Uniqueness of mainly dipolar magnetic fields recovered from directional data

We show that a knowledge of either the signed or the unsigned direction of a potential field on a given smooth surface S , which separates the space into a volume containing the sources and a volume free of sources, sometimes gives enough information for the whole field to be recovered within the free volume, except for a constant multiplier (positive, for the signed case). We show that the best parameter to be considered on the surface S is the number n of loci where the field is known to be either zero (no direction) or normal to the surface. In the case of sources lying outside S ('external-sources' directional problem) we prove that the dimension of the space of solutions is no larger than n –1. This implies uniqueness for the external-sources directional problem when n = 2. In the case of sources lying inside S ('internal-sources' directional problem), we distinguish fields with monopole sources (such as the gravitational field) from those without monopole sources (such as the magnetic field). For gravitational fields, we show that the dimension of the space of solutions cannot exceed n . We note that the only situation of interest is the one for which n = 1, which implies in practice that the surface S is an isopotential and that the problem has a unique solution. For magnetic fields, we show that the dimension of the space of solutions cannot exceed n –1. It follows that the problem has a unique solution when n = 2. This shows in particular that a geomagnetic field with only two poles (south and north magnetic poles) can be recovered, except for a constant multiplier (positive, for the signed case) from directional data gathered at the Earth's surface. Finally, we note that our results are not restricted to the 3-D space and can readily be extended to two dimensions and higher dimensions.     

Two geomagnetic excursions during the Brunhes chron recorded in Chinese loess-palaeosol sediments

Detailed palaeomagnetic integrated with rock magnetic studies have been carried out on a loess-palaeosol sequence in Baoji, Shaanxi province, southern Chinese Loess Plateau. For most samples stepwise thermal demagnetization revealed two well-defined magnetization components. A low-temperature component (LTC), which was isolated between 100 and 200 °C, is consistent with the present geomagnetic field direction. A high-temperature component (HTC), which was isolated between 250 and 620–680 °C, shows normal, reversed or transitional polarities. Our new magnetostatigraphy revealed two distinct geomagnetic excursions recorded in loess unit of L5 and palaeosol unit of S7, respectively, and the Matuyama-Brunhes (M-B) polarity boundary in loess unit of L8. Rock magnetic experiments demonstrated that the specimens from the excursion zones have the same magnetic properties as those from the Brunhes normal or Matuyama reversed polarity zones. Measurements of anisotropy of magnetic susceptibility (AMS) showed that the sediments have primary sedimentary fabrics. Based on the palaeoclimatological and magnetostratigraphic age models, the middle Brunhes excursion in loess L5 is dated at 413–433 ka, and the early Brunhes excursion is estimated to occur 23–33 ka after the M-B reversal. Comparing with previously reported geomagnetic excursions in the Brunhes chron, the middle Brunhes excursion (L5) is likely global. For the early Brunhes excursion (S7), we need further studies to examine its global occurrence.     

Geomagnetic disturbance fields: an analysis of observatory monthly means

SUMMARY
This work quantifies the extent to which disturbance phenomena contribute to the observed geomagnetic field on the time-scale of months to years. A deterministic approach was adopted in which geomagnetic monthly means were analysed in the time domain. By presupposing the time dependence of the external and induced field variations, which we assume to vary as the aa geomagnetic index, we arrived at an estimate of the relative amplitude of the disturbance to each component of the field at a number of observatories. In all some 58 000 geomagnetic monthly means from 59 observatories operating this century were analysed. Special attention was paid to the selection and validation of the data as otherwise the numerical computations would have been unduly compromised.
The results consist of 177 estimates of the relative amplitude of disturbance, one for each of three orthogonal components north ( X ), east ( Y ) and vertically down ( Z ) at each observatory. The disturbance to the X component was found to be consistently negative over the whole of the Earth's surface with an intensification in auroral regions. The disturbances to the Z component were found to be smaller than that for X except in high latitudes. Mean disturbances to the Y component were smaller still. Results were in general consistent with the dipole field of the magnetospheric ring current, aligned with, though of opposite polarity to, the Earth's main field. Typical amplitudes of the mean disturbance field from month to month were of the order 10 nT.
The results can be used to estimate the variation of the disturbance field. Subtracting this from both monthly and annual means yields an improved estimate of the field originating in the core and its secular variation. Some examples are presented.     

Day-to-day variability of geomagnetic hourly amplitudes at low latitudes

A study of the variability of the amplitude of Sq at a fixed hour from one day to the next at nine stations from the dip equator to about 22° north of it has produced interesting results. The amplitude and sign of the variability change virtually randomly, making the mean practically zero. The variability occurs at all hours of the day. Its magnitudes in the components D, H and Z have the same diurnal variation, which peaks in the noon period like Sq(H) in low latitudes, and a weak seasonal variation that peaks at the June solstice (local summer). It is demonstrated that changes in the current intensities of the equatorial electrojet (EEJ) and the worldwide part of the Sq (W Sq) current layers have contrasting phases and can sometimes be in antiphase. Indeed, the changes are mostly independent. Inclusion of the magnetic element D revealed that the EEJ current system has not only an east–west but also a north–south component. The study shows that the meridional component of the EEJ current intensity evidenced at the Kodaikanal and Annamalainagar stations is an integral part of the zonal component at Trivandrum. This confirms the results of Rastogi (1996 ) and validates those of Onwumechili (1997 ). The results suggest that ionospheric conductivity mainly controls the magnitude, while the electric field and ultimately winds mainly control the phase and randomness of the day-to-day variability of the hourly amplitudes of Sq . The random component is attributed to local and/or regional atmospheric winds, probably of gravity wave origin.     

A physical model for palaeosecular variation

Summary. A new model to describe the latitude dependence of the angular dispersion of the palaeomagnetic field (palaeosecular variation) is developed following previous models, but with crucial differences. It is shown that if the probability distribution of virtual geomagnetic poles (VGPs) is circularly symmétric about the rotation axis then the geométry of the distribution of field directions is latitude dependent. This has a significant effect on the latitude dependence of dispersion and is accounted for in the model. The dipole and non-dipole parts of the field are not artificially separated but are intimately linked through an observationally determined relation that the time averaged intensity of the non-dipole field is dependent upon the intensity of the dipole field. It is shown that a consequence of this relation is that no knowledge of the probability distribution of the geomagnetic dipole moment is required. This is a fundamental improvement over previous models.
The model provides excellent fits to the palaeodata and, unlike previous models, is not inconsistent with the latitude variation of the non-dipole field dispersion determined from the present field. For the past 5 Ma the point estimate of the VGP dispersion due to dipole wobble is 7.2° and of the VGP dispersion at the equator due to variation in the non-dipole field is 10.6°. This estimate of the dispersion due to variation in the non-dipole field is in excellent agreement with the value predicted from an analysis of the variation in field intensities over the same period. Fits of the model to data from earlier periods indicate that dispersion due to variation in the non-dipole field is essentially independent of the geomagnetic reversal rate while dipole wobble is positively correlated with reversal rate.     

Piezomagnetic potentials due to an inclined rectangular fault in a semi-infinite medium

Analytical solutions for the piezomagnetic potentials are derived for strike-slip, dip-slip and tensile-opening fault motions with arbitrary dip and strike angles, so as to be applicable in various types of earthquakes. These solutions are expressed as the composition of elementary functions which are identical to the magnetic potentials produced by magnetic dipoles, quadrupoles and octupoles distributed on the fault plane and other planes. Therefore, the geomagnetic field changes due to the piezomagnetic effect are expressed by the superposition of the fields produced by these equivalent sources.
Examples of calculated results show characteristic features for various types of fault motions as follows: (1) the pattern of the geomagnetic field changes becomes significantly different depending on the strike direction, although the maximum amplitude is almost the same for all directions; (2) the geomagnetic field change reaches a maximum at a dip angle of 90° for strike-slip and tensile-opening fault motions and at 45° for dip-slip fault motion.     

Analysis of S~p_q current systems by using corrected geomagnetic coordinates

The S~p_q equivalent current system of the quiet day geomagnetic variation in the polar region is very complicated. It is composed of several currents, such as the ionospheric dynamo current and the auroral electrojet caused by the field aligned current. S p q is unsymmetrical in both polar regions. In this paper, the S p q current systems are analyzed in the corrected geomagnetic coordinates (CGM) instead of the conventional geomagnetic coordinates (GM), and the symmetries of the S p q current in different systems are compared. Then the causes of S p q asymmetry in the GM coordinates are discussed; the effects of each component in S p q are determined.     

A palaeomagnetic study of fracture fills in the Holy Cross Mountains of Central Poland and its application in dating tectonic processes

Calcite and sedimentary fills in fractures cutting the Upper Devonian carbonates in the Holy Cross Mountains (HCM) were dated palaeomagnetically by comparison with the apparent polar wander path (APWP). Haematite-bearing calcite possessed well-defined components of natural remanent magnetization (NRM), which were preserved under thermal demagnetization to temperatures of approximately 500 °C, when specimens disintegrated. Although not completely demagnetized, some specimens revealed a stable NRM component before destruction, thus making a component analysis possible. Five components were determined using density point distribution and cluster analysis. One has a mean that is similar to the present-day local geomagnetic vector. The remaining four components yielded palaeomagnetic poles located at: A (70.3°S, 5.5°E), B (71.3°S, 31.2°E), C (48.7°S, 351.0°E, virtual geomagnetic pole), and D (11.6°S, 312.3°E). Antipodal polarities found in the fracture fills, together with dissimilarities in magnetization found in calcite and hosting carbonates, indicate the lack of simultaneous remagnetization, and different times of remanence acquisition for the rocks under comparison. Taking both palaeomagnetically inferred palaeolatitudes and regional tectonics into consideration, a Mesozoic (Cretaceous?) age is estimated for palaeopoles A and B, a Permian age for pole C, and a Carboniferous age for pole D. These age determinations are in line with the calcite ages estimated from isotopic studies. A comparative palaeomagnetic study performed on a well-dated Upper Devonian neptunian dyke of limestone and a Lower Triassic clastic vein yielded virtual geomagnetic poles (VGPs) close to the APWP for Baltica. Generally, the remanence from fracture fills may be useful for dating related tectonics, karst phenomena and mineralization processes.     

A geomagnetic scattering theory for evaluation of earth structure

Summary. Structural features of the Earth's lower crust and upper mantle can be mapped by the analysis of temporal geomagnetic fluctuations using the electromagnetic scattering theory developed in this paper. Decomposing geomagnetic field fluctuations at the Earth's surface into an excitation part and a scattered part forms the basis of a power series development. The vertical field component is interpreted as a scattering of the excitation field. The horizontal gradient and geomagnetic depth sounding methods are special cases of the theory developed. The horizontal gradient sounding method has a tensorial aspect which has not been recognized before; it should be included to obtain correct penetration depth parameter evaluations from field data.     

Palaeomagnetism of the Proterozoic Zig-Zag Dal Basalt and the Midsommersø Dolerites, eastern North Greenland

Summary. Palaeomagnetic investigations are reported from 24 sites in the Proterozoic Zig-Zag Dal Basalt Formation and 12 sites in the Midsominersø Dolerites of eastern North Greenland. The Zig-Zag Dal Basalt is a typical tholeiitic flood basalt sequence, and dolerite intrusions in the underlying sandstones are thought to be genetically related to the basalts.
After a detailed AF demagnetization programme 19 sites in the basalts and 10 sites in the dolerites reveal one stable component of magnetization, probably of TRM and/or CRM origin residing in small single domain titano-magnetite grains. The degree of anisotropy has not affected the direction of the remanent magnetization. The maximum axis of the anisotropy ellipsoid is parallel to the flow direction of the magma, whereas the minimum axis is perpendicular to the flow plane.
Only one polarity of the geomagnetic field was found. The mean palaeomagnetic pole positions for the two rock types are not significantly different (basalt: 12.2°S, 62.8°E with A ₉₅= 3.8°; dolerites: 6.9°S, 62.0°E with A ₉₅ = 5.1°). After correction for Phanerozoic drift of Greenland the two mean poles compare closely to a relevant North American APW-curve for 1250–1350 Ma, in good agreement with Rb-Sr isochron ages of 1250 Ma obtained for the intrusives. The palaeogeographical position of Greenland was near equator with the major geographical axis orientated E-W.     

甘肃黄土高原春旱的气候特征及预测方法

利用甘肃黄土高原55个气象站在1968-2000年间的春季降水、气温资料, 计算了春季干湿指数, 划分了春旱标准, 用REOF方法进行了气候分区, 分析了其时空分布特征和变化规律, 计算了其与欧亚500hPa高度场、赤道北太平洋海温和高原加热场的相关关系, 建立了甘肃黄土高原春旱的均生函数预测模型。结果表明, 干旱有三个高发区, 频率为36%~57%, 约2~3年一遇, 且有增加的趋势。春旱与当年高原500hPa高度场、赤道北太平洋海温及上年盛夏高原加热场呈正相关, 与前期冬季高原加热场呈负相关, 所建立的预报模型有一定的预报能力。     

Geomagnetic evidence for fluid upwelling at the core-mantle boundary

Summary. Previous studies, both geomagnetic and seismic, have been unable to show conclusively whether or not there is fluid upwelling at the core-mantle boundary. Here a new method is developed, in which an attempt is made to invert geomagnetic secular variation data measured at the Earth's surface for a frozen-flux purely toroidal core-mantle boundary (CMB) velocity field, under the assumption that the mantle is electrically insulating and flux is frozen in at the CMB. These data have previously been inverted for the core-mantle boundary radial secular variation, from which the appropriate fit between model and data is known. Two different main field models were used to assess the effect of uncertainty in its radial component at the CMB. The conclusions were the same in both cases: frozen-flux purely toroidal motions provide a poor fit. A statistical test allows very firm rejection of the hypothesis that the residuals are not significantly larger, whereas there is no statistical difference between the residuals of inversions for radial secular variation and frozen-flux velocity fields at the CMB if upwelling and down-welling is included. The inherent non-uniqueness in the velocity field obtained is not of concern, since only their statistical properties are utilized and no physical significance is attached to the flows obtained.     

Taking into account truncation problems and geomagnetic model accuracy in assessing computed flows at the core-mantle boundary

SUMMARY
Since the time Roberts & Scott (1965) first expressed the key 'frozen flux' hypothesis relating the secular variation of the geomagnetic field (SV) to the flow at the core surface, a large number of studies have been devoted to building maps of the flow and inferring its fundamental properties from magnetic observations at the Earth's surface. There are some well-known difficulties in carrying out these studies, such as the one linked to the non-uniqueness of the flow solution [if no additional constraint is imposed on the flow (Backus 1968)] which has been thoroughly investigated. In contrast little investigation has been made up to now to estimate the exact importance of other difficulties, although the different authors are usually well aware of their existence. In this paper we intend to make as systematic as possible a study of the limitations linked to the use of truncated spherical harmonic expansions in the computation of the flow. Our approach does not rely on other assumptions than the frozen flux, the insulating mantle and the large-scale flow assumptions along with some simple statistical assumptions concerning the flow and the Main Field. Our conclusions therefore apply to any (toroidal, steady or tangentially geostrophic) of the flow models that have already been produced; they can be summarized in the following way: first, because of the unavoidable truncation of the spherical harmonic expansion of the Main Field to degree 13, no information will ever be derived for the components of the flow with degree larger than 12; second, one may truncate the spherical harmonic expansion of the flow to degree 12 with only a small impact on the first degrees of the flow. Third, with the data available at the present day, the components of the flow with degree less than 5 are fairly well known whereas those with degree greater than 8 are absolutely unconstrained.     

Local time variation of geomagnetic transfer functions

The local time (LT) variation of the geomagnetic transfer function at the 32-min period was examined for observatories distributed worldwide. Two distinct variation types (types 1 and 2) were found in the real part of A. Type 1 is conspicuous at lower latitudes and its seasonal variation is small, whereas type 2 is found at higher latitudes and has its maximum in summer. These two types of LT variation are seen globally and are conspicuous when solar activity is high. The amplitudes of both types of variation vary from 0.018 to 0.078, and are independent of the mean values at each observatory. These values are relatively small, but the amplitude of Chambon la Foret is larger than the mean value, which shows that Au changes its sign in local time. The amplitudes of type 1 and 2 variations decrease and increase with geomagnetic latitude, respectively. These features suggest that they are generated by some global external fields. The most probable cause is the Sq field, although the Dp field may contribute to type 1 variation. On the other hand, for the islands of the Pacific Ocean at low latitudes, such as Honolulu and Chichijima, the type 1 variation appears not in the real but in the imaginary part of A, which suggests that currents induced in the ocean also contribute to the local time variation.     

The change in Sq(H) amplitude on Abnormal Quiet Days

Summary. Analysis of geomagnetic data has shown that the superposed northward magnetic field, which reduces the S _q( H ) amplitude at northern mid-latitude stations on Abnormal Quiet Days, and increases the amplitude at stations on the equatorward side of the S _q focus, builds up in amplitude over four to five days before the AQD occurs, and subsides over a similar period after the AQD. It is inferred indirectly that the azimuthal component B_y of the interplanetary magnetic field varies similarly. Data for the opposite meridian show that the imposed field reverses to a southward direction at lower latitudes. The inferred currents to account for these fields are believed to flow in the ionosphere, but to arise from magnetospheric electric fields induced by the solar wind-transported IMF.     

Significance of the sign changing of the imaginary arrows in geomagnetic induction investigation

Summary. In this investigation, we carry out a two-dimensional study of the dependence of the imaginary Parkinson arrows on the frequency of the inducing geomagnetic field. Our results demonstrate that the imaginary arrows reverse direction as the inducing period varies. Therefore, we consider that there is no way to fix a consistent sign convention for the imaginary arrows even when the time factor is taken into account. We find that in the twodimensional case there exists a characteristic period T _c at which the phase difference between the vertical and horizontal magnetic components is zero. It is anticipated that T _c is related to the parameters of the conductivity anomaly and the status of the half-space host.     

Observation of electric currents in the Alaska oil pipeline resulting from auroral electrojet current sources

Summary. Currents in the 1.28 × 10³ km Alaska oil pipeline, induced from the ionospheric, auroral electrojet, were measured at three sites, near Fairbanks, Paxson and Valdez, Alaska, using a gradient configuration of two fluxgate magnetometers. The observed pipeline current magnitudes, which reached 50 A during times of mild geomagnetic activity, displayed a linear relationship with the electric earth potential. Using the induction relationship between the electric and magnetic fields and the typical spectral composition of the geomagnetic field at high latitudes, I obtained a spectral appearance of the current that shows a maximum in the range of 4.5- to 10-min period. Near Fairbanks the pipeline current amplitudes, I (Amperes), could be represented, approximately, by I = 0.65 B _x T ^−0.5, where B _x(nT) is the north—south geomagnetic field variation amplitude and T (min) is its apparent period. There is much less pipelines current at the sites south of Fairbanks. A previously established relationship between the local electric field and the planetary geomagnetic activity index, Ap , permitted a prediction of the pipeline current surge amplitudes in the Fairbanks region as approximately I = 5.0 Ap . Current surges larger than 500 A may be expected rather often in the Alaska pipeline during large geomagnetic storms.     

Geomagnetic field analysis - I. Stochastic inversion

Summary. Most of the Earth's magnetic field and its secular change originate in the core. Provided the mantle can be treated as an electrical insulator, stochastic inversion enables surface observations to be analysed for the core field. A priori information about the variation of the field at the core boundary leads to very stringent conditions at the Earth's surface. The field models are identical with those derived from the method of harmonic splines (Shure, Parker & Backus) provided the a priori information is specified appropriately.
The method is applied to secular variation data from 106 magnetic observatories. Model predictions for fields at the Earth's surface have error estimates associated with them that appear realistic. For plausible choices of a priori information the error of the field at the core is unbounded, but integrals over patches of the core surface can have finite errors. The hypothesis that magnetic fields are frozen to the core fluid implies that certain integrals of the secular variation vanish. This idea is tested by computing the integrals and their standard and maximum errors. Most of the integrals are within one standard deviation of zero, but those over the large patches to the north and south of the magnetic equator are many times their standard error, because of the dominating influence of the decaying dipole. All integrals are well within their maximum error, indicating that it will be possible to construct core fields, consistent with frozen flux, that satisfy the observations.     

Study and observation of the great solar event in July 2000 at cusp latitude

A series of solar flare and coronal mass ejection (CME) event occurred in July 2000, particularly the largest flare (X5.7/3B) with CME on 14th of July since 1989, which stimulated a great geomagnetic storm with D st index reaching -300 nT. A number of data have been obtained from the Chinese Antarctic Zhongshan Station (ZHS, INT Lat. 74.5°, L≈14), which is located at cusp latitude, and from the ACE satellite. After analyzing these data we have got the results as follows: a lot of solar high energy particles penetrated into the polar ionosphere and ionized it, which significantly increased the cosmic noise absorption (CNA) and blanked the DPS-4 data for more than two days. The magnetic pulsation in Pc 3/5 frequency band on the ground has a high relation with the fluctuation of interplanetary magnetic field (IMF) B z, which shows the contribution of interplanetary magnetohydrodynamical (MHD) waves to the Pc 3/5 pulsation on the ground. The Pc 3/5 pulsation was intensified much during the great magnetic storm. The H component of the magnetic field at ZHS varied with the southern value of IMF B z but lagged behind for about 8 10 h. While D st index responded to the variation of the IMF B z very quickly, which suggested that the magnetic storm occurred at low latitude firstly and then effected the ionospheric current at high latitude.     

南极布兰斯菲尔德海峡沉积物的地磁场长期变与定年

对位于布兰斯菲尔德海峡东北部的沉积物岩心D1-7进行了初步环境磁学和古地磁研究,获得了连续的相对地磁场强度和方向。沉积物岩性总体为灰色软塑性粘土,中下部出现一层黑色火山灰层。结合该孔沉积物和有孔虫AMS¹⁴C测年结果（王汝建等未发表资料）,相对地磁场强度及其方向提供了12 ka以来连续的定年标尺,其中相对地磁场强度与具有相似沉积速率的南美Laguna Potrok Aike湖泊记录对比提供了六个对比点;同时特征剩磁倾角和磁偏角提供了另外六个对比点。磁化率各向异性分析揭示了全新世早、中和晚期岩心所在位置底流（南极深层水~1000 m）发生了阶段性显著变化,同时磁性矿物含量、粒度、沉积物湿密度等也发生了相应的变化。这些环境磁学和沉积学的变化主要受控于南极相应纬度处的太阳辐射量以及与辐射量相关的夏季季风降水量的变化,降水量增加导致磁性矿物粒度变细。D1-7也记录了一些千年尺度旋回变化,但是南极地区目前缺乏与之相似分辨率的气候参数记录,无法进一步探讨这些气候事件的缘起和分布范围。对比发现,地磁场长期变产生的年龄与沉积物全样有机碳AMS¹⁴C测年结果之间存在系统的差异,在6 ka以来比有机碳年龄年轻,在6 ka之前则比有机碳年龄老。南极布兰斯菲尔德海峡内各种不同水体的混合以及在全新世全球升温背景下冰川的动态变化和由此引起的中、深层水变化,都是造成水体性质复杂的原因。而地磁场强度和方向变化则不受水体性质的影响,因此可以提供更合理的年龄信息。自12 ka至今,25 cm/ka的平均沉积速率表明南极布兰斯菲尔德海峡地区整个全新世内稳定和丰富的沉积物供应。