阶Taylor多项式方法建立了各分量的地磁模型,接着对模型中各分量的纬度和经度进行微分,计算得到各分量的水平梯度值,并绘制了相应分量沿南北方向和东西方向的水平梯度分布图,最后通过Zmuda多项式方法,基于地面模型值以及水平梯度值计算了高空(100 km)的各分量磁场值,并分析了水平梯度分布规律以及各分量随垂直高度的变化.结果表明:地磁场北向分量X、垂直分量Z、总强度F和磁倾角Ⅰ分量的水平梯度主要随纬度变化,其中X、Z和F分量随纬度减少而梯度降低,东向分量y和磁偏角D分量的水平梯度不仅随纬度变化,而且随经度变化,F分量的南北向梯度值在我国中心地区最大.在垂直方向,X、Z和F分量的强度分别随高度的上升而近似线性减小,在100 km高度处,强度变化平均值分别为-4.629 nT/km、-15.368 nT/ km和-16.226 nT/km,y分量强度随高度上升而呈近似线性增加,其平均变化值为0.166 nT/km,而D和Ⅰ分量基本不发生变化.     

Effects of geomagnetic disturbances in power spectra of atmospheric waves in the dynamo region of the ionosphere

The dynamics of wave disturbances in the ionospheric E region in the band of periods of thermal tidal waves and waves of planetary scales (T = 48, 72, and 192 h) has been studied based on the variations in the horizontal component of the geomagnetic field, observed at Paratunka and Barrow observatories in September–October 1999. It has been found that, at midlatitudes during high geomagnetic activity, the intensity of oscillations in the power spectra with T = 24 and 12 h varies with a periodicity of 16 days different from the periodicity of changes in the ΣKp index. The maximal deviations of these periods from the values under quiet conditions coincide with the maximal changes in the ΣKp index. The variations in the 48–192 h band of periods (especially with T ～192 h) intensify simultaneously with increasing geomagnetic activity. The intensity of this harmonic is several times as high as that of the harmonic with T ～ 24 h. The periodicity of changes in the harmonics intensity within the 48–192 h band coincides with the periodicity of changes in the ΣKp index. In the polar ionosphere, the effect of high geomagnetic activity is observed as an increase in the variations with a quasi-period of T ～ 24 h and as an appearance of variations in the 48–192 h band with the periodicity coinciding with the maximums in the ΣKp index variations.     

Steady flows at the top of the core from geomagnetic field models: The steady motions theorem

Abstract

It is demonstrated that the steady tangential velocity v_s at the closed surface δK of a perfect fluid conductor bounded by a rigid, impenetrable exterior can be uniquely determined from knowledge of the normal component of the time varying magnetic flux density B _n, on δK. In the context of a simple earth model consisting of an electrically insulating mantle surrounding a perfectly conducting core, the assumption of steady flow provides enough extra information to eliminate the toroidal ambiguity in B _nv and to allow derivation of a unique, global flow at the top of the core from a model of the geomagnetic field.     

Nonlinear and multifractal approaches of the geomagnetic field

Recent nonlinear dynamics techniques have been developed to analyse chaotic time series data. We first summarize the procedure which gives an appropriate reconstruction of the unknown dynamics from scalar measurements in a pseudophase space. It permits, firstly, the representation of the trajectories of the dynamical system—they define an attractor when the system is dissipative—by preserving its topological properties. We then present the invariant measures and ergodic quantities such as the multifractal spectrum and Lyapunov exponents which can be estimated on the reconstructed attractor. The multifractal analysis provides us with a characterization of the scaling energy of the process whereas the Lyapunov exponent gives another statistical measure of the stability of the dynamics. The estimation of these quantities was tested on synthetic data. The nonlinear and multifractal analyses were finally applied to the hourly mean values of the magnetic field recorded at the Eskdalemuir (ESK) observatory over 79 years (692,520 data measurements for each component). The estimations of a 5-dimensional pseudo-phase space and a positive Lyapunov exponent confirm the possibility of low-dimensional deterministic chaos in the magnetic field observations at ESK observatory. The correlation between the solar activity (the Wolf number), the unstable nature of the magnetic field, and the singularity spectrum points out the forcing of the solar cycles on the dynamics of the magnetic field at ESK observatory.     

Coupled motions of the inner core and possible geomagnetic implications

As the inner core is a good electrical conductor any ambient magnetic field would diffuse into it on a time scale long compared to several thousand years, and conversely be frozen there on shorter time scales. From the observations that the dipole component of the Earth's magnetic field has been inclined persistently to the spin axis over hundreds of thousands of years, and that the dipole drifts and decays significantly more slowly than the nondipole field, it is suggested that the external dipole is simply a manifestation of a field frozen in an inclined inner core. It is shown that the much neglected gravitational restoring torque can be significant for an inclined inner core, so much so that its motion is in the main determined by gravity, with electromagnetic and inertial coupling effects being of secondary importance. A regular precession of the inner core is shown to be possible where its spin axis drifts westward relative to the mantle with a period of ～ 7000 y. Some preliminary calculations of the possible motions of a gravitationally coupled mantle-inner core system are shown.     

利用大地电磁站间阻抗估算磁暴引起的大地电场

由磁暴引起的地下感应电场(geomagnetic induction electric field,GIE)会影响电网的安全稳定运行,GIE的大小取决于磁暴时磁场的变化率和周围地下介质的电性结构.本文利用在地表观测的磁场与电场数据,首先求得频率域实际地下三维大地电磁站间阻抗,再结合磁暴时段的磁场数据,计算GIE的频谱,最后通过傅里叶反变换,得到GIE时间序列.本文以日本地区三个长期观测的电磁电台站为例,讨论了站间阻抗的长期稳定性,并选取一次典型的磁暴事件,对本文方法进行了验证.结果表明,合成的GIE与实测数据基本一致,说明利用大地电磁站间阻抗,结合地磁台站数据,可以高精度合成GIE.本文方法有助于定量评价磁暴发生时产生的GIE对电网可能造成的破坏作用.     

Rock magnetism and the reversal of the geomagnetic field

Summary The present paper deals with the inverse polarization of rocks. At present there are two schools of thought to explain the inverse polarization. On the one hand, it is assumed that the geomagnetic field might have been reversed in those periods, when the rock formations took place. On the other it is advocated that it might be due to some intrinsic property of the rocks. To distinguish between the two theories, the author has studied the thermal demagnetization of a large number of rock samples from the Isle of Mull and has come to the conclusion that the inverse polarization is not due to an intrinsic property of the rocks as suggested byNéel, but to the reversal of the geomagnetic field. Some experimental details are also described in the paper.     

A statistical model of the geomagnetic field

Summary A statistical model of the geomagnetic field is derived, based on the assumption of an axial geocentric dipole field of strengthH _e at the equator perturbed by randomly directed components of constant magnitudeh. The model fits the dispersions found from an analysis of the 1945 field, and the ratioh/H _e obtained for this field and from the palaeomagnetic data both average to about 0.4. The model predicts that during reversal of the dipole field, the field intensity falls to between 0.2 and 0.4 of the steady field intensity, and this agrees with estimates made from the palaeomagnetic observations.     

The fine structure of the geomagnetic field

It was shown in our previous works that the dipole part of the geomagnetic field direction is mainly represented by the 1200-yr variation. According to some indications, the residual of the dipole part of the field, the so-called δ variation, may be classified as standing waves. Average values of δ are calculated for each hemisphere. In this work, the difference values equal to the δ variations for each territory minus δ averages over hemispheres (western or eastern) are calculated. The resulting values, fine structure (FS) variations, characterize the FS of the geomagnetic field. The study of the activity of the FS variations and specific features of their N-S and E-W behavior and the comparative analysis of dynamic characteristics (activity and rate) give grounds to classify the FS variations (as well as the δ variations) as standing waves of the nondipole field.     

海洋地磁三分量测量技术

与拖曳式总场测量相比,海洋地磁三分量测量能够获得更多的地磁场矢量信息,并能通过船载测量在更大海区范围内进行.本文从船载三分量测量和拖曳三分量测量两个方面总结了国外的发展现状,分析了海洋地磁三分量测量中船磁(载体磁场)标定和载体定姿两个关键技术,并结合我国海洋磁测发展现状建议首先发展船载海洋地磁三分量测量系统.     

Long-term variations in geomagnetic and solar activities and secular variations of the geomagnetic field components

Summary After the removal of the eleven-year periodicity, long-term patterns of the aa indices of geomagnetic activity and of Wolf's sunspot numbers are defined. The positions of maxima and minima exhibit the same regularities as the secular variations of the geomagnetic filed components. This result is associated with the motion of the Sun round the barycentre of the solar system.Presented at symposium Planet 88, Tihany, September 1988.