Determination of the Cole-Cole parameters in polarizable media from logging data

The paper presents the solution to an axially symmetric problem of the electromagnetic field excited by an electric dipole and a current in a half-infinite cable in a cylindrically layered polarizable medium. The polarization of the medium is described by the Cole-Cole formula, including such parameters as the conductance, polarizability, response time, and attenuation coefficient. The spatiotemporal structures of the field in polarizable and nonpolarizable homogeneous media are compared. The apparent Cole-Cole parameters are defined and determined for a model problem of a cylindrically layered medium.     

金属护栏对洛阳地震台地电阻率干扰定量分析

自2018年12月起,因洛阳地震台测区内安装金属护栏,该台地电阻率出现异常变化。为正确评估此次影响,结合洛阳地震台电测深曲线、岩性资料建立了三维水平层状结构模型,利用有限元法计算了测区内金属护栏对洛阳地震台地电阻率观测的影响。同时,建立典型“H”型电性结构模型,分析了不同属性的金属导线对地电阻率观测的影响。结果显示：①金属护栏是洛阳地震台此次地电阻率年变异常的主要影响因素。当位于测区内影响系数为负的区域时,金属护栏引起地电阻率的趋势性上升;当位于影响系数为正的区域时,金属护栏引起地电阻率的趋势性下降。②不同属性的金属导线对地电阻率观测的影响不同。导线与测道夹角减小、导线长度增加、导线电阻率减小以及导线横截面积增加等均会导致干扰源对地电阻率年变影响作用增强。     

二维频率测深边界单元法正演计算

在二维层状介质中含有横向非均匀体的地电断面情况下，对电偶源的偶极长度作了延长，并选取了适当的基本解及无穷远边界条件，因而将相应的含源谐变电磁场的边值问题转化为较简单的边界积分方程．用边界单元法求出了相应的电磁场分量，进而计算阻抗视电阻率，并对这一算法作了相应的检验．     

基于二次耦合势的广域电磁法有限体积三维正演计算

与可控源音频大地电磁（CSAMT）相比,广域电磁法通过采用全区视电阻率定义,突破了卡尼亚视电阻率所需的远区条件限制,极大拓展了可控源电磁观测区域和探测深度.考虑到电偶源激发场的三维特征以及地下复杂三维结构,为提高广域电磁数据解释精度,本文实现了基于二次耦合势的广域电磁法三维正演计算.该算法利用Helmholtz定理将麦克斯韦方程转化为库伦规范下的磁矢势和电标势耦合方程,有效改善了离散所得大型线性方程组的谱性质,并通过强加散度条件来消除电场伪解的影响.此外,采用散射场方法,其中一次场使用准解析法求解,二次场使用有限体积法求解,克服了局部激发场源奇异性问题.通过与一维层状模型下电偶源产生的电磁场准解析解对比,验证了本文算法的正确性.在此基础上,利用本文的正演算法对比分析了广域电磁法与CSAMT对典型三维目标体的探测能力,结果表明在相同的观测条件下,广域电磁法能够更准确地反映地下目标体信息,拥有更优的分辨能力.     

Resistivity and induced polarization response of a thin sheet

The relevant potential theory is given for a current point source in the presence of a conductive slab embedded in a homogeneous host region of infinite extent. The thin sheet representation is obtained from the exact integral formulation by a simple mathematical limit process. The same result is also deduced directly at the outset by applying a thin sheet boundary condition. The apparent resistivity for a two electrode array is then computed for the case where the bore hole intersects the thin sheet at right angles. The corresponding results for the dilution factor, relevant to the induced polarization response, are also obtained. It is shown that the apparent resistivity and the dilution factor are constant when the potential and the current electrode straddle the sheet but there is a characteristic decrease as the electrodes move away from the sheet.     

Dynamic plate-soil interaction - finite and infinite, flexible and rigid plates on homogeneous, layered or Winkler soil

An integral method to calculate the solution of a homogeneous or layered soil due to a harmonic point load is described. An infinite plate at the surface of the soil can be introduced in this integration in wavenumber domain, too. Finite structures on the soil are calculated by a combined finite element and boundary element method, which makes use of the point load solution of the soil. The compliance functions for a vertical point load and some vibration modes are calculated for realistic parameters of the plate and the soil and for a wide range of frequencies. The influence of the stiffness of the soil and the foundation is investigated, showing that the soil mainly affects the low-frequent response whereas the structural properties are more important at higher frequencies. A rigid approximation of flexible plates is only found at low frequencies, if the elastic length is used as the radius of a rigid disk. At higher frequencies, a characteristic behaviour of the flexible plate of approximately is observed, what is in clear contrast to the compliance of rigid foundations. A plate on a visco-elastic support (Winkler soil) shows similar displacements as a plate on a homogeneous half-space, but the maximal stresses between the plate and the soil are considerably smaller which is found to be more realistic for a plate on a layered soil. For practical applications, a normalized diagram and some explicit formulas of the exact and the approximate solutions of an infinite plate on a homogeneous half-space are given, which is a useful model to represent the soil-structure interaction of flexible foundations.     

A new method for geoelectrical investigations underwater1

A new electrical method is proposed for determining the apparent resistivity of multi-earth layers located underwater. The method is based on direct current geoelectric sounding principles. A layered earth model is used to simulate the stratigraphic target. The measurement array is of pole-pole type; it is located underwater and is orientated vertically. This particular electrode configuration is very useful when conventional electrical methods cannot be used, especially if the water depth becomes very important. The calculated apparent resistivity shows a substantial quality increase in the measured signal caused by the underwater targets, from which little or no response is measured using conventional surface electrode methods. In practice, however, different factors such as water stratification, underwater streams or meteorological conditions complicate the interpretation of the field results. A case study is presented, where field surveys carried out on Lake Geneva were interpreted using the calculated apparent resistivity master-curves.     

井下地电阻率观测中地表电流干扰影响计算

本文把地电阻率台站地下介质简化为水平三层均匀介质模型,以点电流模拟地表干扰电流,针对对称四极观测装置,计算了在不同电性结构中的不同深度观测时,地表电流干扰源对对称四极装置地电阻率观测的影响,计算得到:地表干扰源对电阻率观测的影响取决于电性结构的类型和层参数、供电电极和测量电极的埋深以及避开干扰源的距离.本文研究结果对实施井下电阻率观测中台址电性结构的选择、电极埋深、干扰源避让距离等有参考意义.     

GEOELECTRIC AXIAL DIPOLE SOUNDING CURVES FOR A CLASS OF TWO-DIMENSIONAL EARTH STRUCTURES*

With the aim of studying the behaviour of geoelectric axial dipole vertical soundings over complex geology, a systematic theoretical approach is presented for a class of earth structures characterized by horizontal and vertical parallel boundary planes. The two-dimensional cylindrical bodies of infinite length and rectangular cross-section are constrained to have resistivities satisfying Alfano's condition at every intersection line of the graticule, in order to adopt the image-point theory. A detailed analysis is performed for models with any number of horizontal boundaries and two vertical discontinuities. The apparent resistivity formulas are obtained and selected apparent resistivity curves are drawn for different parameter combinations and various directions of the sounding expansion axis. The class under consideration contains as a particular case the HVC model elaborated in Alpin's monograph, where only a small collection of master curves is available for the axial array. The reconstruction of those curves by the present formulation shows the existence of large discrepancies. A test based on the transformation to equivalent half-Schlumberger sounding curves supports the conclusion that an unidentified error must exist in some part of the theoretical approach of the Russian researchers. Finally, some field sounding curves based on geothermal and volcanological surveys are presented and interpreted by complete curve matching, essentially to show the applicability of the theoretical solutions.     

斜阶跃电流激励下多匝小回线瞬变电磁场延时特征

采用Duhamel积分对斜阶跃电流激励的瞬变电磁场进行直接计算,应用叠加原理得到了多匝小回线全域瞬变电磁响应.研究了多匝小回线的早、晚延时临界条件以及等磁矩单匝大回线与多匝小回线的延时和关断时间特征,分析了电阻率、厚度等参数变化时斜阶跃电流对层状模型瞬变响应的影响特征,最后采用实测数据验证了关断效应的校正效果.结果显示,回线边长越小或表层电阻率越大,瞬变响应越早离开早期并进入晚期.多匝小回线的关断时间远大于等磁矩的单匝大回线,但由前者激发的瞬变响应进入晚期的时间却大幅提前,更有利于晚期条件下各种理论公式的使用.斜阶跃影响校正结果显示,增加多匝小回线的匝数可以扩展反演深度的范围,减少匝数则可以提高反演电阻率的精确性;实测数据处理结果显示校正方法产生了一定的效果.本研究补充了多匝小回线瞬变电磁理论内容,研究结果可以为复杂环境中小尺寸多匝线圈的工作参数选择提供参考.     

EFFICIENT COMPUTATION OF TRANSIENT SOUNDING CURVES FOR WIRE SEGMENTS OF FINITE LENGTH USING AN EQUIVALENT DIPOLE APPROXIMATION1

Calculations of emf induced in a vertical axis coil by a current step in a straight wire segment of finite length were carried out using an equivalent dipole placed along the source wire. An approximation is valid for homogeneous and layered earth models. The location of the equivalent dipole is calculated by forcing the early- and late-time asymptotes of the transient sounding curve of the equivalent dipole to match those of the finite wire. This approximation works because the early-time asymptote of the emf depends on the component of the receiver position which is parallel to the wire while the late-time asymptote does not. Analytical integration of the early-time asymptote yields an expression for the equivalent dipole location in closed form. The coil can be placed anywhere in the vicinity of the finite wire. Square or rectangular loop sources can be simulated by one or more finite wire segments depending on the source-receiver geometry. The equivalent radius calculated for central loop soundings agrees well with the value derived using a circular loop with the same area as the square loop. Results show that acceptable sounding curves can be generated by the equivalent dipole for coils placed as close as 0.5 source lengths from the finite wire segment. Higher accuracy can be obtained by splitting the finite wire into two or more subsegments. Results for layered models are slightly better than homogeneous earth models when the resistivity increases with depth and slightly worse for models with resistivity decreasing with depth. Approximate calculations are about 10 times less expensive than exact calculations depending on the method used for the numerical integration.     

THEORETICAL ANALYSIS OF APPARENT RESISTIVITY OVER A DYKE OF ARBITRARY SHAPE*

This paper deals with the apparent resistivity as observed on the surface due to a dyke of arbitrary shape. In order to give a closed analytical solution it has been necessary to assume that the dyke is either perfectly conductive or resistive relative to the enclosing medium. Furthermore we have considered an infinite line source instead of a conventional point current source; however a simple integral transform is given to transform the point-source-data into the line-source-data. So the present study is equally useful where line sources are inconvenient to handle. Besides considering the conventional method of electrical surveying (bipole method) where the source and sink are separated by a finite distance, we have considered a new variation (unipole method) where the source and sink are separated by an infinite distance, and the source is split into two separate sources each of half strength. A series of apparent resistivity curves for both methods are presented for different parameters of the dyke. The usefulness of these curves lies mainly in the fact that they may provide the necessary guide-lines for semi-quantitative interpretation of the observed data.     

The location of infinite electrodes in pole–pole electrical surveys: consequences for 2D imaging

In 2D-multielectrode electrical surveys using the pole–pole array, the distance to ‘infinite electrodes' is actually finite. As a matter of fact, the available cable length generally imposes a poor approximation of theoretical location of these electrodes at infinity. This study shows that in most of the cases, the resulting apparent resistivity pseudosection is strongly distorted. Numerical simulation validated by field test also shows that a particular finite array provides results that are as close as possible to the ones of the ideal pole–pole array. This is achieved when two conditions that are weaker than an infinite location are fulfilled: (i) the ‘infinite electrodes' are placed symmetrically on both sides of the in-line electrodes with a spread angle of 30° and (ii) the length of ‘infinite lines' is at least 20 times the greatest distance between in-line electrodes. The electrical 2D image obtained with this enhanced array is the least distorted one with respect to the pole–pole image. The apparent resistivities are generally underestimated, but this deviation is almost homogeneous. Though the shift cannot be determined a priori, the interpretation of such an image with direct or inverse software designed for pole–pole data provides an accurate interpretation of the ground geometry.     

地表点电流对地电阻率观测的影响

将地电阻率台站地下介质简化为水平层状均匀介质模型,以点电流模拟地表干扰电流源,针对对称四极观测装置,计算干扰源电流增减及位置变化对地电阻率观测的影响。结果表明,地电阻率的受干扰程度取决于地表干扰点电流的大小、在测区的方位及距中心点的距离。     

THE CROSS-HOLE MAGNETOMETRIC RESISTIVITY (MMR) RESPONSE OF A DISC CONDUCTOR*

The cross-hole variant of the magnetometric resistivity (MMR) method requires two bore holes in the vicinity of a conductive target. In the first, two fixed current electrodes are located, one above the other. They are linked to a low frequency current source by cables, the whole system forming a vertical current bipole. In the second, a sensitive coil measures the axial magnetic field as a function of depth. For a uniform earth, if both holes are vertical, the measured component vanishes by symmetry. However, the presence of a local conductor channels the current and causes an anomalous magnetic component which is interpreted to indicate the position, shape and relative conductance of the target. Mineral deposits are often lamellar in form. The conductive disc is the simplest bounded lamella for which MMR responses may be computed. It is excited by a single current source on its axis. The second source and the surface of the earth are assumed to be far away, a valid assumption for down-hole measurements. The numerical method introduces a new integral equation describing the interaction of current dipoles located in the plane of the disc. The equation is solved analytically for a disc of infinite radius, a layer, and the result is compared with a corresponding known boundary value solution. The computed radial current in the disc and the magnetic field generated by it are described in terms of a current channelling number. The magnitude of the computed field is of the order of one nanoTesla for a typical mining problem.     

Two-dimensional resistivity imaging and modelling in areas of complex geology

A system is described for the automatic measurement of electrical resistivity pseudo-sections. This comprises a linear array of up to 32 electrodes connected through a multicore cable to a computer controlled switching module and a resistivity meter. The processing of the measured sections to produce two-dimensional true resistivity images of the subsurface is briefly described. Some account is given of the capabilities and limitations of the technique. This is illustrated by a series of computed constant separation traverses for models of simple subsurface structures. Examples of processed images derived from sections measured in areas of relatively complex geology follow, a comparison being made of the interpretations obtained using an automatic imaging method and a manual iterative approach. It is concluded that with the equipment and software so far developed, in areas of modest subsurface geological complexity where some control is available and where the structures are essentially two-dimensional, then good approximations to the true geoelectric sections can be obtained down to depths of between 100 and 200 m.     

Pole-dipole resistivity sounding technique for shallow investigations in hard rock areas

Theory of the pole-dipole resistivity sounding technique and its application in the hard rock areas for shallow groundwater exploration is presented in this paper. The different components of electric field produced by the point source of current, situated over the ground surface, are measured by a dipole placed at a large distance from the source. The theory of the method is rather simple, suggesting two configurations, namely radial pole-dipole and axial pole-dipole. Theoretical expressions derived for the apparent resistivity over layered Earth are directly related to the Schlumberger apparent resistivity, whereas expressions for geometrical factor for pole-dipole and Schlumberger configuration are different. The proposed technique has been tested in actual field conditions having different rock types. A few examples are presented along with Schlumberger sounding curves which confirm the applicability of the proposed sounding technique.     

2.5D forward modeling and inversion of frequency-domain airborne electromagnetic data

Frequency-domain airborne electromagnetics is a proven geophysical exploration method. Presently, the interpretation is mainly based on resistivity—depth imaging and one-dimensional layered inversion; nevertheless, it is difficult to obtain satisfactory results for two- or three-dimensional complex earth structures using 1D methods. 3D forward modeling and inversion can be used but are hampered by computational limitations because of the large number of data. Thus, we developed a 2.5D frequency-domain airborne electromagnetic forward modeling and inversion algorithm. To eliminate the source singularities in the numerical simulations, we split the fields into primary and secondary fields. The primary fields are calculated using homogeneous or layered models with analytical solutions, and the secondary (scattered) fields are solved by the finite-element method. The linear system of equations is solved by using the large-scale sparse matrix parallel direct solver, which greatly improves the computational efficiency. The inversion algorithm was based on damping least-squares and singular value decomposition and combined the pseudo forward modeling and reciprocity principle to compute the Jacobian matrix. Synthetic and field data were used to test the effectiveness of the proposed method.     

Response evaluation of interconnected electrical substation equipment using real‐time hybrid simulation on multiple shaking tables

In an attempt to quantify the conductor cable effect on substation electrical equipment, real‐time hybrid simulation (RTHS) is conducted on interconnected equipment using two shaking tables. For this purpose, the existing RTHS system with advanced control capabilities at the Pacific Earthquake Engineering Research Center structural laboratory is enhanced to accommodate the simultaneous use of two shaking tables. An experimental parametric study is conducted to investigate the conductor cable effect using this system with a two‐table RTHS setup. Post insulators of disconnect switches, important components of substations that are usually tested with conventional methods for evaluating their seismic performance, are utilized as experimental substructures for realistic representation of the electrical equipment. Various global and local response parameters, including accelerations, forces, displacements, and strains, are considered to evaluate the effect of the tested conductor cable configuration for a wide range of support structure configurations, which are modeled in the computer as analytical substructures. The experimental parametric study results indicate that the conductor cable has a significant effect on the response of the interconnected equipment over the whole range of investigated support structures and needs to be explicitly considered for seismic testing of electrical equipment. Copyright © 2016 John Wiley & Sons, Ltd.     

Detecting lateral resistivity inhomogeneities with the Schlumberger array

A method of detecting lateral resistivity inhomogeneities with a multi-electrode cable for the Schlumberger array is presented. Using such a cable system, two dipole-dipole soundings are gathered in addition to the Schlumberger sounding at each point. Offset differences calculated from the dipole-dipole data give qualitative information about lateral resistivity inhomogeneities. Results from 1D modelling can give quantitative information about the 2D resistivity distribution since the dipole-dipole soundings are made to either side of the Schlumberger sounding point. Examples from two different locations in Norway are shown. At Reinøya, northern Norway, a dipping layer, confirmed by refraction seismic data, was identified. In a sedimentary basin with a contamination plume at Haslemoen, southern Norway, the method has revealed lateral variations in resistivity. In both cases, the Schlumberger soundings could be fitted with a 1D resistivity model.