Electromagnetic response of a buried cylindrical conductor for sheet and line current sources

A major problem in electromagnetic induction studies in regions of localized source fields, such as the auroral and equatorial electrojet regions, is the source effect. Using an analytical model, the electromagnetic response of a buried conducting cylinder to sheet current and line current excitations has been studied for the period rangeT=5 s to 24 h. The validity of the numerical results obtained from the analytical model are compared with the numerical results obtained from a finite difference model. The results show that for periods less than 30 min, there is no significant difference in the response of the cylinder to both source fields. However, significant differences are observed at longer periods. It was also observed that the equivalent height at which a uniform sheet current at 100 km above the earth's surface can be approximated by a line current varies as a function of the source period.     

Quasi-static transient response of a covered permeable inhomogeneous cylinder to a line current source

Summary Transient electromagnetic response of a cylindrical conductor covered by (a) an insulated and (b) a galvanically connected coaxial shell has been obtained. The exciting pulse is produced by switching off a long alternating current source. The study incorporates the influence of magnetic permeability contrast of the cylinder with the surrounding medium and also that of the inhomogeneity in the conductivity. The generalised initial value problem is significant in the study of certain geomagnetic anomalies. The results will also aid to the interpretation of induction prospecting data for elongated porphyry conducting mineral deposits.N.G.R.I. Contribution No. 71-280.     

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.     

Electromagnetic transient response of a small wire loop buried in a homogeneous conducting earth

Summary The analysis extends previously obtained results for the transient magnetic fields of small loops in the presence of a homogeneous conducting half-space. Here, the secondary scattering of pulses by a buried target loop is examined for the case where both the source and receiver loops are located at the surface. While the response of the buried or target loop is orders of magnitude below the primary response, there is a significant difference in the respective transient waveforms. Thus, the results have possible application to mine rescue using a passive detection technique.     

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.     

Spin-up of a two-layer fluid in a rotating cylinder

Abstract

we report the results of experiments on the spin-up of two layers of immiscible fluid with a free upper surface in a rotating cylinder over a wide range of internal Froude numbers. Observations of the evolution of the velocity field by particle tracking indicates that spin-up of the azimuthal velocity in the upper layer take much longer than in a homogeneous fluid. Initially, spin-up occurs at a rate comparable to that of homogeneous fluid but, at high internal Froude number, a second phase follows in which the remaining lative motion decays much more slowly. Quantitative comparison of these measurements to the theory of Pedlosky (1967) shows good agreement.

Visualization of the interface displacement during spin-up detected the presence of transient azimuthal variations in the interface elevation over a wide range of Froude (F), Ekman (E), and Rossby (ε) number. nalysis of the occurrence of the asymmetric variations using the parameter space (Q, F), where Q = E ^1/2/ε, suggested by the baroclinic instability theory and experiments of Hart (1972), showed that the flow was stable for Q > 0.06 with no discernable dependence on F. This result, together with the prediction of Pedlosky's theory that radial gradient of potential vorticity in the two layers have opposite signs, suggests at the baroclinic instability mechanism was responsible for the asymmetries. The location and timing of these instabilities may account for the discrepancies between the observations and the Pedlosky (1967) theory.     

三分量感应水平线圈系在薄层中的响应特性研究

三分量感应仪器最初的设计目的是测量薄交互层的电导率和层厚.建立0.3m三层和五层薄交互层模型,用COMSOL有限元软件三维数值计算三分量阵列感应8个水平线圈系子阵列响应,详细分析其响应特征与线圈间距和层厚的关系.结果表明,三层模型中的水平子阵列响应特征由其发射、屏蔽和接收在薄层中的位置决定,发射、屏蔽和接收进出薄层,在响应曲线上均有一定表现.当发射和主接收间距小于薄层厚度时,可有效分辨薄层.当发射和屏蔽之间的距离小于层厚时,可利用主接收进出薄层特征点识别薄层厚度.否则,由于发射、屏蔽和接收在层中的位置关系复杂和响应变化大,无法有效分辨薄层.此外,测井响应受围岩影响较大,读数不等于薄层的电导率.研究成果对三分量阵列感应仪器设计和测井响应解释评价具有重要的理论和实际意义.     

Model tests and numerical analyses on horizontal impedance functions of inclined single piles embedded in cohesionless soil

Horizontal impedance functions of inclined single piles are measured experimentally for model soil-pile systems with both the effects of local soil nonlinearity and resonant characteristics.Two practical pile inclinations of 5° and 10° in addition to a vertical pile embedded in cohesionless soil and subjected to lateral harmonic pile head loadings for a wide range of frequencies are considered.Results obtained with low-to-high amplitude of lateral loadings on model soil-pile systems encased in a laminar shear box show that the local nonlinearities have a profound impact on the horizontal impedance functions of piles.Horizontal impedance functions of inclined piles are found to be smaller than the vertical pile and the values decrease as the angle of pile inclination increases.Distinct values of horizontal impedance functions are obtained for the ’positive’ and ’negative’ cycles of harmonic loadings,leading to asymmetric force-displacement relationships for the inclined piles.Validation of these experimental results is carried out through three-dimensional nonlinear finite element analyses,and the results from the numerical models are in good agreement with the experimental data.Sensitivity analyses conducted on the numerical models suggest that the consideration of local nonlinearity at the vicinity of the soil-pile interface influence the response of the soil-pile systems.     

Steady-state response of a stratified half-space subjected to a horizontal arbitrary buried uniform load applied at a circular area

This paper outlines a method of analysis of the steady-state dynamic response of a stratified soil to a horizontal time-harmonic loading applied at a circular area. It is assumed the load to be uniformly distributed over the contact area and embedded at an arbitrary depth. It is shown that by means of application of integral Hankel transform, the problem can be reduced to a form of a single integral, which can be taken numerically. Results of the numerical simulations for an embedded horizontal impulse load are presented to demonstrate the efficiency of the developed procedure.     

The effect of the oceans and sedimentary cover on global magnetovariational field distribution

Electromagnetic fields excited by long-period geomagnetic variations were calculated for spherical earth models with the realistic inhomogeneous surface layer. Calculations were also carried out for the model with the double inhomogeneous layer. The modelling results did not display the same level of distortions which had been observed experimentally. The revealed contradiction may be explained by a possible existence of significant inhomogeneities in the earth mantle.     

伪随机编码源电磁响应的精细辨识

与传统阶跃源激励方式相比, 采用m序列伪随机编码对发射源波形进行编码, 提高了电磁探测的深度和分辨能力.然而受这种编码源发射波形自相关旁瓣效应的影响, 使得对大地冲激响应的精细辨识效果受到一定限制.为了解决这一问题, 在以往相关辨识方法研究的基础上, 进一步考虑发射自相关旁瓣的影响, 首先提出一种由收发互相关中高精度提取大地冲激响应的数学方法; 然后通过数值模拟给出了m序列编码源大地冲激响应的精细辨识结果; 同时对以m序列为发射波形的勘探系统相关参数选择进行了分析; 最后利用本文提出的方法对野外实测数据进行辨识处理, 通过与其他EM方法结果进行对比, 证明了本文提出方法的可靠性.     

Time domain BEM analysis of dynamic response of a cylinder embedded in soil with frictional slip at the interface

A 2D time domain boundary element method (BEM) is developed to study the dynamic response of a cylinder embedded in soil. The interface is assumed in contact with Coulomb friction. For the incident wave strong enough, local slip may occur along the interface. We suppose a pressure enough high is applied on the interface so that separation is impossible. The present problem is indeed a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip and stick regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embedded in an infinite solid. Numerical results for the near field solutions are presented. The nonlinear nature of the system is discussed.     

华北近十年来水平运动动态与地震活动危险区的讨论

根据华北地区1999年和2001年两期高精度GPS观测结果，通过与1992，1995，1996年和1999年这几期资料的比较，发现近两年的运动与前有所不同，主要表现为：（1）阴山单元和鄂尔多斯单元之间显示为压性运动的性质，但比较微弱，它们之间的边界带上似乎有左旋走滑运动，但从整体上看并不显著。（2）晋冀鲁单元和燕山单元的整体活动性不如以前，各单元内部存在着较明显的差异运动，并山单元和晋冀鲁单元的北部存在着比较显著的东西向挤压，北京地区则表现为南北向挤压。（3）晋冀鲁单元南部与胶辽鲁苏单元的南部的趋势活动呈张性，优势运动方向为东南，这样的结果可能表明，华北目前存在着应力扰动行为，大同与天津之间的区域是受其影响最大的地区，该区有可能成为未来几年中强地震活动的一个主体地区。     

Group theoretic reduction of the electromagnetic impedance matrix for large-contrast symmetric prisms in a layered earth

Calculation using integral equations of the electromagnetic response of a geologic body which is much more conductive than the surrounding media requires the use of both current pulse and current tube basis functions. The impedance matrices for such cases can be large and expensive to form, factor, and solve. However, if the surrounding media is layered and the scatterer is symmetric under symmetry operations which preserve the depth of transformed points, then we can apply group representation theory to drastically reduce storage and computation requirements. I discuss this application of group representation theory in detail, using the symmetry groupC ₂ for purposes of illustration. In a sample calculation for a body which is invariant under the symmetry operations of the groupC ₂ , storage was reduced by a factor of 4, matrix formation time was reduced by a factor of 2, and the sum of matrix factorization and solution times was reduced by a factor of 10.     

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.     

乌加河地震台水平摆、水管倾斜仪同震响应对比分析

选取2013—2015年乌加河地震台水平摆和水管仪记录的13个地震资料,对比分析同震响应特征。分析认为:对于同一地震,水平摆最大响应幅度大于水管仪,且响应延迟时间略小;水管仪和水平摆同震响应持续时间与震级成正比。结果表明,该地震台水平摆和水管仪记录同一地震的最大响应幅度、延迟和持续时间,对远震和近震均具有不同程度的响应。     

Complex image method for calculating electric and magnetic fields produced by an auroral electrojet of finite length

The electromagnetic field due to ionospheric currents has to be known when evaluating space weather effects at the earths surface. Forecasting methods of these effects, which include geomagnetically induced currents in technological systems, are being developed. Such applications are time-critical, so the calculation techniques of the electromagnetic field have to be fast but still accurate. The contribution of secondary sources induced within the earth leads to complicated integral formulas for the field at the earths surface with a time-consuming computation. An approximate method of calculation based on replacing the earth contribution by an image source having mathematically a complex location results in closed-form expressions and in a much faster computation. In this paper we extend the complex image method (CIM) to the case of a more realistic electrojet system consisting of a horizontal line current filament with vertical currents at its ends above a layered earth. To be able to utilize previous CIM results, we prove that the current system can be replaced by a purely horizontal current distribution which is equivalent regarding the total (= primary + induced) magnetic field and the total horizontal electric field at the earths surface. The latter result is new. Numerical calculations demonstrate that CIM is very accurate and several magnitudes faster than the exact conventional approach.     

Generalized reflection and transmission coefficients for seismic sources in a multi-layered spherical earth model

Summary A method of propagating the components of the displacement across interfaces in a multi-layered spherical earth model is presented. It is useful both for explosion sources and tangential dislocation sources, buried in an arbitrary layer of the model. Combined with known techniques, our method yields a useful tool for generating synthetic seismograms for earthquake sources in realistic earth models.     

A direct method of interpreting gravity and magnetic anomalies: The case of a horizontal cylinder

Summary A new method of interpreting the gravity and magnetic anomalies is introduced with special reference to the magnetic anomalies of a horizontal cylinder. The method consists of calculating the functions of the anomaly and its distance from an arbitrary point. These form a simple linear equation with coefficients related to the parameters defining the body. Since each observation forms a separate linear equation, the required normal equations are formed by the method of least squares and solved for the coefficients and hence for the various parameters defining the target. The discussion here is confined to the vertical magnetic anomalies. The application of the method to horizontal and total field anomalies of two dimensional bodies is also outlined.