顾及多方向观测值权比反演地球重力场的动力积分法

考虑到不同坐标系下各个方向观测值对反演地球重力场的频谱贡献不同,建立了顾及多方向观测值权比的动力积分法,并利用该方法反演了高精度的GOCE HL-SST卫星重力场模型.首先,分析了不同坐标系下各个方向观测值与地球重力场信息的响应关系,其中惯性系(IRF)下X、Z方向的观测值分别对扇谐系数、带谐系数最为敏感,Z方向的解算精度在全频段均略高于X、Y方向;地固系(EFRF)下各个方向的独立解算精度均与能量守恒法的解算精度相当;局部指北坐标系(LNOF)下X、Z和Y三个方向的解算精度依次递减,且Y方向在47阶附近有明显"驼峰"现象.其次,比较了不同坐标系下顾及三个方向观测值权比的加权解算模型,其中加权联合解算模型精度在20至70阶次均明显优于等权解算模型,在带谐项和共振阶次精度提升明显,且LNOF下的加权联合解算精度要优于IRF和EFRF.最后,比较了GOCE和CHAMP卫星的模型解算精度,采用本文计算方法,仅利用2个月GOCE轨道观测值解算的模型精度优于包含更长观测时段信息的AIUB-CHAMP01S和EIGEN-CHAMP03S模型,且略优于ASU-GOCE-2months模型.     

Forward computation of the magnetic field of a 3D body with arbitrary boundary and continually varying magnetization

The forward computation of the gravitational and magnetic fields due to a 3D body with an arbitrary boundary and continually varying density or magnetization is an important problem in gravitational and magnetic prospecting. In order to solve the inverse problem for the arbitrary components of the gravitational and magnetic anomalies due to an arbitrary 3D body under complex conditions, including an uneven observation surface, the existence of background anomalies and very little or no a priori information, we used a spherical coordinate system to systematically investigate forward methods for such anomalies and developed a series of universal spherical harmonic expansions of gravitational and magnetic fields. For the case of a 3D body with an arbitrary boundary and continually varying magnetization, we have also given the surface integral expressions for the common spherical harmonic coefficients in the expansion of the magnetic field due to the body, and a very precise numerical integral algorithm to calculate them. Thus a simple and effective method of solving the forward problem for magnetic fields due to 3D bodies of this kind has been found, and in this way a foundation is laid for solving the inverse problem of these magnetic fields. In addition, by replacing the parameters and unit vectors in the spherical harmonic expansion of a magnetic field by gravitational parameters and a downward unit vector, we have also derived a forward method for the gravitational field (similar to that for the magnetic case) of a 3D body with an arbitrary boundary and continually varying density.     

The contribution of magnetospheric currents toSq

Since the discovery of the magnetosphere, it has been known that the currents flowing in the magnetosphere contribute toSq, the regular daily variation in the earth's surface magnetic field. The early models, however, were not very accurate in the vicinity of the earth. The magnetospheric contribution toSq has therefore been recalculated by direct integration over the three major magnetospheric current systems; magnetopause, tail and ring. The finite electrical conductivity of the earth, which increases the horizontal and decreases the vertical components of the magnetospheric field at the earth's surface, has been taken into account. The magnetospheric currents are found to contribute 12 nanotesla to the day to night difference in the mid-latitudeSq pattern for steady, quiet magnetospheric conditions. They also contribute to the annual variation in the surface field and must be considered an important source of the observed day to day variation in theSq pattern.     

Polar regionSq

Geomagnetically quiet day variations in the polar region are reviewed with respect to geomagnetic field variation, ionospheric plasma convection, electric field and current. Persistently existing field-aligned currents are the main source of the polar regionSq. Consequently, the morphology and variability of the polar regionSq largely depend upon both field-aligned currents and ionospheric conductivity. Since field-aligned currents are the major linkage between the ionosphere and the magnetosphere, the latter is controlled by solar wind state, in particular, the interplanetary magnetic field, the polar regionSq exhibits remarkable IMF dependence.     

Comparison of the sector and conventional spherical harmonic analyses of the solar magnetic field on the photosphere,source surface,and in the Earth’s orbit on July 10–20, 2004

The results of a spherical harmonic analysis and a sector spherical harmonic analysis of the solar magnetic field on the photosphere, source surface, and in the Earth’s orbit on July 10–20, 2004, were compared. It was found that the field values according to a sector harmonic analysis are an order of magnitude as large as the same values according to a spherical harmonic analysis and differ in the configuration. A twocomponent magnetic field structure was revealed: short-range sources are better described by a sector spherical harmonic analysis; long-range sources are better described by a spherical harmonic analysis. This is caused by the different depths of the occurrence of sources below the photosphere.     

The upper mantle conductivity analysis method using observatory records of the geomagnetic field

The electrical conductivity of the Earth's upper mantle can be inferred from geomagnetic quiet-day,Sq, variations recorded at the world's observatories using the, coefficients of a spherical harmonic analysis (SHA) that separate the external (source) and internal (induced) parts of the surface field. The conductivity profile determined from such an analysis can be sensitive to special characteristics of the quiet field itself as well as the separation techniques employed. This review of the Sq-analysis features critical to a conductivity derivation is pictorially presented along with the equations for application of theSchmucker (1970) technique to theSHA coefficients for a conductivity determination. Three examples illustrate the use of these equations with differentSq models.     

On the Spectral Decomposition of Geopotential and Temperature Fields in the Stratosphere

The spectral structure of stratospheric fields (temperature and geopotential) is analyzed in terms of spherical harmonics in an effort to study the long-term behaviour of large-scale circulation patterns, as well as their connections to some extra-terrestrial effects. The daily meteorological data from the Free University Berlin (FUB) cover more or less the period 1976–1996 and are available for stratospheric levels of 50, 30 and 10 hPa. The analysis of the annual cycle of spherical harmonics is introduced, and changes of the principal wave components are compared with the changes in different sets of solar, geomagnetic and global circulation indices. This paper also deals with interannual variability with special emphasis on quasibiennial oscillations (QBO) and El Nino and Southern Oscillations (ENSO). Although this is a rather preliminary study, the decomposition of the stratospheric field into complex spherical harmonics seems to be a powerful technique in investigating and qualifying the response of the global atmospheric system to the changes in solar and geomagnetic activity, and in qualifying the relationships between large-scale circulation patterns and various oscillations such as QBO or ENSO, Using this technique, reasonable strong connections were found between wave numbers and interannual factors, and these connections were tentatively interpreted in terms of statistics. A very high degree of correlation was found for the four-trough shape of the polar vortex.     

欧洲及其邻区MAGSAT卫星磁异常冠谐模型

通过对欧洲及其邻近地区 MAGSAT 卫星黎明资料进行了处理,得到1°×1°卫星磁异常网格值。本文使用冠谐分析方法,计算该地区卫星矢量磁异常（ΔX,ΔY,ΔZ）冠谐模型。球冠极点位于33°N和26°E,球冠半角为40°.冠谐模型的截断指数为18。根据卫星磁异常冠谐模型和地磁场球谐模型 DGRF1980,计算卫星总强度磁异常（ΔF）的冠谐一球谐模型。根据卫星磁异常的理论模型,计算并绘制不同高度（300,400,500km）的理论卫星磁异常图。对冠谐模型和大磁异常进行了分析和讨论。     

Inversion of potential field data using the structural index as weighting function rate decay

Nonparametric inverse methods provide a general framework for solving potential‐field problems. The use of weighted norms leads to a general regularization problem of Tikhonov form. We present an alternative procedure to estimate the source susceptibility distribution from potential field measurements exploiting inversion methods by means of a flexible depth‐weighting function in the Tikhonov formulation. Our approach improves the formulation proposed by Li and Oldenburg (1996, 1998) , differing significantly in the definition of the depth‐weighting function. In our formalism the depth weighting function is associated not to the field decay of a single block (which can be representative of just a part of the source) but to the field decay of the whole source, thus implying that the data inversion is independent on the cell shape. So, in our procedure, the depth‐weighting function is not given with a fixed exponent but with the structural index N of the source as the exponent. Differently than previous methods, our choice gives a substantial objectivity to the form of the depth‐weighting function and to the consequent solutions. The allowed values for the exponent of the depth‐weighting function depend on the range of N for sources: 0 ≤N≤ 3 (magnetic case). The analysis regarding the cases of simple sources such as dipoles, dipole lines, dykes or contacts, validate our hypothesis. The study of a complex synthetic case also proves that the depth‐weighting decay cannot be necessarily assumed as equal to 3. Moreover it should not be kept constant for multi‐source models but should instead depend on the structural indices of the different sources. In this way we are able to successfully invert the magnetic data of the Vulture area, Southern Italy. An original aspect of the proposed inversion scheme is that it brings an explicit link between two widely used types of interpretation methods, namely those assuming homogeneous fields, such as Euler deconvolution or depth from extreme points transformation and the inversion under the Tikhonov‐form including a depth‐weighting function. The availability of further constraints, from drillings or known geology, will definitely improve the quality of the solution.     

利用半参数核估计法预报全球电离层总电子含量

本文将半参数平差模型引入电离层球谐函数系数的预报中,建立了半参数球谐函数模型(Semiparametric-Spherical Harmonic,Semi-SH)来预测全球电离层总电子含量.首先,通过快速傅里叶变换获得球谐函数系数的周期和振幅,将振幅高的主周期归入趋势函数,振幅低的剩余周期归入随机信号,建立了半参数模型,同时利用核估计方法拟合趋势函数,解算随机信号,并在时间域上进行外推,得到了预报时间的球谐函数系数,代入15阶电离层球谐函数模型,最后得出电离层总电子含量(Total Electron Content,TEC)的预报值.本文基于欧洲定轨中心(CODE)发布的球谐函数系数进行电离层TEC长期预报和短期预报分析,其中长期预报采用四年预报两年的模式对球谐函数系数进行预报,短期预报设计了三个算例,采用前30天预报后一天的模式,分别预报1天、滑动预报7天和滑动预报30天.实验结果表明:长期预报能够较好地反映全球电离层TEC的变化趋势和波动情况,Semi-SH模型对全球电离层TEC平均值(Mean TEC global,MTEC_global)的拟合值和预报值与M...     

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1°-averaged surface free-air gravity anomalies and POGO satellite magnetometer data for the United States, Mexico and Central America illustrate the capabilities of the method.     

Method for determining the geomagnetic activity index based on wavelet packets

A method for determining quiet daily variations (Sq curve) in automatic mode and calculating the K index of geomagnetic activity based on wavelet packets has been proposed. The method makes it possible to reproduce the Bartels technique and includes the separation of geomagnetic signal informative components, determination of geomagnetic field disturbances, and the formation of quiet daily variations. The method effectiveness was proved experimentally.     

Gabriel graph of geomagnetic Sq variations

This paper describes the pattern of geomagnetic solar quiet day, Sq, variations recorded at the Indian geomagnetic observatories. The extent to which the high and low latitude ionosphere is interlinked electromagnetically during periods of quiet geomagnetic conditions is a point of debate. The concept of Gabriel graph is applied to derive the boundaries for the variations of horizontal, vertical, and declination components of the earth’s magnetic field during geomagnetically quiet periods. Data of the six Indian geomagnetic observatories (Alibag, Hyderabad, Nagpur, Pondicherry, Visakapatnam, and Trivandrum) are considered for this analysis. This graph theoretical model is complementary to the classical data analysis techniques. Analytical method and the results of the analysis are presented in the paper.     

Factors influencing long range dependence in streamflow of European rivers

Investigating long range dependence of river flows, especially in connection with various climate and storage related factors, is important in order to improve stochastic models for long range dependence and in order to understand deterministic and stochastic variability in long‐term behaviour of streamflow. Long range dependence expressed by the Hurst coefficient H is estimated for 39 (deseasonalized) mean daily runoff time series in Europe of at least 59 years using five estimators (rescaled range, regression on periodogram, Whittle, aggregated variances, and least squares based on variance). All methods yield estimates of H > 0.5 for all data sets. The results from the different estimators are significantly positively correlated for all pairs of methods indicating consistency of the methods used. Correlations between H and various catchment attributes are also analysed. H is strongly positively correlated with catchment area. Apparently, increasing storage with catchment area translates into increasing long range dependence. H is also positively correlated with mean discharge and air temperature and negatively correlated with the mean specific discharge and the seasonality index (maximum Pardé coefficient). No significant correlation is found between the Hurst coefficient and the length of the analyzed time series. The correlations are interpreted in terms of snow processes and catchment wetness. Copyright © 2012 John Wiley & Sons, Ltd.     

三度剩余磁力异常源全方位成像的理论和方法

首先在球坐标系中导出了三度磁性体的“拟引力位”V（p）、“拟引力场”F（p）、磁位U（p）、总磁场T（p）和任意方向磁场分量（p户）等球谐级数正演通式．然后,采用（p）,F（p）和V（p）等3个球谐级数正演通式,建立了复杂条件下三度剩余磁力异常源全方位成像方法．最后,给出了“成像”理论方法体系的应用实例．     

Topological invariants of field lines rooted to planes

Abstract

Two open curves with fixed endpoints on a boundary surface can be topologically linked. However, the Gauss linkage integral applies only to closed curves and cannot measure their linkage. Here we employ the concept of relative helicity in order to define a linkage for open curves. For a magnetic field consisting of closed field lines, the magnetic helicity integral can be expressed as the sum of Gauss linkage integrals over pairs of lines. Relative helicity extends the helicity integral to volumes where field lines may cross the boundary surface. By analogy, linkages can be defined for open lines by requiring that their sum equal the relative helicity.

With this definition, the linkage of two lines which extend between two parallel planes simply equals the number of turns the lines take about each other. We obtain this result by first defining a gauge-invariant, one-dimensional helicity density, i.e. the relative helicity of an infinitesimally thin plane slab. This quantity has a physical interpretation in terms of the rate at which field lines lines wind about each other in the direction normal to the plane. A different method is employed for lines with both endpoints on one plane; this method expresses linkages in terms of a certain Gauss linkage integral plus a correction term. In general, the linkage number of two curves can be put in the form L=r + n, |r|≦1J2, where r depends only on the positions of the endpoints, and n is an integer which reflects the order of braiding of the curves.

Given fixed endpoints, the linkage numbers of a magnetic field are ideal magneto-hydrodynamic invariants. These numbers may be useful in the analysis of magnetic structures not bounded by magnetic surfaces, for example solar coronal fields rooted in the photosphere. Unfortunately, the set of linkage numbers for a field does not uniquely determine the field line topology. We briefly discuss the problem of providing a complete and economical classification of field topologies, using concepts from the theory of braid equivalence classes.     

各向异性半空间上方垂直磁偶极子电磁场的球面波展开式

文中推导出单轴各向异性媒质半空间上方垂直磁偶极源电磁场的精确解析表达式. 应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式. 该展开式数学物理意义明显，并且不受场点和源点的位置、媒质的物性参数和频率等条件的限制. 利用本文的结果可十分方便地计算和分析任意场点处的电磁场分布.     

C-RESPONSE OF GEOMAGNETIC DEPTH SOUNDING ON A 1D THIN SHELL MODEL

This paper tries to formulate the C-response of geomagnetic depth sounding(GDS)on an Earth model with finite electrical conductivity. The computation is performed in a spherical coordinate system. The Earth is divided into a series of thin spherical shells. The source is approximated by a single spherical harmonic P₁⁰ due to the spatial structure of electrical currents in the magnetosphere. The whole solution space is separated into inner and external parts by the Earth surface. Omitting displacement current, the magnetic field in the external space obeys Laplacian equation, while in the inner part, due to the finite conductivity, the electromagnetic fields obey Helmholtz equation. To connect the magnetic fields in the inner and external space, the continuity condition of magnetic fields is used on the Earth surface. The external magnetic fields are expressed by the inner and external source coefficients, from which a new parameter called C-response is computed from the inner coefficient divided by the external coefficient, thus normalizing the actual source strength. The inner magnetic fields in each layer can be recursively derived by the continuity boundary condition of both normal and tangential components of the magnetic field from the initial boundary condition at core-mantle-boundary. The consistency of our C-responses with that from a typical 1-D global model validates the accuracy of the proposed algorithm. Numerical results also show that the C-response estimated from the geomagnetic transfer function method will deviate exceeding 5%from the actual response at longer periods than about 10⁶s, which means that ignoring the curvature of the Earth at extreme long periods will make inversion result unreliable. Therefore, an accurate C-response should be computed in order to lay a solid foundation for reliable inversion.     

Iterative Spherical Downward Continuation Applied to Magnetic and Gravitational Data from Satellite

In the last few decades, satellites have acquired various potential data sets hundreds of kilometers above the Earth’s surface. Conventionally, these global magnetic and gravitational data sets are approximated by using spherical harmonics that allow straightforward work with both fields outside the Earth’s mass. In this article, we present an alternative approach for working with potential data in mass-free space given over a regular coordinate grid on a spherical surface. The algorithm is based on an iterative scheme and the Poisson integral equation for the sphere. With help from the Fourier transform, global potential (magnetic or gravitational) data can efficiently be continued from a mean orbital sphere down to a reference surface without using the spherical harmonics. This is illustrated both with simulated magnetic field data and with real data from the satellite gradiometry mission GOCE. In the case of simulated magnetic data and the downward continuation for 450 km, we have achieved a root mean square at the level of 0.05 nT, while it was <1 E (eotvos) for real GOCE data continued for 250 km. The crucial point is to apply the algorithm twice as a large part of noise can be removed from the input data.