Induced magnetic field of the equatorial electrojet at the surface of the Earth

Summary. The northward component of the induced magnetic field due to the equatorial electrojet at the Earth's surface is calculated using a more realistic local time variaton of the external field due to the electrojet than is provided for by models of the electrojet currently used in induction calculations. It is seen that appreciable induction effects can be expected about an hour before local noon for the kind of local time variation considered. Our results are in qualitative agreement with direct observations of Earth currents in the equatorial region in Nigeria. At local times when observable induction effects are present, the magnetic field due to the electrojet is necessarily three-dimensional; hence in order to obtain the internal part directly from the observed total field due to the electrojet at the Earth's surface, a three-dimensional formulation is required.     

Seismic scattering in the upper crystalline crust based on evidence from sonic logs

Telluric distortion occurs when electric charges accumulate along near-surface inhomogeneities. At low frequencies, the electric currents associated with these charges can be neglected compared to currents induced deeper in the Earth. At higher frequencies, the magnetic fields associated with these currents may be significant. Some parameters describing the distortion magnetic fields can be estimated from measured magneto-telluric impedance matrices. For regional magnetic fields aligned with regional strike directions, parameters associated with the distortion magnetic field component parallel to the regional magnetic field are undeterminable, whereas parameters associated with the distortion magnetic field component perpendicular to the regional magnetic field can be estimated. Optimal estimates are straightforward even for the realistic case of measurement errors that are correlated between elements of a measured impedance matrix. In a simple example of a 1-D anisotropic model with anisotropy direction varying with depth, the modelling of distortion magnetic fields results in regional impedance estimates corresponding more closely to the responses of uncoupled isotropic models, allowing sensible interpretation of an additional one and a half decades of data.     

极光区高空物理过程与磁层-电离层耦合

极区高空物理现象之观测具有悠久历史。对极区地磁、电离层和极光现象的深入考察将地球物理的研究领域扩展到了外层空间,并提出了太阳风－磁层－电离层－热层间耦合这一重要课题。耦合物理机制的证实不仅是火箭、卫星探测的重要贡献,而且也是基于对地面雷达和遍及全球大陆的地磁台站、电离层垂测站之长期观测成果。对流电场、一区和二区场向电流、电离层扰动电流系（包括极光区电集流）,以及电导率的分布和变化乃是一有机整体,对其每一环节的深入认识均与对整体的全面了解密不可分。有关的理论和模式研究则有助于人们深入理解各个耦合过程的相互关系,以及其各发展阶段中不同物理过程的相对重要性。     

A study of two polar magnetic substorms with a two-dimensional magnetometer array

Summary. The paper reports studies of the three-dimensional magnetospheric—ionospheric current systems which produced polar magnetic substorms on 1974 September 7 and September 18. The data were magnetic perturbation fields observed with a two-dimensional array of 23 three-component magnetometers located in western Canada beneath the auroral oval. In an earlier study of a substorm of September 11 (Bannister & Gough) the fields fitted calculated field for a Boström Type 1 current loop with field-aligned currents at east and west ends of the ionospheric segment, and with uniform current density across the width. The substorms here reported could not be modelled with uniform current density. An inverse method due to Oldenburg was therefore used to estimate current density distributions, and satisfactory fits of calculated to observed field resulted. Each substorm was modelled at six representative epochs. In general the principal ionospheric current seem by the array was westward. At four epochs of the September 7 substorm and throughout the September 18 substorm, significant eastward ionospheric current (or its equivalent in terms of the fields produced) was observed north of the westward electrojet. Northwestward bends in the ionospheric current segments were found at four epochs on September 7 and at three epochs on September 18. As in the September 11 substorm (Paper 1), these bends were either west of or close to magnetic midnight. In some cases the bends may follow the auroral oval, but in others they are sharper and may be associated with the Harang discontinuity. East of geomagnetic the ionospheric currents tend to run in a constant geomagnetic midnight latitude range. The developments of the three substorms, of September 7, 11 (Paper 1) and 18, are compared. They showed a variety of shifts in longitude, though all moved eastward relative to magnetic midnight.     

南极中山站极光电集流分布特征分析

本文通过 1 997年在南极中山站观测的极光和所对应的地磁场扰动 ,利用 AU、AL、AE指数描述极光电集流在南极中山站的分布规律及其强度 ,我们发现东向极光电集流强度是正值 ,西向极光电集流强度是负值 ,从绝对值来说 ,西向极光电集流强度大于东向极光电集流强度。南极中山站夏季的极光电集流强度大于冬季的极光电集流。秋夏冬季节的东向极光电集流在72 0～ 1 44 0分 (世界时 1 2～ 2 4时 )的分布规律的拟合曲线类似口朝上的抛物线形 ;西向极光电集流在 72 0～ 1 44 0分这段时间的分布规律的拟合曲线类似正弦波形。了解了极光电集流在南极中山站的分布特征 ,有利于极区电离层和磁层耦合及极光动力学的研究。     

径向行星际磁场下的场向电流的统计学研究

基于CHAMP卫星高精度磁场观测数据,对2001—2009年径向行星际磁场(RIMF, radial interplanetary magnetic fields)条件下的场向电流的分布特征进行了统计学分析, 并与2001—2009年期间场向电流的平均强度进行了对比研究, 结果表明：正午时刻场向电流的平均强度对地偶极子倾角有明显线性依赖, 冬夏季电流强度比值约为3左右, RIMF条件下冬夏季比值降为2;相对年平均值来说, RIMF条件下行星际磁场总幅度、重联电场、太阳风动压均有所减小, AE指数减弱, Dst指数略有降低;在通常情形下重联电场是场向电流很好的控制参数, 但是在RIMF下, 重联电场不再与电流强度相关;北半球电流强度在向地IMF条件下大于向日IMF, 而南半球则相反, 虽然RIMF条件下场向电流的均值小于年平均值, 但是正午时段场向电流强度大于年平均值的概率大约为0.2, RIMF条件下仍然有地磁扰动事件(比如亚暴事件)发生。     

Electric field at the seafloor due to a two-dimensional ionospheric current

The relation between the seafloor electric field and the surface magnetic field is studied. It is assumed that the fields are created by a 2-D ionospheric current distribution resulting in the E-polarization. The layered earth below the sea water is characterized by a surface impedance. The electric field at the seafloor can be expressed either as an inverse Fourier transform integral over the wavenumber or as a spatial convolution integral. In both integrals the surface magnetic field is multiplied by a function that depends on the depth and conductivity of the sea water and on the properties of the basement. The fact that surface magnetic data are usually available on land, not at the sea surface, is also considered. Test computations demonstrate that the numerical inaccuracies involved in the convolution method are negligible. The theoretical equations are applied to calculate the seafloor electric fields due to an ionospheric line current or associated with real magnetic data collected by the IMAGE magnetometer array in northern Europe. Two different sea depths are considered: 100 m (the continental shelf) and 5 km (the deep ocean). It is seen that the dependence of the electric field on the oscillation period is weaker in the 5 km case than for 100 m.     

极区电离层F区加热激发极低频波研究

"极区电急流天线"辐射依赖于低电离层D/E区背景电急流,而高电离层F区极低频调制加热,可产生抗磁性电流,形成极低频波辐射源。利用电离层F区一维时变加热数值模型,采用全波解算法研究高纬Troms(69.59°N,19.23°E)地区电离层F区极低频调制加热。模拟结果表明,极区高电离层激发的极低频波与极区低电离层激发的结果不同。加热泵波的有效辐射功率(effective radiated power,ERP)、调制频率及电离层背景对极低频波强度有着重要影响。     

Three-dimensional induction in a non-uniform thin sheet at the surface of a uniformly conducting earth

Summary. A new method for solving problems in three-dimensional electromagnetic induction in which the Earth is represented by a uniformly conducting half-space overlain by a surface layer of variable conductance is presented. Unlike previous treatments of this type of problem the method does not require the fields to be separated into their normal and anomalous parts, nor is it necessary to assume that the anomalous region is surrounded by a uniform structure; the model may approach either an E- or a B -polarization configuration at infinity. The solution is expressed as a vector integral equation in the horizontal electric field at the surface. The kernel of the integral is a Green's tensor which is expressed in terms of elementary functions that are independent of the conductance. The method is applied to an illustrative model representing an island near a bent coastline which extends to infinity in perpendicular directions.     

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.     

A comparison of analytic and numerical results for a two-dimensional control model in electromagnetic induction – I. B-polarization calculations

Summary. A conducting slab of finite thickness divided into three segments of different conductivities and overlying a perfect conductor is proposed as a suitable two-dimensional 'control' model for testing the accuracy of the various numerical modelling programs that are available for calculating the fields induced in the Earth by an external, time-varying magnetic source. An analytic solution is obtained for this control model for the case of the magnetic field everywhere parallel to the conductivity boundaries ( B -polarization). Values of the field given by this solution for a particular set of model parameters are calculated at selected points on the surface and on a horizontal plane inside the conductor, and are tabulated to three figure accuracy for reference. They are used to check the accuracy of the results given by the finite difference program of Brewitt-Taylor & Weaver and the finite element program of Kisak & Silvester for the same model. Improved formulae for calculating the derived electric field components in B -polarization are first developed for incorporation in the finite difference program, and these give surface electric fields within 1 per cent of the analytic values, while all three field components inside the conductor are calculated to better than 96 per cent accuracy by the finite difference program. The results given by the finite element program are not quite so satisfactory. Errors somewhat greater than 10 per cent are present and although the program requires much less disk space it takes rather more CPU time to complete the calculations.     

The use of equivalent current systems in the interpretation of Geomagnetic Deep Sounding data

Summary. Many geomagnetic variation anomalies are probably caused by the channelling, through small-scale bodies, of electric currents induced in much larger conductors elsewhere. Consequently, the direct interpretation of anomalous magnetic fields by modelling the electromagnetic response of conductive structures may give misleading results. It is suggested that, rather than attempting to proceed directly from the electromagnetic fields to conductivity models, we should instead take the intermediate step of determining the distribution of anomalous current flow.
Maps of the anomalous fields over a conductive structure can be generated from inter-station transfer functions. If it is assumed that the internal currents are concentrated in a thin sheet at a specified depth, the equivalent current system in the sheet can be computed directly from the vertical magnetic field. The most straightforward method of performing this calculation is to compute the Fast Fourier Transform of the magnetic field data, and then to apply a wavenumber filter.
The presence of any vertical currents invalidates the thin sheet model. However, if the spatial distribution of a horizontal component of the anomalous magnetic field is also known, the presence of any vertical currents can be detected directly, and their position determined. The value of the methods is illustrated by applying them to the interpretation of a Geomagnetic Deep Sounding survey of the Kenya rift valley.     

Forward modelling of direct current and low-frequency electromagnetic fields using integral equations

We present a semi-analytical, unifying approach for modelling the electromagnetic response of 3-D bodies excited by low-frequency electric and magnetic sources. We write the electric and magnetic fields in terms of power series of angular frequency, and show that to obey Maxwell's equations, the fields must be real when the exponent is even, and imaginary when it is odd. This leads to the result that the scattering equations for direct current fields and for fields proportional to frequency can both be explicitly formulated using a single, real dyadic Green's function. Although the underground current flow in each case is due to different physical phenomena, the interaction of the scattering currents is of the same type in both cases. This implies that direct current resistivity, magnetometric resistivity and electric and magnetic measurements at low induction numbers can all be modelled in parallel using basically the same algorithm. We make a systematic derivation of the quantities required and show that for these cases they can all be expressed analytically. The problem is finally formulated as the solution of a system of linear equations. The matrix of the system is real and does not depend on the type of source or receiver. We present modelling results for different arrays and apply the algorithm to the interpretation of field data. We assume the standard dipoledipole resistivity array for the direct current case, and vertical and horizontal magnetic dipoles for induction measurements. In the case of magnetometric resistivity we introduce a moving array composed of an electric dipole and a directional magnetometer. The array has multiple separations for depth discrimination and can operate in two modes. The mode where the predominant current flow runs along the profile is called MMR-TM. This mode is more sensitive to lateral variations in resistivity than its counterpart, MMR-TE, where the mode of conduction is predominantly perpendicular to the profile.     

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.     

Electromagnetic fields in a halfspace scattered by a buried sphere by the method of transformation of local elements

Summary. A problem in modelling electromagnetic fields used in exploration geophysics is treated mathematically. Analytical expressions are obtained for the electric field due to a harmonic current in a horizontal loop on or above a conducting ground in which is buried a conductive and permeable sphere (ore body). The loop is coaxial with the sphere. For a general time-varying current in the loop, the analysis is carried to the stage where a Fourier inversion can be used to obtain readily the electric field in the time-domain. A new relationship between spherical and cylindrical wave functions is obtained as a transformation of local elements.
Solution of this problem has not been presented before in this form. Lee's solution of 1975 which uses an integral-equation formulation treats a similar problem without taking account of differences in magnetic permeability. The effects of magnetic permeability may have important and useful implications for geophysical explorations.     

B-polarization induction in two generalized thin sheets at the surface of a conducting half-space

Summary. A new closed-form solution is obtained analytically for a B- polarization induction problem of geophysical interest, in which a local region of the Earth is represented by a generalized thin sheet at the surface of and in electrical contact with a uniformly conducting half-space. The generalized sheet, first introduced by Ranganayaki & Madden, is a mathematical idealization of a double layer which consists, in this problem, of two adjacent half-planes with distinct conductances representing a surface conductivity discontinuity such as an ocean—coast boundary, underlain by a uniform sheet of finite integrated resistivity representing the lower crust. The resistive sheet exerts a considerable mathematical influence on the solution causing, under certain conditions, an additional pole to appear in one of the forms of contour integral by which the solution can be expressed; it also weakens or eliminates field singularities that would otherwise occur at the conductance discontinuity. A numerical calculation is made for model parameters typifying an ocean—coast boundary underlain by a highly resistive crust. It is found that the residue of the pole associated with the resistive sheet dominates the solution for this example, the main consequence of which is a huge increase in the horizontal range over which the induced currents adjust themselves between the different 'skin-effect' distributions at infinity on either side of the model. Moreover the solution shows that this 'adjustment distance' has a more complicated dependence on the conductance and integrated resistivity of the sheet than that given simply by the square root of their product which was the length parameter proposed by Ranganayaki & Madden.     

Transient electromagnetic fields about an infinitesimally long grounded horizontal electric dipole on the surface of a uniform half-space

Summary. Laplace and Bessel Transforms are used to solve for the transient behaviour of the electromagnetic fields after switching off a steady current in a grounded infinitesimal horizontal dipole on the surface of a uniformly conducting half-space. Simple analytic expressions, which are valid for times sufficiently long after the switch that displacement terms can be ignored, are obtained on the surface of the half-space for the electric field and the time derivative of the magnetic field. At the instant of switching an infinitesimally long image becomes established directly under the source dipole. It is the diffusion of this image which gives the vertical magnetic field and horizontal electric fields their transient behaviour. During the transient, there is also a decaying charge distribution on the surface.     

An Integral Equation and its Solution for some Two-and Three-Dimensional Problems in Resistivity and Induced Polarization

Summary. The potential, U , about a point electrode, at the surface of a layered ground in which there is an heterogeneity embedded, satisfies the integral equation:
Here, U * and σ* are the corresponding quantities for the potential and conductivity without the heterogeneity. The integral is taken over the surface of the heterogeneity, ∂ U /∂ n is the normal derivative (in the direction of the outward normal) of U , and G is a Green's function.
Solutions to this equation can readily be found by using the Galerkin method of solving integral equations. The solutions of this equation when the heterogeneity is a sphere or a cylinder in a uniform ground or beneath a conductive overburden are the most readily found.
When the solution of the integral has been found for the potential it is a simple matter to calculate the apparent resistivity or chargeability for any electrode configuration.     

An improved geomagnetic data selection algorithm for global geomagnetic field modelling

A spherical harmonic degrees 60, global internal field model is described (called BGS/G/L/0706). This model includes a degree 15 core and piecewise-linear secular variation model and is derived from quiet-time Ørsted and Champ satellite data sampled between 2001.0 and 2005.0. For the satellite data selection, a wide range of geomagnetic index and other data selection filters have been used to best isolate suitably quiet magnetospheric and ionospheric conditions. Only a relatively simple, degree one spherical harmonic, external field model is then required. It is found that a new 'Vector Magnetic Disturbance' index ( VMD ), the existing longitude sector A indices, the auroral zone index IE , and the polar cap index PC are better than Kp and Dst at rejecting rapidly varying external field signals at low, middle, auroral and polar latitudes. The model quality is further enhanced by filling spatial and temporal gaps in the quiet data selection with a second selection containing slightly more disturbed data. It is shown that VMD provides a better parametrization than Dst of the large-scale, rapidly changing, external field. The lithospheric field model between degrees 16 and 50 is robust and displays good coherence with other recently published models for this epoch. BGS/G/L/0706 also shows crustal anomalies consistent with other studies, although agreement is poorer in the southern polar cap. Intermodel coherency reduces above about degree 40, most likely due to incompletely filtered signals from polar ionospheric currents and auroral field aligned currents. The absence of the PC index for the southern hemisphere for 2003 onwards is a particular concern.     

Electromagnetic response of an arbitrarily shaped three-dimensional conductor in a layered earth—numerical results

Summary. In an earlier work, mathematical formulation on computing the electromagnetic response of an arbitrarily shaped three-dimensional inhomogeneity in a layered earth had been worked out using an integral equation technique. The method has been used to show its efficacy by computing numerical results. Introducing suitable changes of variables the secondary contributions to Green's dyadic are put in the form of convolution integrals and are computed using a digital linear filtering scheme. The matrix equation is solved for the unknown electric fields in the inhomogeneity. The scattered fields are then calculated at the surface of the Earth using the appropriate Green's dyadic. The performance of the computations has been shown by comparing the numerical results with those obtained by analogue modelling as well as by other numerical schemes. The use of digital linear filtering saves an enormous amount of computer time.
The effects of varying excitation-frequency, conductivity of the host medium and that of the overburden have been studied in detail for a horizontal loop system traversing over a two-layered earth with a prismatic inhomogeneity situated in the lower conducting half space.