The perturbation of geomagnetic fields by two-dimensional and three-dimensional conductivity inhomogeneities

Summary A numerical method is used to calculate the geomagnetic fields associated with a three-dimensional conductivity anomaly. Fields associated with a two-dimensional model are also studied numerically for a range of frequencies and apparent resistivity curves for the two models are compared with that calculated for a layered earth. The apparent resistivity curves for both the three-dimensional model and the two-dimensional model differ considerably from the layered case, and it is evident that if a layered model is used for interpretation the results may be very misleading.     

A numerical study of the topographic effect on electromagnetic fields in a three-dimensional conductivity model

Summary The topographic effect on electromagnetic fields in a three-dimensional conductivity model is investigated using a finite-difference numerical method. The model is that of a conducting block buried in the host Earth beneath a conducting hill. The altitude effect as well as the effect of conductivity of the hill has been studied by comparing the results for the field components at the surface of the hill with those at the surface of a flat half-space. The results indicate that both altitude and the hill conductivity influence the behaviour of the electromagnetic fields. For certain traverses beyond the edge of the block, it is seen that the variations in some field components are mainly due to the topographic effect and that the contribution from the block itself is negligible.     

The perturbation of alternating geomagnetic fields by discontinuities with high conductivity contrasts

The perturbation of alternating geomagnetic fields by conductivity discontinuities is considered. A numerical method is used to solve the two-dimensional induction problem. Models in which the conductivity contrast between conductive regions is great, such as between oceanic and continental regions, are considered. The perturbation field distributions for models with higher conductivity contrasts are compared with lower conductivity contrast models using a method recently developed by Jones (1972). Total field solutions are obtained for several models by using a very large grid as well as a folding-in technique. Results from the two methods for the various models are compared. It is found that the folding-in technique offers an alternative method for handling higher conductivity contrasts.     

Electromagnetic induction of a three-dimensional conductivity inhomogeneity in a two-layer earth

Summary The results of numerical computations of the electromagnetic field induced in a two-layer model of the Earth with a three-dimensional inhomogeneity (a block) in the subsurface layer are given. Several recommendations are given which have enabled the solution of a complicated system of integral equations and the computation of the field at the Earth's surface in an effective way. The analysis of the obtained solution has proved that, in an anomalous electromagnetic field, the field of the horizontal electric dipole, oriented in the direction of the exciting field, is predominant. A number of practically usable diagrams and approximative formulae is given.     

Electromagnetic induction of a three-dimensional conductivity inhomogeneity in the two-layered earth

Summary The calculation of the elements of Green's tensor function is presented for solving the problem of the electromagnetic induction by means of a vector integral equation. A two-layered Earth is considered as the medium, the surface layer including a three-dimensional conductivity inhomogeneity. Use is made of the boundary condition requiring the vertical component of the electric current to be zero at the Earth's surface which partly simplifies the theoretical computation. Long-period asymptotics of the individual complicated functions, occurring in Green's tensor function as well as in the tensor function required to calculate the components of the anomalous magnetic field at the surface of the halfspace, were effected. With the aid of these asymptotics one can obtain estimates of the functions occurring in the theoretical analysis of the problem.     

On the behaviour of the induction arrows over a buried conductive plate — a numerical model study

Two-dimensional numerical model calculations, employing a finite difference technique, are used to study the behaviour of the induction arrows, for a range of periods, for a conductive plate of (i) semi-infinite and (ii) finite width in uniform and layered resistive hosts. The results for the conductive plate at the surface of the host have application to a uniform-depth ocean, while the results for the plate buried at some depth in the resistive host have application to a conductive sill in a resistive Earth. The numerical results indicate that for a profile over the plate-host vertical interface the in-phase arrows for all periods and locations point towards the conductive plate, while the quadrature arrows at periods near the characteristic period of the model are oppositely directed on either side of the interface so as to point towards each other and towards the interface for nearby locations, both over the conductive plate and the resistive host. Further, the quadrature arrow undergoes a second reversal over the resistive host at a distance from the interface that is somewhat dependent on the period. Thus, at either side of the location of this second reversal, the quadrature induction arrows are again oppositely directed, but pointing away from each other, with the arrows near the interface pointing towards, and the more distant arrows pointing away from the conductive plate. The period range for the quadrature-arrow reversal is characteristic of conductivities and layer depths. The features of the quadrature-arrow sign reversals at and near the interface are in accordance with the earlier laboratory analogue model results of Hebert et al. for the Newfoundland coastal region and Nienaber et al. for a conductive plate in a resistive host.

It is suggested that in practice the sign reversal of the quadrature arrow may aid in locating a conductor-host interface, and that if the conductivity of the host is known, the maximum in the anomalous vertical magnetic field response may permit an approximate determination of the conductive-layer depth.     

线源地震影响场计算模型

传统的烈度衰减关系一般是由历史地震等震线资料拟合得到,但基于历史震例进行统计回归所得到的椭圆衰减模型往往不能够反映大地震时的地震衰减特点。尝试提出一种基于点源模型改进的线源地震影响场计算模型,引入地表破裂尺度对原有烈度衰减模型进行长轴上的修正,以期达到生成结果与强震实际烈度相拟合的目的,并可实现极震区震害的快速评估和计算。     

Horizontal magnetic dipole over an inhomogeneous earth model with exponential variation of conductivity

The paper outlines the formulation of the problem of calculating the electromagnetic field components due to a horizontal magnetic dipole placed over a multilayered earth model with one of the layers having exponential variation of conductivity with depth. Analytical solutions and numerical computations are performed for three-layered earth models possessing the described conductivity variation in the transition layer. It is assumed that the conduction currents dominate the displacement currents. Results presented here show the influence of the transition layer thickness and the conductivity contrast between the top and the bottom layers on electric and magnetic field components. The results show a characteristic dependence on the conductivity inhomogeneity.     

Transient ULF Electric and magnetic fields of an electrical current source in a medium with continuously varying conductivity

Recent analytical studies of ULF electromagnetic fields in the atmosphere are reviewed. These fields have their origin in the discharge of thunderclouds. The problem for a vertical electrical dipole source played in an atmosphere where the conductivity increases exponentially with altitude is described. The analytical expressions for the electric and magnetic field, which vary in time and space, are approximately obtained by a vector potential. It is seen that the amplitudes of the pulse decrease with both increases of the horizontal distance and the gradient of the conductivity. However, the shapes of the pulse are almost constant.On leave from the Department of Electronic Engineering, Gumma University Kiryu, 376, Japan     

Electromagnetic induction in a spherical model of the earth with a real distribution of near-surface conductivity

The current functions calculated for a spherical Earth model with real near-surface conductivity distribution are presented. The system is excited by a uniform external field of three different polarizations.     

非零长线源与偶极源的电磁响应比较分析

电磁测深方法中经常采用长线源进行激励,并用偶极源进行近似解释.要将长线源近似成偶极源必须满足一定的几何条件.本文通过对长线源与偶极源的电磁响应进行推导计算,并分类进行比较分析,得知在长线源几何尺寸相对于长线源到观测点的距离可以比拟时,长线源激励的电磁响应在早、中期与偶极源有较大的偏差,在晚期逐步趋于一致.因此,建议在采用非零长线源进行电磁测深的数据处理中,先进行电磁响应数据的相关修正处理.     

A three-dimensional numerical model of advection and diffusion of urban source pollutants

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The magnetospheric disturbance ring current as a source for probing the deep earth electrical conductivity

Two current rings have been observed in the equatorial plane of the earth at times of high geomagnetic activity. An eastward current exists between about 2 and 3.5 earth radii (Re) distant, and a larger, more variable companion current exists between about 4 and 9 Re. These current regions are loaded during geomagnetic substorms. They decay, almost exponentially, after the cessation of the particle influx that attends the solar wind disturbance. This review focuses upon characteristics needed for intelligent use of the ring current as a source for induction probing of the earth's mantle. Considerable difficulties are found with the assumption thatDst is a ring-current index.     

Analysis of source location errors for a magnetic dipole buried in a laterally inhomogeneous conducting earth

Summary A numerical model is used to simulate a vertical magnetic dipole (VMD), with time harmonic excitation, buried under a segmented overburden. Results are presented in terms of readily measured field quantities. Of special interest are the ellipticities of the magnetic field in the vertical and horizontal planes. These turn out to be very sensitive to the lateral variation of the conductivity structure. Other parameters, such as the vertical magnetic field on the surface, are much less influenced. It is suggested that the combination of such measurements should lead to an optimum system for source location in application to mine rescue operations.     

磁偶极子梯度张量的几何不变量及其应用

磁梯度张量系统姿态的变化将影响梯度场测量和数据解释的精度,使得具有坐标变换不变性特点的张量不变量成为磁梯度张量数据解释的研究热点.本文在对磁偶极子产生的磁梯度张量进行特征值分析的基础上得到了:测量点与磁偶极子位置形成的位置矢量、磁偶极子磁矩矢量与绝对值最小的特征值对应的特征向量垂直;位置矢量和磁矩矢量与最大及最小特征值对应的特征向量共面,且两矢量间的夹角可由磁梯度张量矩阵的特征值表示.最后,将本文所得磁偶极子梯度张量的几何不变量用于磁性目标的跟踪中,取得了较好的实时跟踪效果.     

海洋环境中水平电偶极子电磁场特征分析

海洋环境中人工源电磁信号可以用来进行海洋资源勘查、钻前储层评价以及海洋环境中的通信,具有重要的研究意义.为了研究可控源装置在海洋环境中产生的电磁响应特征,本文针对典型海洋层状导电模型,利用由虚界面法获得的电磁场表达式,结合离散复镜像法实现了长导线源产生的电场和磁场的计算.通过数值计算结果可以看出:1)不同的场分量的空间分布规律不同;2)不同方向的Ex分量相对Hy分量受空气波的影响较小,故海洋电磁法勘探应选用Ex分量测量,而海洋通讯系统应选择接收Hy信号;3)同线方向Ex分量相对于赤道方向对海底高阻层的反映明显.本文的研究内容对海洋可控源电磁法测量方式的选择以及通信技术的研究具有指导意义.     

电离层-均匀地球模型中地表水平电偶极子激发的电磁场

本文在电离层-均匀地球模型中使用Debye势方法,在电磁场一般性边界条件下导出了地表水平电偶极子源在地球介质中激发的电磁场的表达式.对球Bessel函数使用指数函数近似,并采用加速算法,计算了地表及地下的电磁场.其正确性得到理论计算和实际观测数据的多方面支持.结果表明,在收发距离大于1000 km,电磁场强度很稳定,几乎没有衰减的迹象;电磁场受电离层的影响很大,由于电离层高度升高或电导率减小引起的电磁场幅度的减少可以达到50%,但是由电场和磁场得到的视电阻率变化却很小.     

Analogue model measurements for a horizontal magnetic dipole embedded within a conducting medium

The validity of an analogue model method employing a horizontal magnetic dipole source situated within a conducting layer for the cases of a poorly conducting model earth and a highly conducting model ocean is studied by comparing model magnetic field measurements with theoretical calculations. The model is then used to study one example for each case; the response of a conducting cylinder simulating an ore body embedded in the earth, and the response of a conducting wedge simulating a shelving ocean.     

The sub-surface magnetic fields produced by a line current source on a non-flat earth

Summary A simple cylindrical model is employed to estimate the effect of non-flatness of the ground on the sub-surface electromagnetic field from a current-carrying cable on the surface. It is shown that, if the surface curvature is sufficiently small, the fields in the cylinder model are very similar to those for the conducting half-space model of the earth employed earlier. The results can be used to provide estimates of expected errors in electromagnetic direction-finding of a buried receiving terminal.The research reported here was supported in part by the Mine Safety Center, U.S. Bureau of Mines.     

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.