Modelling of space weather effects on pipelines

The interaction between the solar wind and the Earth's magnetic field produces time varying currents in the ionosphere and magnetosphere. The currents cause variations of the geomagnetic field at the surface of the earth and induce an electric field which drives currents in oil and gas pipelines and other long conductors. Geomagnetically induced currents (GIC) interfere with electrical surveys of pipelines and possibly contribute to pipeline corrosion.In this paper, we introduce a general method which can be used to determine voltage and current profiles for buried pipelines, when the external geoelectric field and the geometry and electromagnetic properties of the pipeline are known. The method is based on the analogy between pipelines and transmission lines, which makes it possible to use the distributed source transmission line (DSTL) theory. The general equations derived for the current and voltage profiles are applied in special cases. A particular attention is paid to the Finnish natural gas pipeline network.This paper, related to a project about GIC in the Finnish pipeline, thus provides a tool for understanding space weather effects on pipelines. Combined with methods of calculating the geoelectric field during magnetic storms, the results are applicable to forecasting of geomagnetically induced currents and voltages on pipelines in the future.     

Global electrical currents

Summary The atmospheric electrical structure of the earth is postulated to be controlled by a motivating force in the lower ionosphere which is produced by interaction between neutral atmosphere tidal circulations and the ionospheric plasma in the presence of the earth's magnetic field. Associated electric fields power the dynamo currents through the Hall effect with a resulting development of a gross electric potential distribution in the lower ionosphere. Asymmetries in these hemispheric potential distributions result in exospheric current flows in lowL-shells and larger differences in potential produced by dynamo return current flows in high magnetic latitudes result in strong currents through highL-shells between auroral zones. Vertical thunderstorm currents with their associated lightning discharges effectively connect the earth to a low potential region of the dynamo circuit and thus supply the earth with an average negative charge which motivates a leakage tropospheric electrical circuit. In addition, the dynamo currents maintain the magnetic polar regions at different potentials with a resulting electrical exchange with the solar wind through the earth's near space. These considerations indicate that observed electrical and variable magnetic phenomena near the earth are all part of a single comprehensive electrical current system.This paper was read byH. Dolezalek in an abbreviated form supplied by the author.     

SELF POTENTIAL AND CURRENT CHANNELLING*

Anomalies in self potential (SP) are usually explained in terms of geochemical activity. However, there are other sources of current which cause complications in the interpretation. In particular, DC telluric currents can be generated outside the survey region. Contrasts in resistivity cause current channelling and secondary voltages can be induced by leakage. The effect can be demonstrated using network theory and internal sources can be emphasized by subtraction. Joint surveys are required to demonstrate correlations with apparent resistivity.     

用于肺功能检测的生物电阻抗断层成像系统

介绍了一种对人体内电阻抗分布进行成像的医学成像系统,并将其应用于肺通气的观察。该系统采用32体表电极进行阻抗测量,用加权反投影算法进行图象重构。文中给出了恒流源、测量电路、控制电路的设计和重构方法研究。同时,得到了一些初步的在体实验结果。     

层状介质中三维大地电磁模拟

本文发展了积分方程法用于层状介质中三维不均匀体的大地电磁模拟算法（简称MT）.分为二个步骤:第一步,异常体用等效的散射电流代替,通过层状介质中的格林函数,建立以散射电流为未知参数的积分方程;第二步,把求得的散射电流乘上相应的格林函数,即得地面上的二次电磁场,由此而计算出各种MT响应. 文中采用了数值滤波与插值、群变换以及格林矩阵带状化三个方面的数值处理方法,提高了计算效率.通过与已发表的三维MT计算结果对比及格林函数互易性检验,表明了该算法的正确性.在此基础上,进行了数值模拟,初步讨论了三维MT曲线的畸变特点.     

电阻抗层析成像的电导网络解法

阻抗ＣＴ技术是通过在物体的边界进行一些电测量来重建内部阻抗分布。本文提出利用网络理论来解决阻抗ＣＴ的一种新的重建方法。首先将非均匀电导分布区域离散化为具有一些节点的电导网络，然后在边界节点上施加一组正交的电流激励，测量感生出的电压。根据网络论，这样就可利用网络的节点方程来进行求解．为求得最符合观测值的节点电导矩阵Ｇ的估计，我们从Ｇ的性质中提取了两类约束，根据广义投影理论，采用施加约束的迭代方法来重建这一反映电导分布的节点电导矩阵Ｇ．计算机模拟表明，迭代是收敛的并且能得到较好的重建结果。     

Recordings and occurrence of geomagnetically induced currents in the Finnish natural gas pipeline network

A project implemented to study the effects of space weather on the Finnish natural gas pipeline was started in August 1998. The aims of the project were (1) to derive a model for calculating geomagnetically induced currents (GIC) and pipe-to-soil (P/S) voltages in the Finnish natural gas pipeline, (2) to perform measurements of GIC and P/S voltages in the pipeline and (3) to derive statistical predictions for the occurrences of GIC and P/S voltages at different locations in the pipeline network.GIC and P/S voltage were recorded at a compressor station. The GIC measurement was made with two magnetometers, one right above the pipe, and another at the Nurmijärvi Geophysical Observatory about 30 km southwest. The largest GIC since November 1998 has been 30 A. The P/S voltage recording was stopped in May 1999, but GIC is still measured.GIC statistics were derived based on the recordings of the geomagnetic field at Nurmijärvi. The geoelectric field was calculated by using the plane wave model. This field was input to the general pipeline model resulting in the distribution of currents and P/S voltages at selected points in the pipeline. As could be expected, the largest P/S voltage variations occur at the ends of the pipeline network, while the largest GIC flow in the middle parts.     

2.5D direct‐current resistivity forward modelling and inversion by finite‐element–infinite‐element coupled method

To reduce the numerical errors arising from the improper enforcement of the artificial boundary conditions on the distant surface that encloses the underground part of the subsurface, we present a finite‐element–infinite‐element coupled method to significantly reduce the computation time and memory cost in the 2.5D direct‐current resistivity inversion. We first present the boundary value problem of the secondary potential. Then, a new type of infinite element is analysed and applied to replace the conventionally used mixed boundary condition on the distant boundary. In the internal domain, a standard finite‐element method is used to derive the final system of linear equations. With a novel shape function for infinite elements at the subsurface boundary, the final system matrix is sparse, symmetric, and independent of source electrodes. Through lower upper decomposition, the multi‐pole potentials can be swiftly obtained by simple back‐substitutions. We embed the newly developed forward solution to the inversion procedure. To compute the sensitivity matrix, we adopt the efficient adjoint equation approach to further reduce the computation cost. Finally, several synthetic examples are tested to show the efficiency of inversion.     

Model of magnetosphere-ionosphere interactions in the field of auroral electrojets

The magnetosphere and ionosphere are coupled into a power circuit by field-aligned currents. If there were only Hall current in the ionosphere, the problem of magnetosphere-ionosphere interaction would not have arisen. Field-aligned currents could be seen as emerging as a result of the break in the magnetospheric current across the tail, since the Hall current is divergence-free and does not perform any work. In fact, the current in the ionosphere is complex. It always has a Pedersen component, and the ionosphere is a real energy consumer. Together with energy, an extrinsic electrical current should flow into the ionosphere. The current coming from the generator in front of the bow shock is a part of the extrinsic current. The aim of this paper is to generalize the previously obtained partial solution to the problem of magnetosphere-ionosphere interactions in the region of auroral electrojets, also taking into account the generation of the extrinsic current in front of the bow shock.     

Geoelectricity: atmospheric charging and thunderstorms

The “classical picture of the global circuit” — i.e. of atmospheric charging by thunderstorm clouds — is shown to be inconsistent. Thunderstorm overall voltages ∫Edz are (only) of order MV, slightly above fairweather voltages, insufficient to charge the ‘geocapacitor’. Instead of charging the ionosphere (via Wilson currents), thunderstorms occasionally discharge towards it, with emitted spectra ranging from the visible up to gamma-ray energies. Fairweather charging takes place, so we claim, via the negative drizzle of the ‘heavy’ aerosols, of radii between 0.1 μm and 0.1 mm in the troposphere.     

Direct current electric potential computation in an inhomogeneous and arbitrarily anisotropic layered earthl

We consider the calculation of the electrical field quantities, electric potential and the vertical component of the total volume density of electric current, in a horizontally layered, piecewise homogeneous and arbitrarily anisotropic earth due to a system of direct current point sources. By applying Fourier transformation with respect to the horizontal space coordinates to the static field equations, the field quantities are obtained as the solutions of the system of transform-domain differential equations in the vertical (depth) coordinates. A recurrence scheme has been given to compute the tranform-domain field quantities at any depth. The corresponding space-domain quantities are then obtained by inverse Fast Fourier Transformation (FFT). A complete computer program has been developed for computing the electric potentials at any depth of the layered earth, which is composed of an arbitrary number of anisotropic layers with arbitrary conductivity tensors. By considering the point sources at different depths from the surface, equipotential contours on the surface of arbitrarily anisotropic layered earth models are given.     

三维坑道直流聚焦法超前探测的电极组合研究

在坑道超前探测方法中,直流电阻率法原理和操作简单,应用前景广阔,其中侧向聚焦电阻率法应用在测井中已经成为一种常用方法.本文研究了三维坑道直流聚焦法电极组合,首先计算分析了两个同性点电源的电流分布规律,指出由于电流的相互排斥作用,电流密度在这两个点电源的中垂线下一定深度处产生最大值,这个深度与这两个点源之间的距离成正比.基于上述原理,设计出三种电极组合：四点电源、五点电源和九点电源布极方式.其次,用三维有限单元数值模拟的方法计算了上述三种电极系的空间电位分布,得出九点电源方式对电流聚束效果较好,而且当主电极电流小于屏蔽电极电流时效果最好.     

Near surface geophysical surveys with a high frequency mutual impedance measuring system

Relationships for the mutual impedance of horizontal coplanar, vertical coplanar, perpendicular and vertical coaxial loop antenna arrays operating at a high frequency, located over a layered conducting medium, have been derived. The relationships take into account the occurrence of displacement currents in both the free space and the conducting medium. The relations can be used for calculating the earth parameters in geophysical prospecting. The use of high frequency antenna array makes it possible to determine distributions of apparent resistivity as well as apparent electrical permittivity. The potential application of the measurements of mutual impedance of loop antennas operating at a high frequency to the geophysical examinations is presented. The measuring system developed for this purpose is described. A simple method of interpreting the mutual impedance measurements to obtain the traces of apparent resistivity and apparent permittivity of the investigated earth is given.     

Current–voltage relationship

Potential drops accelerate ions and electrons along magnetic field lines and create currents flowing into and out of the ionosphere. Kinetic exospheric models similar to those developed for the polar wind have been used to determine the current density as a function of the electrostatic potential difference. In the upward current region of the auroral zone, the current–voltage relationship depends on the number density and temperature of the hot plasma of the plasmasheet and is quasi-linear for 100 V<V<10 kV.This linear relationship cannot be extrapolated to return current regions, where the current is carried by the ionospheric electrons. FAST observations have shown significant potential drops in the return current regions, suggesting there a contribution of an anomalous resistance to the current–voltage relationship. The goal of the present paper is to describe and summarize the features of the field-aligned currents and of the various forms of current–voltage relationships in magnetospheric physics as well as the successive historical steps between their discovery and first formulation in 1973 and their most recent sophisticated ones.     

3D modelling and sensitivity in DC resistivity using charge density

A three‐dimensional (3D) electrical resistivity modelling code is developed to interpret surface and subsurface data. Based on the integral equation, it calculates the charge density caused by conductivity gradients at each interface of the mesh, allowing the estimation of the potential everywhere without the need to interpolate between nodes. Modelling generates a huge matrix, made up of Green's functions, which is stored by using the method of pyramidal compression. The potential is compared with the analytical and the numerical solutions obtained by finite‐difference codes for two models: the two‐layer case and the vertical contact case. The integral method is more accurate around the source point and at the limits of the domain for the potential calculation using a pole‐pole array. A technique is proposed to calculate the sensitivity (Jacobian) and Hessian matrices in 3D. The sensitivity is based on the derivative with respect to the block conductivity of the potential computed using the integral equation; it is only necessary to compute the electrical field at the source location. A direct extension of this technique allows the determination of the second derivatives. The technique is compared with the analytical solutions and with the calculation of the sensitivity according to the method using the inner product of the current densities calculated at the source and receiver points. Results are very accurate when the Green's function that includes the source image is used. The calculation of the three components of the electric field on the interfaces of the mesh is carried out simultaneously and quickly, using matrix compression.     

Soil‐structure system frequency and damping: Estimation from eigenvalues and results for a 2D model in layered half‐space

This paper presents a formulation for estimation of the frequency and damping of a soil‐structure interaction system based on the classical modal analysis and solving the system eigenvalue problem. Without loss of generality, the structure is represented by a single degree of freedom oscillator, while the soil effects are included through impedance functions for in‐plane motion of a 2D rigid foundation. For the results presented in this paper, the impedance functions were computed by the indirect boundary element method for a rectangular foundation embedded in a soil layer over elastic bedrock. The study shows that the classical modal‐analysis approach works well, with the exception of squat, stiff structures, even though the impedance functions are frequency‐dependent and the soil‐structure interaction system does not possess normal modes. The study also shows that system frequency and damping are independent of the wave passage effects, contrary to findings of some previous studies, and that the site conditions, represented by the soil‐layer thickness and stiffness contrast between bedrock and soil layer, have significant influences on both system frequency and system damping. Finally, the paper examines the accuracy of some of the simple methods for estimation of these two system parameters and comments on some conflicting conclusions of previous studies about the effects of foundation embedment.     

上地幔橄榄石电导率影响因素及高压相变初探

人们对上地幔标志性矿物橄榄石的认识，基本上是经历一个从直流到交流，又从交流到阻抗谱的认识过程．本文主要通过对橄榄石电导率的影响因素出发，包括温度、压力、铁镁比值、氧逸度等因素的影响和制约．用目前国际高温高压学术界公认的阻抗谱技术探讨了橄榄石在高压下的相变，并在此基础上，进一步研究地球物理学家非常关心的热点问题-冷地幔的实验室的模拟，并作了充分的论证．     

层状各向同性多孔介质中井间地震的数值计算

依据Ｂｉｏｔ理论，提出计算理论地震图的相应传播矩阵算法，并针对井间地震震源和检波器的不同配置进行数值计算，结果表明，本文算法高频可达１０００Ｈ２以上．文中算例说明利用震源和检波器相对于储油层的不同位置，可从反射震相记录波形上的差异，判定储油层存在与否．     

大地电磁法三维共轭梯度反演研究

Based on the analysis of the conjugate gradient algorithm, we implement a threedimensional （3D） conjugate gradient inversion algorithm with magnetotelluric impedance data. During the inversion process, the 3D conjugate gradient inversion algorithm doesn＇ t need to compute and store the Jacobian matrix but directly updates the model from the computation of the Jacobian matrix. Requiring only one forward and four pseudo-forward modeling applications per frequency to produce the model update at each iteration, this algorithm efficiently reduces the computation of the inversion. From a trial inversion with synthetic magnetotelluric data, the validity and stability of the 3D conjugate gradient inversion algorithm is verified.     

高压变电站抗震可靠性分析(一)

讨论了高压变电站中电气主接线系统的抗震可靠性分析问题,主要分析了高压变电站中常见的双母线系统的抗震可靠性。通过系统的可靠性关系和建立系统的可靠性分析准则,给出了双母线系统在各个抗震准则条件下的可靠性的表达形式。最后进行了实例分析。