地球主磁场模型

主磁场建模是一项综合性的研究工作,它涉及主磁场理论、磁场测量、数据同化、模型表达、模型解释以及模型运用等多方面的研究.本文综述了近五十年来德国、丹麦和美英各国研究者提出的数十个地球主磁场模型,回顾了主磁场模型研究方面的进展,概述了模型的描述以及建模的理论基础和方法.     

Dynamic geomagnetic field models

A review of modern dynamic models of the Earth’s magnetosphere (the A2000 paraboloid model and Tsyganenko’s T01 model) is presented. For the magnetic storm of January 9–11, 1997, the results of joint calculations of the magnetospheric magnetic field are presented and contributions of the large-scale magnetospheric currents to the D _st variations are analyzed. Both models were shown to be well consistent with measurement data; the contribution of the magnetotail current system to D _st is comparable to the contribution of the ring current. At the same time, the relative dynamics of magnetospheric current systems are different in different models. The differences in the magnetic field variation profiles for various current systems calculated by the A2000 and T01 models are explained by model parameterizations.     

A theoretical analysis of the observed variability of the geomagnetic dipole field

We present a detailed analysis of the Sint-800 virtual axial dipole moment (VADM) data in terms of an Ω mean field model of the geodynamo that features a non-steady generation of poloidal from toroidal magnetic field. The result is a variable excitation of the dipole mode and the overtones, and there are occasional dipole reversals. The model permits a theoretical evaluation of the statistical properties of the dipole mode. We show that the model correctly predicts the distribution of the VADM and the autocorrelation function inferred from the Sint-800 data. The autocorrelation technique allows us to determine the turbulent diffusion time τ_d=R²/β of the geodynamo. We find that τ_d is about 10–15 kyr. The model is able to reproduce the observed secular variation of the dipole mode, and the mean time between successive dipole reversals. On the other hand, the duration of a reversal is a factor 2 too long. This could be due to imperfections in the model or to unknown systematics in the Sint-800 data. The use of mean field theory is shown to be selfconsistent.     

地磁长期变化信号提取和模型预测精度评估

高精度地磁场信息在地球物理导航等领域有着广泛应用,一般依靠地磁场模型来预测未来磁场的时空状态变化特征.本文基于中国大陆10个地磁基准台站2009—2022年的连续矢量观测数据,通过月均值年差分和主成分分析方法剔除外源干扰场,进一步去除岩石圈磁场,提取得到了主磁场长期变化信号,并将其与IGRF和WMM系列主磁场模型结果进行对比.通过引入绝对误差、均方根误差等指标,定量评估了IGRF-12和WMM2015模型在中国大陆区域内1—5年尺度的预测精度.结果表明,IGRF-12和WMM2015模型均能总体反映我国大陆主磁场长期变化趋势,两者总场强度的5年均方根误差分别为54.19 nT和15.86 nT,WMM2015模型预测的7个地磁要素的精度均优于IGRF-12.模型误差会随时间逐渐增大,两模型总场强度的1年期最大误差为13 nT,5年期最大误差可达153.65 nT,难以满足高精度定向钻井等领域的地磁导航需求,因此,有必要结合地磁台等观测资料,研制年周期地磁场快速长期变化模型.

     

The deviation of the total geomagnetic field direction from the dipole field direction as a manifestation of the non-dipole field

Summary The angle between the total geomagnetic field direction and the axial dipole field direction was computed for the whole of the Earth's surface for the epoch 1945. It was supposed that the dipole field exerts a latitude-dependent influence on the surface manifestation of the non-dipole field. A modifying function of latitude was estimated to eliminate this influence. The isolines of the resulting quantity were plotted.     

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。     

Spatial power spectra of the crustal geomagnetic field and core geomagnetic field

Lowes (1966, 1974) has introduced the function R_n defined by $\text{R}{}^{\mathrm{n}}\text{=(n + 1)}\text{∑}\text{m=0}\text{∞}\text{[(g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{+ (h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{]}\text{where}\text{g}{}_{\mathrm{n}}{}^{\mathrm{m}}\text{and}\text{h}{}_{\mathrm{n}}{}^{\mathrm{m}}$ are the coefficients of a spherical harmonic expansion of the scalar potential of the geomagnetic field at the Earth's surface. The mean squared value of the magnetic field B = ??V on a sphere of radius r > α is given by $\text{〈}\text{B}\text{·〉 =}\text{∑}\text{n=1}\text{∞}\text{R}{}^{\mathrm{n}}\text{(}\text{a/}\text{r}\text{)}{}^{\mathrm{2n=4}}\text{where}\text{a}$ is the Earth's radius. We refer to R_n as the spherical harmonic spatial power spectrum of the geomagnetic field.In this paper it is shown that Rⁿ = R^M_n = R^C_n where the components R_n^M due to the main (or core) field and R_n^C due to the crustal field are given approximately by $\text{R}{}^{\mathrm{M}}{}_{\mathrm{n}}\text{= [}\text{(n =1)/}\text{(n + 2)}\text{](1.142 × 10}{}^9\text{)(0.288}{}^{\mathrm{n}}\text{Λ}{}^2\text{R}{}^{\mathrm{C}}{}_{\mathrm{n}}\text{= [}\text{(n =1){[1 — exp(-n/290)]/}\text{(n/290)} 0.52 Λ}{}^2\text{where}\text{Iγ = 1 nT}$. The two components are approximately equal for n = 15.Lowes has given equations for the core and crustal field spectra. His equation for the crustal field spectrum is significantly different from the one given here. The equation given in this paper is in better agreement with data obtained on the POGO spacecraft and with data for the crustal field given by Alldredge et al. (1963).The equations for the main and crustal geomagnetic field spectra are consistent with data for the core field given by Peddie and Fabiano (1976) and data for the crustal field given by Alldredge et al. The equations are based on a statistical model that makes use of the principle of equipartition of energy and predicts the shape of both the crustal and core spectra. The model also predicts the core radius accurately. The numerical values given by the equations are not strongly dependent on the model.Equations relating average great circle power spectra of the geomagnetic field components to R_n are derived. The three field components are in the radial direction, along the great circle track, and perpendicular to the first two. These equations can, in principle, be inverted to compute the R_n for celestial bodies from average great circle power spectra of the magnetic field components.     

Multipole models of the geomagnetic field: Construction of the Nth approximation

The fact that the geomagnetic potential, as well as magnetic induction and its gradient, can be represented with an arbitrary accuracy in the scope of multipole models has been justified programmatically and analytically. The obtained expressions are brief and can be utilized in analytical and computer-based studies using methods of computer algebra and numerical computations. Previously unknown analytical expressions for the components of the first seven multipole tensors, expressed in terms of the Gaussian coefficients, have been obtained for applied problems of space dynamics. An algorithm that makes it possible to construct analytical expressions for the arbitrary-order multipole tensor and magnetic induction vector components in any finite approximation has been developed.     

Intermittence and peculiarities of a statistic characteristic of the geomagnetic field in geodynamo models

The analysis of the statistical characteristics of the geomagnetic field generated in the numerical geodynamo models has shown that the distribution of the spherical harmonic coefficients in some cases is not Gaussian but, instead, has much in common with the Laplace distribution. The shape of the corresponding histograms depends on the time scale, which allows interpreting the obtained data in terms of a mixture of Gaussian distributions. The similar effects associated with the intermittence were observed in the experiments in a turbulent fluid flow. Hence, the behavior of secular variations in the magnetic field of the Earth should perhaps be described in terms of a mixture of several Gaussian stationary processes corresponding to switching between the different regimes of geodynamo generation.     

Anomalies in the secular variations in the main geomagnetic field in the context of the hierarchic dipole model

The developed dynamic model of the main geomagnetic field (MGF) includes the sources of three levels, which have existed and continuously changed during the 100-year period. The spatial-temporal dynamics of the secular variations in MGF has been considered based on this model. It has been indicated that, at different times, the formation of anomalies (located in similar regions) depended on the total dynamics of different combinations of sources, including a change in the parameters of the dipoles of the secondorder smallness. Anomalies generated by the dynamics of the dipoles of the third-order smallness do not evidently manifest themselves in the total secular variations but are responsible for the specific shapes of isodynamic lines. Based on the stability and continuity of the constructed model, the conclusion is made that long-living turbulent flows of different scales can exist in the liquid core.     

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.     

Some models of the geomagnetic field in western Europe from 1960 to 1980

Achache et al.'s averages over 10 west European observatories of the annual mean magnetic components X, Y, Z are studied from 1953 to 1979. A 1970 jerk is fitted to the data by least squares, and the fit is quantitatively compared with that of a polynomial having the same number of free parameters as the jerk (a quintic). A crude correction for the 11-y sunspot cycle is also attempted. The jerk and quintic are equally good fits to X, the jerk is clearly better for Y, and the quintic is modestly better for Z. The jerk amplitudes of X and Z but not Y depend heavily on whether a sunspot correction is made, and such a correction may be required to estimate the energy of the internal part of the jerk in the manner of Malin and Hodder. The sunspot correction to Y probably cannot be brought above the noise because it is small and highly correlated with both the jerk and the quintic. The sunspot corrections to X and Z are statistically significant but depend on whether the core signal is taken as a jerk or a quintic. Courtillot and Le Mouël's physical model for the jerk predicts that the jerk amplitudes of X, Y, Z will be proportional to the longitudinal derivatives of X, Y and Z. This prediction is roughly verified for the magnitudes but not the signs; it is just possible that the signs in X and Z are not statistically significant.     

过去2000年以来地磁偶极子的长期变化

利用地磁场模型资料,计算和分析了公元0～2000年的地磁场偶极子磁矩和地磁北极位置的长期变化。结果表明:过去2000年中,地磁场的偶极子磁矩并非一直减小,有近400年的时间是持续增长的。地磁北极位置的移动并不均匀,在纬度方向的变化范围只有10°左右,经度方向变化有255°。     

时空统一的三维中国地磁场模式应用初步研究

利用１９５０．０，１９６０．０，１９７０．０，１９８０．０，１９９０．０等年代的地磁资料，建立了时空变量统一的三维中国地磁基本场模式。结果表明，所建立的时空变量统一的三维中国地磁基本场模式是成功的，可行的。本文还以此模式场作为正常场，计算出１９７０．０年中国地磁异常场，并把地磁异常与地质构造（岩性分布）相比较，发现两者有着密切的关系。     

The palaeogeomagnetic field strength,variations in reversal frequency,and geomagnetic dynamo models

Abstract

The geomagnetic field and its frequent polarity reversals are generally attributed to magnetohydrodynamic (MHD) processes in the Earth's metallic and fluid core. But it is difficult to identify convincingly any MHD timescales with that over which the reversals occur. Moreover, the geological record indicates that the intervals between the consecutive reversals have varied widely. In addition, there have been superchrons when the reversals have been frequent, and at least two, and perhaps three, 35-70 Myr long superchrons when they were almost totally absent. The evaluation of these long-term variations in the palaeogeophysical record can provide crucial constraints on theories of geomagnetism, but it has generally been limited to only the directional or polarity data. It is shown here that the correlation of the palaeogeomagnetic field strength with the field's protracted stability during a fixed polarity superchron provides such a constraint. In terms of a strong field dynamo model it leads to the speculation that the magnetic Reynolds number, and the toroidal field, increase substantially during a superchron of frequent reversals.     

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.     

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.