Induction in a layered plane earth by uniform and non-uniform source fields

A review of electromagnetic induction in a multi-layered earth is built around a development of the general theory from first principles. Induction by transient and periodic fields and by dipole and electrojet sources are discussed and the method of complex images is briefly described. The review concludes with a discussion of induction by elementary harmonic sources whose non-uniformity is characterised by Price's ν-parameter and which include the uniform source field (ν=0) as a special case. The conditions under which the source may be assumed uniform for computing the surface impedance and other ratios of field components are examined.     

层状介质中水平磁偶极子电磁场空间分布特征

针对岩层中介电常数和磁导率随深度变化的情况,给出水平磁偶极子源电磁场的水平或垂直空间分布特征及相应的变化规律。采用Kong给出的汉克尔（Hankel）J0变换线性滤波器（241点）和汉克尔J1变换线性滤波器（241点）算法,选用均匀大地和两层地电模型,讨论介质的介电常数和磁导率变化时的水平磁偶极子电磁场空间分布特征。计算结果表明,磁场的峨分量幅值与磁导率反相关;磁场H2和电场Ey分量随着磁导率的增大而增大;低频电磁测深中介电常数变化时对电磁场基本没有影响。     

基于CM4模型的中国大陆地区地磁场时空分布特征分析

本文利用第四代地磁场综合模型（Comprehensive Model 4,CM4）,计算了1982-2001年中国大陆地区同一经度链和同一纬度链上地磁台站的磁层源磁场及其感应场、电离层源磁场及其感应场的地磁北向分量X、东向分量Y、垂直分量Z的模型值,分析了各场源磁场随时间和空间的变化特征。结果表明:在时间上,经度链和纬度链台站的磁层源磁场及其感应场均呈现出11年和27天周期性变化。电离层源磁场及其感应场具有明显的季节变化,不同年份相同季节变化形态一致但幅度不同。在空间分布上,经度链和纬度链台站磁层源磁场及其感应场的年变化幅度呈现出不同变化特征,电离层源磁场及其感应场在经度链上变化特征不同,而纬度链台站的数值基本一致。日变化分析显示,磁静日和磁扰日期间,模型数据与台站实测数据变化一致性较好,相关性较高。     

CSAMT全区电阻率法数值模拟及应用探讨

常规的可控源电磁法理论在计算视电阻率公式上,多半采用其电磁场的渐近特征,难以直接反映全区视电阻率的值,及直观地显现地下介质的地质构造.文中采用水平偶极子激发的电磁场,提出了电场的全区精确表达式,直接计算出大地电阻率.利用汉克尔数值滤波算法和逆样条插值算法对水平层状电磁场进行正演计算,并与计算的卡尼亚视电阻率的对比和野外试验结果表明：该方法的结果在远区等价卡尼亚电阻率,在近区和过渡带则明显地改善了卡尼亚电阻率的非波场区场畸变,从而能更好地接近基底的真电阻率,更形象地反映了地下介质的垂向电性变化.     

Results of recent studies of electrical conductivity of sub-surface structure in parts of the western and mid-western states of Nigeria

Summary A mathematical structure that takes into account the spatial non-uniformity of the source field distribution has been applied to geomagnetic data collected in Nigeria.A heuristic modelling technique, whose inverse exists, has been employed to obtain four-to sixlayered conductivity models of the earth.The results represent further delineation of fine structure in the sub-surface profile beneath Nigeria. An attempt is made to correlate these results with the feasible geological structure of the area.     

Analysis of the geomagnetic induction tensor

The geomagnetic induction tensor is a means of summarizing the response of the earth at a given observing site to a geomagnetic variation source field. In this paper the characteristics of the tensor elements are examined, both generally and for the special cases of one-dimensional and two-dimensional geologic structure. The first-order model is taken of uniform source fields originating external to a semi-infinite half-space. Graphical ways of presenting the information contained in an induction tensor are explored, including ellipses of rotation, polar diagrams, and diagrams analogous to the Mohr circles of elasticity theory. Criteria to distinguish “two-dimensional” data from “three-dimensional” data are established. The advantages of simultaneously recording “normal” and “anomalous” variations are demonstrated in terms of the extra tensor elements which may then be estimated. The most practical way of presenting information from many stations on a map may be by drawing, for each site, arrows which summarize the response in the vertical field and quadrics which summarize the response in the horizontal field.     

Electromagnetic induction in the earth due to stationary and moving sources

A new approach to the theory of electromagnetic induction is developed that is applicable to moving as well as stationary sources. The source field is considered to be a standing wave generated by two waves travelling in opposite directions along the surface of the earth. For a stationary source the incident waves have velocities of the same magnitude, however for a moving source the velocities of the two incident waves are respectively increased and decreased by the velocity of the source. Electromagnetic induction in the earth is then considered as refraction of these waves and gives, for both stationary and moving sources, the magnetotelluric relation: $$\frac{{ - E_y }}{{H_x }} = \left( {\frac{{i\omega \mu }}{\sigma }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - i\frac{{v^2 }}{{\omega \mu \sigma }}} \right)^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $$ where ν is the wavenumber of the source, μ is the permeability (4π·10^?7) and σ is the conductivity of the earth. ω is the angular frequency of the variation observed on the earth. For a stationary source the observed frequency is the same as the source frequency, however the effect of moving a time-varying source is to make the observed frequency different from the frequency of the source. Failure to recognise this in previous studies led to some erroneous conclusions. This study shows that a moving source isnot “electromagnetically broader” than a stationary source as had been suggested.     

CONDUCTING SPHERE IN ELECTROMAGNETIC INPUT FIELD*

A frequency-domain analysis is outlined for a conducting sphere in a uniform Input field: inequispaced alternating half-sine wave pulses. The Barringer Input air-borne electromagnetic exploration system uses such source fields. Theoretical profiles of Hρ(t), the horizontal magnetic component over the sphere from different elevations and for various conductivity and geometrical factors are presented. Based on these results some useful features such as penetration and detectibility are discussed.     

Transient electromagnetic surveys with unimodal transverse magnetic field: ideas and results

The theory behind transient electromagnetic surveys can be well described in terms of transverse magnetic and transverse electric modes. Soundings using transverse magnetic and transverse electric modes require different source configurations. In this study, we consider an alternating transverse magnetic field excitation by a circular electric dipole. The circular electric dipole transmitter is a horizontal analogue of the vertical electric dipole. Offshore surveys using circular electric dipole might represent an alternative to the conventional marine controlled‐source electromagnetic method at shallow sea and/or for exploring relatively small targets. Field acquisition is carried out by recording either electric or magnetic responses. Electric responses bear information on the 1D structure of a layered earth and successfully resolve high‐resistivity targets in marine surveys. Land‐based circular electric dipole soundings are affected by induced polarisation. On the contrary, magnetic responses are absent on the surface of a 1D earth, and as a result, they are very sensitive to any and even very small 3D conductivity perturbations. In addition, they are sensitive to induced polarisation or some other polarisation effects in the subsurface. At present, circular electric dipole transmitters and magnetic receivers are successfully used in on‐land mineral and petroleum exploration.     

地震电离层异常电场模拟及初步研究

强地震会造成电离层电场发生异常变化.基于大气层-电离层电动力学理论对地震电离层异常电场开展数值模拟和研究,将理论推导出来的电离层异常电场方程扩展到球面坐标系中,并且考虑到电离层层电导率的各向异性,建立新的地震电离层异常电场模式.引进一个电离层层电导率经验公式(Nopper and Carovillano,1979),对中低纬度地震电离层异常电场特性进行数值模拟.模拟结果表明:附加电流引起电离层异常电场范围远大于自身在地表上的分布.且发生在低纬地区的异常电场主要成分是纬向电场,在东西两侧显偶极子分布.在额外电流分布相同的情况下,夜晚生成的异常电场更显著,存在昼夜差异.     

地震的感应磁效应（二）

本文是“地震的感应磁效应（一）--三维电磁感应的数值理论”一文的继续。首先从理论和实际计算两个方面证明了三维电磁感应数值方程解的唯一性、收敛性和稳定性,从而充实了作为研究地壳、上地幔电性结构横向不均匀性理论基础的“三维数值方法”。作为这一理论方法的实际应用,文中对不同源场周期和具有不同埋藏深度的三维电导率异常体进行了模拟计算,以研究地震感应磁效应的大小、空间分布特征和频率特性。模拟计算结果表明,对于周期从数秒到数分钟的地磁短周期变化,若电导率异常体的线度与5至7级地震的震源体积大体相当,其电导率较原背景电导率高近一个量级,其感应磁效应主要特征为:在异常体正上方,地面磁场的水平分量变化最大,相对变化量约30％;在异常体于源场方向一致的两侧,垂直分量变化最大,相对变化量约40-50％。因此,观测短周期地磁场的异常变化,有可能是监测地震孕育过程地下电性变化的一种试验途径。但由于上述异常强度在空间上衰减迅速,所以观测必须接近震源区,这对测点的选择是个不利的因素。     

The calculation of perturbation and induction arrows for a three-dimensional conductivity model and dipole source fields

A numerical method is used to calculate the electromagnetic fields associated with a three-dimensional conductivity anomaly. The source field is due to horizontal magnetic dipoles placed at two different positions with respect to the conductivity anomaly. The transfer functions and related perturbation and induction arrows associated with the fields are calculated and compared with the arrows obtained from a uniform source calculation. The results show the source effect on the induction arrows and indicate that the perturbation arrows provide a method of outlining the spatial extent of the anomaly. The transfer function calculations are made for both exact and approximate normal fields. In the transfer function calculation the anomalous fields are correlated with a normal field as suggested by Schmucker (1970) and Cochrane and Hyndman (1970).     

Electric field data in inductive source electromagnetic surveys

Measurement of the electric field data due to an inductive loop source in a controlled source electromagnetic survey is not common, because electric field data, usually involving grounded electrodes, are expensive to acquire and difficult to interpret. With the recently developed capability of versatile three‐dimensional inversion, we revisit the idea of measuring electric field in a large ground loop survey for mineral exploration. The three‐dimensional modelling and inversion approach helps us quantitatively understand the detectability and recoverability of the proposed survey configuration. Our detectability study using forward modelling shows that the relative anomaly (percentage difference) in electric field does not decay with a lower induction number, but the conventional magnetic field data (dB/dt) does. Our recoverability study examines how much and what kind of information can be extracted from electric field data for the reconstruction of a three‐dimensional model. Synthetic inversions show the following observations. (i) Electric field data are good at locating lateral discontinuity, whereas dB/dt has better depth resolution. (ii) Electric field is less sensitive to the background conductivity and, thus, is prone to misinterpretation because of a bad initial model in inversion. We recommend warm‐starting the electric field inversion with an initial model from a separate dB/dt inversion. (iii) Electric field data may be severely contaminated by near‐surface heterogeneity, but an inversion can recover the deep target concealed by the geologic noise. (iv) Even one line of single‐component electric field data can greatly improve the horizontal resolution in a dB/dt inversion. Finally, we investigate a field dataset of both electric field and dB/dt measurements at a uranium deposit. The field example confirms that the electric field and magnetic field data contain independent information that is crucial in the accurate recovery of subsurface conductivity. Our synthetic and field examples demonstrate the benefit of acquiring electric field data along with magnetic field data in an inductive source survey.     

Theoretical models for electromagnetic induction in the oceans

The different methods and techniques employed in the theory of electromagnetic induction in thin sheets are reviewed and the methods for approximation to the solution are indicated. These depend on whether the sheet is closed or finite and on whether the integrated conductivity and/or the frequency of variations is high or low.Results for induction in finite sheets which are suitable for ocean modelling are given. These include sheets of perfect conductivity and sheets of finite conductivity which is either discontinuous or continuous at the boundary. The dependence of the “coastline effect” for a global ocean on the location of the edge of the continental shelf, the period of variation of the external field and the conductivity of the underlying earth is explained.     

矿井全空间孔中瞬变电磁响应积分方程法数值模拟研究

基于地面-钻孔瞬变电磁法,将发射源布设于煤矿巷道中,而将接收探头放置在钻孔内,从上至下依次观测,形成矿井巷道-钻孔瞬变电磁法.为了研究巷道全空间条件下巷道-钻孔瞬变电磁场的响应特征,选取煤层底板受水害威胁的代表性地层为研究对象,建立煤层底板存在含水低阻地质异常体的三维数学模型,采用积分方程法进行数值模拟,结果表明：相对高阻的煤层侧帮对孔内垂向感应电动势的影响较小,而对孔内水平感应电动势除浅部约30 m内影响相对较大外,对深部影响较小.当煤层底板含水平低阻板状异常体时,在对异常体的纵向分辨率和异常响应的延续时间方面,孔内感应电动势的水平分量相对优于垂向分量,但垂向感应电动势的幅值强于水平感应电动势.因此,实际观测时,不仅要观测孔内感应电动势的垂向分量,也要观测水平分量.     

THE INDUCTIVE RESPONSE OF A HORIZONTAL CONDUCTING CYLINDER BURIED IN A UNIFORM EARTH FOR A UNIFORM INDUCING FIELD*

The inductive response of a conducting horizontal cylinder embedded in a uniform earth is studied using numerical results obtained for an analytical solution for the problem of a conducting cylinder buried in a homogeneous earth for the case of a uniform inducing field. A check of the validity of the numerical results is made by a comparison with analogue model measurements for a number of cases. Numerical results for a range of cylinder radii (a = 1–10 km), depths of burial (d= 0–4 km), conductivity contrasts (σ₂= 10^?2-10 Sm^?1), and source frequencies (f= 10^?1-10^?4 Hz) of interest in the interpretation of magnetotelluric field measurements are presented. The results indicate that for a uniform inducing field the conductivity and depth of burial of a horizontal cylindrical inhomogeneity are best determined through a measurement of the amplitudes H_y, H_z and E_x and the phases φ_y and Ψ_x.     

Sensitivity and inversion of marine electromagnetic data in a vertically anisotropic stratified earth

The controlled‐source electromagnetic (CSEM) and magnetotelluric method (MT) are two techniques that can be jointly used to explore the resistivity structure of the earth. Such methods have, in recent years, been applied in marine environments to the exploration and appraisal of hydrocarbons. In many situations the electric properties of the earth are anisotropic, with differences between resistivity in the vertical direction typically much higher than those in the horizontal direction. In cases such as this, the two modes of the time‐harmonic electromagnetic field are altered in different ways, implying that the sensitivity to the earth resistivity may vary significantly from one particular resistivity component (scalar, horizontal or vertical) to another, depending on the measurement configuration (range, azimuth, frequency or water depth). In this paper, we examine the sensitivity of the electromagnetic field to a vertically anisotropic earth for a typical set of configurations, compare inversion results of synthetic data characterizing a vertically anisotropic earth obtained using the isotropic and anisotropic assumptions and show that correctly accounting for anisotropy can prevent artefacts in inversion results.     

位于导电介质中三维导体的电磁响应

本文给出一种用积分方程法配合有限差分法计算位于导电介质中三维导体的电磁响应的新途径,在二层大地条件下给出了具体计算方法和结果。详细讨论了围岩介质的导电性对导体异常的影响。这对于开展低阻覆盖层地区的电磁法工作具有一定的指导意义。     

位于导电介质中三维导体的电磁响应

本文给出一种用积分方程法配合有限差分法计算位于导电介质中三维导体的电磁响应的新途径,在二层大地条件下给出了具体计算方法和结果。详细讨论了围岩介质的导电性对导体异常的影响。这对于开展低阻覆盖层地区的电磁法工作具有一定的指导意义。     

The electromagnetic response of a horizontal electric dipole buried in a multi‐layered earth

The electromagnetic response of a horizontal electric dipole transmitter in the presence of a conductive, layered earth is important in a number of geophysical applications, ranging from controlled‐source audio‐frequency magnetotellurics to borehole geophysics to marine electromagnetics. The problem has been thoroughly studied for more than a century, starting from a dipole resting on the surface of a half‐space and subsequently advancing all the way to a transmitter buried within a stack of anisotropic layers. The solution is still relevant today. For example, it is useful for one‐dimensional modelling and interpretation, as well as to provide background fields for two‐ and three‐dimensional modelling methods such as integral equation or primary–secondary field formulations. This tutorial borrows elements from the many texts and papers on the topic and combines them into what we believe is a helpful guide to performing layered earth electromagnetic field calculations. It is not intended to replace any of the existing work on the subject. However, we have found that this combination of elements is particularly effective in teaching electromagnetic theory and providing a basis for algorithmic development. Readers will be able to calculate electric and magnetic fields at any point in or above the earth, produced by a transmitter at any location. As an illustrative example, we calculate the fields of a dipole buried in a multi‐layered anisotropic earth to demonstrate how the theory that developed in this tutorial can be implemented in practice; we then use the example to examine the diffusion of volume charge density within anisotropic media—a rarely visualised process. The algorithm is internally validated by comparing the response of many thin layers with alternating high and low conductivity values to the theoretically equivalent (yet algorithmically simpler) anisotropic solution, as well as externally validated against an independent algorithm.