混合物整体电导率和各成分电导率的关系

文中给出了混合物中电场方程的平均形式,在此基础上推导出了混合物整体电导率和各成分电导率的关系,并通过类比给出了混合物整体介电常数和各成分介电常数的关系,作为所得结果的应用,给出了岩石的电导率公式。     

混合物整体电导率的研究

研究由几种导体成分掺杂的混合物的整体电导率.对欧姆定律求平均,得到混合物电导率定义.对电流连续性方程求平均,得到混合物中电场增量方程.求电场增量方程在同种成分上的平均,并结合混合物电导率定义,得到混合物电导率公式.现有的三种混合物结构下电导率公式（电导率串联公式、并联公式和整体各向同性混合物电导率公式）都是混合物电导率公式的特例.进一步分析得出结论,混合物整体电导率是各成分电导率与整体电导率结构并联后的体积串联.     

格子玻耳兹曼方法计算混合物整体电导率

本文采用格子玻耳兹曼方法计算混合物的整体电导率．整体电导率与各组分的电导率、体积分数和混合物结构有关．数值计算方法的有效性通过两相混合物并联或串联模型的解析解加以验证．对随机分布模型的计算发现格子玻耳兹曼方法得到的电导率落在H S理论边界内．对Al Bi合金整体电导率的数值模拟结果和实验结果非常相近．对饱和水岩石的介电常数的计算与实验结果相比误差较小．格子玻耳兹曼方法为混合物的整体电导率的计算提供了一个有效的途径.     

混合物电导率公式及其在测井解释中的应用

从电场的微分方程出发,得出了混合物电导率的两个公式:1.关于导体和导体形成的混合物的电导率公式;2.关于导体和绝缘体形成的混合物的电导率公式。将这两个公式应用于测井解释,对解释泥质砂岩的双水模型作了有效的改进。     

混合物介电常数的新公式

本文给出了混合物介电常数的新公式并用一个例子验证了新公式的有效性.此公式可以代替现有的公式应用到测井解释中,以提高解释的精度.     

双相混合物等效介电常数探地雷达数值研究

等效介电常数是混合物微观结构的宏观表征,与介质的属性参数密切相关.在传统随机介质建模理论的基础上,通过增加量化约束限定条件,精准控制双相混合物各组成物质的体积占比,建立了 22个体积占比相同、孔隙粒径尺度不等和20个孔隙粒径尺度相等、体积占比不同的双相混合物介质模型,进行探地雷达数值模拟,研究超宽频带条件下双相混合物各组成物质体积占比和孔隙粒径大小对其等效介电常数及探地雷达波场特征的影响.结果表明:对于各组成物质体积占比相同、孔隙粒径尺度不等的双相混合物,其等效介电常数基本相同,说明混合物等效介电常数主要取决于其各组成物质的体积占比及其介电常数,但由于混合物内部孔隙粒径尺度不等,其电磁散射强度和能量衰减损失存在明显差异;对于孔隙粒径尺度相等、体积占比不同的双相混合物,其空气体积占比越小,等效介电常数越大,与Rayleigh模型、CRIM模型等混合物等效介电常数经验公式计算结果差值越小、吻合越好,同时,其散射波振幅强度和波形杂乱程度越弱,研究结果可为解译双相混合物介质属性参数提供参考和指导.     

二维轴对称介质中电磁波测井的响应函数

单发双收电磁波测井测的是两接收线圈的感应电动势之间的相位差和幅度比及测井响应与地层介电常数和电导率两者有关的一般情况,对此本文推导出其在二维轴对称介质中响应函数公式,给出它的快速算法.通过建立二维非均质反演Jacobi矩阵与响应函数的关系,开辟了Jacobi矩阵快速算法构造的有效途径.从理论上得到了在均匀介质中相位差和幅度比对地层的介电常数和电导率的空间分布探测特性具有交叉互补性的结果,即相位差对电导率（介电常数）的空间分布敏感区域和幅度比对介电常数（电导率）的空间分布敏感区域是相同的.     

用地磁转换函数研究震源区介质的电性变化

以兰州地区视电阻率yx曲线与该地区地磁转换函数变化和中强近震的分析研究为例，从震磁效应的观点出发，发现可用地下电导率值将兰州地区自地表向下分为异常层、过渡层、无异常层和异常层4层，只有异常层中转换函数的模｜A｜、｜B｜，磁方位角均值P及其均方差P，以及总方差Z随时间的变化在地震前有明显异常．由此可推测，异常层与地震活动区地下介质电导率的非均匀性变化有密切关系．此现象为进一步的机理研究提供了一种途径．其内涵和规律，还须深入研究．      

非均匀有耗媒质层介电常数剖面和电导率剖面的重建

本文从微波网络的观点出发，在高频近似下，导出了非均匀有耗媒质在ＴＥ波和ＴＭ波入射时反射系数的近似解析表达式，进而获得重建媒质介电常数剖面和电导率剖面的解析反演公式。研究表明，当媒质的损耗为零时，本文公式退化成无耗媒质的重建公式（１－４）。重建实例证明了本文方法的有效性。     

用地质雷达数据资料反演二维地下介质的方法

从二维麦克斯韦方程组出发推导出反演介电常数和电导率等二维介质物性参数的反演公式.反演的步骤是: 建立初始猜测模型,利用电磁波时间域有限差分法模拟正演数据,用正演数据与观测数据之间的数据残差建立目标函数,通过引入一个由麦克斯韦方程计算的伴随场,将目标函数对介质参数的导数表示成显式形式,应用最优化理论得出对初始猜测模型的修改,用共轭梯度法迭代,最终得到反演结果.用合成数据反演具有粗糙地表的非导电介质的介电常数,用实验数据同时反演介电常数和电导率,并比较了麦克斯韦方程反演结果与声波方程反演结果、波动方程偏移剖面的差异.     

Delineation of sulphide ore-zones by borehole radar tomography at Hellyer Mine, Australia

Velocity and absorption tomograms are the two most common forms of presentation of radar tomographic data. However, mining personnel, geophysicists included, are often unfamiliar with radar velocity and absorption. In this paper, general formulae are introduced, relating velocity and attenuation coefficient to conductivity and dielectric constant. The formulae are valid for lossy media as well as high-resistivity materials. The transformation of velocity and absorption to conductivity and dielectric constant is illustrated via application of the formulae to radar tomograms from the Hellyer zinc–lead–silver mine, Tasmania, Australia. The resulting conductivity and dielectric constant tomograms constructed at Hellyer demonstrated the potential of radar tomography to delineate sulphide ore zones.     

Saturation effect on electrical properties of hematitic sandstone in the audio frequency range using non-polarizing electrodes

This paper is devoted to study the effect of saturation, with distilled water, on AC electrical conductivity and dielectric constant of a fully and partially saturated hematitic sandstone sample (Aswan area, Egypt). The saturation of the sample was changed from full saturation to partial saturation by air drying. Complex resistivity measurements at room temperature (∼16° C) were performed in the frequency range from 10 Hz to 100 kHz. We used non-polarizing Cu/CuSO₄ gel electrodes. Experimental electrical spectra indicate, generally, that the electrical conductivity and dielectric constant vary strongly with water saturation and frequency. The low-frequency electrical conductivity and dielectric constant are supposed to be mainly controlled by surface conduction and polarization of the electrical double layer. Power law behaviours with frequency were noticed. The change in electrical conductivity and dielectric constant with increasing water content is fast at low saturations and slow at high saturations. The behaviour of the electrical conductivity and dielectric constant, with increasing water content, was argued to be the orientational polarization of bound water for very low saturations, displacement of the excess surface charges for relatively low saturations and free exchange of excess ions in double layer with the bulk electrolyte and generation of transient diffusional potentials, which lag behind the applied field for high saturations in addition to membrane polarization on clay and at inter-grain and grain surface water throats having selective charge transport properties. Also, from the data a semi-percolation behaviour was found that has a peak of dielectric constant at a certain concentration and an abrupt change in conductivity at another saturation.     

Measurement of electrical properties of contaminated soil1

We present the measured dielectric constant and conductivity of soil samples contaminated by diesel oil. Measurements of the electrical properties of contaminated soil were carried out using a guarded-electrode sample holder and a parallel-plate sample holder in the frequency range 2–250 MHz. Two different soil samples were measured. Both the dielectric constant and the conductivity of the contaminated soils and uncontaminated soils are compared. The measurement results show that the change in the dielectric constant of soils before and after diesel oil contamination is small but significant. These results provide a basis for using ground-penetrating radar or other high-frequency electromagnetic sensors in the detection of soil contamination.     

Time domain reflectometry measurement principles and applications

Time domain reflectometry (TDR) is a highly accurate and automatable method for determination of porous media water content and electrical conductivity. Water content is inferred from the dielectric permittivity of the medium, whereas electrical conductivity is inferred from TDR signal attenuation. Empirical and dielectric mixing models are used to relate water content to measured dielectric permittivity. Clay and organic matter bind substantial amounts of water, such that measured bulk dielectric constant is reduced and the relationship with total water content requires individual calibration. A variety of TDR probe configurations provide users with site‐ and media‐specific options. Advances in TDR technology and in other dielectric methods offer the promise not only for less expensive and more accurate tools for electrical determination of water and solute contents, but also a host of other properties such as specific surface area, and retention properties of porous media. Copyright © 2002 John Wiley & Sons, Ltd.     

Electrical properties and geochemistry of carbonate rocks from the Qasr El‐Sagha Formation,El‐Faiyum,Egypt

Understanding petrographical, geochemical and electrical properties of rocks is essential for investigating minerals. This paper presents a study of the petrographical, geochemical and A.C. electrical properties of carbonate rock samples. The samples collected show six lithostratigraphic rock units. Electrical properties were measured using a non‐polarizing electrode at room temperature (～20°C) and a relative atmospheric humidity of ～50% by weight in the frequency range from 42 Hz to 5 MHz. The difference in electrical properties between the samples was attributed to the change in composition and texture between the samples. Electrical properties generally change with many factors (grain size, chemical composition, grain shape and facies). The dielectric constant decreases with frequency and increases with conductor composition. The conductivity increases with the increase of conductor paths between electrodes. Many parameters can contribute to the same result of the electrical properties. The main objective of the present study is to shed more light on the relation between the texture and geochemical composition of measured samples (carbonates that contain clays and quartz grains) through electrical laboratory measurements (conductivity and dielectric constant as a function of frequency).     

A contribution to the measurement of frequency dependence of electrical conductivity of rocks

Summary Some errors of method occurring in A. C. measurements of the electrical conductivity of rocks are discussed. It is demonstrated that the difference between A.C. and D.C. conductivities, at given frequency, depends mostly on the magnitude of the D.C. conductivity and magnitude of the dielectric constant.     

Thermal effect of magma intrusion on the electrical properties of magnetic rocks from Hammamat sediments, Cairo, Egypt

The thermal effects of magmatic intrusion on the conductivity and dielectric constant of magnetic rocks from Hammamat sediments, NE desert, Cairo, Egypt (latitude ∼27° and longitude ∼33°) were investigated experimentally in the laboratory using nonpolarizing electrodes. Granitic magma was intruded into the Hammamat sediments, which are a mixture of mainly magnetite with sandstone and due to the thermal effect the area around was extensively heated and altered to different degrees. Due to this magma intrusion, magnetite was transformed (by heating) to hematite to different degrees according to its location from the intrusion. Complex impedance measurements were performed in the frequency range of 10 Hz to 100 KHz at normal temperature (∼20°C) and at a relative humidity of ∼50% RH. Samples were collected at different locations perpendicular to the core of the magma intrusion. Experimental data indicate that the electrical properties vary strongly as we move away (with distance) from the magma intrusion. The conductivity of hematite is ∼10⁻² S/m and that of magnetite is ∼10⁴ S/m. As we move from magnetite to hematite (to the core of the magma intrusion) it is supposed that the conductivity will decrease but it was found that the conductivity increases (which is supposed to be abnormal). The conductivity increases with increasing frequency from ∼10⁻⁸ S/m to ∼10⁻⁵ S/m with almost power‐law dependence on frequency. The conductivity increases in the order of one decade due to the variation from magnetite to hematite. The increase of conductivity, as we move from magnetite to hematite, was argued to be due to the heating that partially or completely melts the samples, thus the porosity of the samples was decreased and accordingly the conductivity and dielectric constant increased. It was also supposed that the grains of the conductor in the samples are coated or isolated with insulator material. A percolation behaviour for the conductivity and dielectric constant, characteristic of random conductor‐insulator mixtures, was found with distance, where continuous paths of the conductive material occur accompanied by peaking of the dielectric constant. Complex impedance plots show that as we move in the direction of altered samples (towards hematite) the relation between real and imaginary impedance changes from a linear form to an arc of a depressed semicircle and increases in depression as we move in the direction of the altered samples, which is consistent with the above interpretation.     

The electric properties of eclogites from the Bohemian Massif under high temperatures and pressures

Summary The D.C. and A.C. electric conductivity and the dielectric constant of a set of 8 eclogites from the Bohemian Massif is studied under high temperatures (200–900°C) and pressures (up to 20 kb). The electric conductivity of the studied eclogites is strongly affected by the content of symplectite minerals: their conductivity increases with their concentration. The average increase of conductivity with pressure between 1 kb and 20 kb is about 50% and is manifested particularly below 4 kb. The correlation between the electric conductivity and the dielectric constant is very high (r=0.975) and allows for the values of one parameter to be estimated from those of another.     

Using neural networks for calibration of time-domain reflectometry measurements

Abstract

Time-domain reflectometry (TDR) is an electromagnetic technique for measurements of water and solute transport in soils. The relationship between the TDR-measured dielectric constant (K_a ) and bulk soil electrical conductivity ([sgrave]_a) to water content (θ_W) and solute concentration is difficult to describe physically due to the complex dielectric response of wet soil. This has led to the development of mostly empirical calibration models. In the present study, artificial neural networks (ANNs) are utilized for calculations of θ_w and soil solution electrical conductivity ([sgrave]_w) from TDR-measured K_a and [sgrave]_a in sand. The ANN model performance is compared to other existing models. The results show that the ANN performs consistently better than all other models, suggesting the suitability of ANNs for accurate TDR calibrations.