A FIELD EXAMPLE OF THE USE OF ANISOTROPY PARAMETERS DERIVED FROM RESISTIVITY SOUNDINGS*

In areas where steep dips are encountered conventional practice in resistivity work has involved orienting arrays favourably in relation to the geological strike. In concealed conditions, however, the geological strike may not be known; moreover, strike may change with depth. Considerable advantage is to be gained, in such circumstances, by the use of crossed square arrays in that these yield orientationally insensitive resistivity measurements and also allow strike determinations and measurements of the effective vertical anisotropy. Two traverses of crossed square array observations are presented, together with one deeper sounding. The results show that, in favourable circumstances, reliable data on concealed strike directions can be obtained, and that the anisotropy findings greatly assist the subsequent interpretation. Model results pertinent to the field material are presented and discussed.     

THE EFFECTS OF ANISOTROPY ON SQUARE ARRAY RESISTIVITY MEASUREMENTS*

An account is given of the use of the square array technique in investigating the surface effects of rotational anisotropy when the axes of anisotropy are inclined to the surface. It is shown that, as with other arrays, two anisotropy parameters and n can be derived by varying the array orientation. On the basis of these considerations, the effects of such anisotropy on the values of the mean apparent resistivity and azimuthal inhomogeneity ratio normally obtained in square array measurements is reviewed. Particular attention is paid to the variation of resistivity with orientation and it is noted that, in areas of moderate anisotropy, this variation is lower for the square than for the Schlumberger array. In addition to this advantage, the azimuthal inhomogeneity ratio obtained from square array measurements may be used to indicate the severity of anisotropy in an area and two field examples of this use are given. Where anisotropy is severe, gross variations of apparent resistivity with orientation are obtained with either square or collinear arrays. In these circumstances, the use of crossed measurements is considered and the particular stability of the crossed square array demonstrated.     

THE OFFSET SYSTEM OF ELECTRICAL RESISTIVITY SOUNDING AND ITS USE WITH A MULTICORE CABLE*†

One of the most troublesome problems in resistivity sounding is caused by the spurious effects of near-surface lateral resistivity variations. It has been found that the effects can be strongly reduced by measuring earth resistances at two electrode array positions such that in one position the lateral effect is a positive contribution to the total measured signal and in the other the contribution is negative. The subsequent combination of the two measurements virtually eliminates the lateral effect. The same technique can also result in a significant reduction in the total number of necessary electrode positions. Consequently the method can be used with a multicore cable system. In this way, in addition to improving the accuracy of the measured results, time and manpower are considerably reduced. Details of the method, examples and comparisons with traditional sounding techniques are given.     

THE INFLUENCE OF ELECTRICAL ANISOTROPY ON MISE À LA MASSE SURVEYS *

In a transversely electrically anisotropic rock mass of arbitrary dip, the potential distribution about an electrode at arbitrary depth is the sum of the whole-space potential about that electrode, plus the whole-space potential about a postulated image electrode displaced up-dip from the source position. Equipotential lines on the rock-air surface are ellipses, elongated parallel to strike, and with centers displaced up-dip from the surface projection of the electrode position. In metamorphosed rocks frequently encountered in mining geophysics, anisotropy is such that elongation is most marked in steeply dipping rocks, with displacement most evident in low to moderate dip. Graphs relating the anisotropy coefficient to displacement and elongation assist in separation of the anisotropy-related effects from those of a significant subsurface conductive body, particularly if surface resistivity sounding establishes the coefficient of anisotropy.     

NUMERICAL MODELLING OF STANDARD AND CONTINUOUS VERTICAL ELECTRICAL SOUNDINGS1

Analytical solutions of vertical electrical soundings (VES) have mostly been applied to groundwater exploration and monitoring groundwater quality on terrains of fairly simple geology and geomorphology on which the electrode arrays are symmetrical (e.g. Schlumberger or Wenner configurations). The sounding interpretation assumes flat topography and horizontally stratified layers. Any deviations from these simple situations may be impossible to interpret analytically. The recently developed GEA-58 geoelectrical instrument can make continuous soundings along a profile with any colinear electrode configuration. This paper describes the use of finite-difference and finite-element methods to model complex earth resistivity distributions in 2D, in order to calculate apparent resistivity responses to any colinear current electrode distribution in terrains in which the earth resistivities do not vary along the strike. The numerical model results for simple situations are compared with the analytical solutions. In addition, a pseudo-depth section of apparent resistivities measured in the field with the GEA-58 is compared with the numerical solution of a real complex resistivity distribution along a cross-section. The model results show excellent agreement with the corresponding analytical and experimental data.     

二维大地电磁各向异性参数对视电阻率的影响研究

大地电磁法是广泛应用于深部地质结构探测、油气和矿产资源勘查等领域的一种地球物理方法.电性各向异性对电磁观测数据有很大影响,但介质各向异性参数对不同模式视电阻率的影响还较少有较为系统的研究.本文基于Maxwell方程组,推导了二维大地电磁场在任意各向异性介质中电场和磁场相互耦合的变分方程,结合有限单元法及并行计算编写了二维大地电磁任意各向异性正演程序,采用三角形网格剖分.验证程序正确性后,以倾斜板状体作为模型来研究三个主轴电阻率及三个旋转欧拉角和四种模式的视电阻率之间的关系.结果表明,主轴各向异性时,xy模式视电阻率几乎只受x方向电阻率影响,yx模式视电阻率主要受y方向电阻率影响,但同时也受z方向电阻率一定影响;三个欧拉角中只有倾角不为零时,yx模式视电阻率受倾角大小的影响较大,xy模式视电阻率几乎不受倾角的影响;只有走向角不为零时,四种模式的视电阻率同时受x、y两个主轴电阻率和走向角的大小的影响.     

任意各向异性介质中三维可控源音频大地电磁正演模拟

在一些地层层理发育的地区,地下介质存在显著的电各向异性,此时基于各向同性模型解释含各向异性效应的可控源音频大地电磁（CSAMT）测深观测数据会导致错误的结果.本文通过引入3×3的对称正定张量表征电导率各向异性,采用非结构四面体网格和矢量有限元方法离散电场满足的矢量Helmholtz方程,并将电磁场源等效为系列电偶极子,实现任意各向异性介质中CSAMT高效数值模拟.本文首先通过层状各向异性模型检验三维有限元算法的精度和有效性,进一步建立三维地电模型研究异常体各向异性和围岩各向异性对CSAMT响应的影响,最后使用视电阻率极性图来识别各向异性电导率主轴方向.数值模拟结果表明,各向异性电导率对CSAMT视电阻率幅值及分布规律都有很大影响,视电阻率极性图能够很好地识别各向异性主轴方向.     

层状方位各向异性介质的视电阻率计算

从电性各向异性的欧姆定律出发，推导了直流电法层状方位各向异性介质中的电位分布、边界条件及视电阻率计算公式．以四极对称装置系统为例，对具有相同各向异性系数的4层模型采用核函数递推法作了理论数值模拟，得到了不同方向的电阻率测深曲线及其等值线形态．结果表明理论公式是正确的，测深曲线既反映了分层介质的电阻率差异，又反映了各层中电阻率的各向异性特征．      

THE USE OF A SQUARE CONFIGURATION IN RESISTIVITY PROSPECTING *

Consideration is given to the use of a configuration of four electrodes set in a square array for resistivity measurements. It is found that, by passing current successively between different pairs of electrodes, an apparent resistivity can be determined which is both more sensitive to the position of the array centre and less dependent on orientation than the measures usually obtained with colinear arrays of electrodes. At the same time the observations made enable the degree of the departure of local conditions from conditions of lateral homogeneity to be assessed. Theoretical and practical examples of the use of this electrode system are given and the use of the system both as a tool in mapping and in depth investigations is considered. It is shown that provided electrode spacings are suitably arranged the results of a probe carried out using the square array can be interpreted by conventional methods. The system is shown to have particular advantages in the investigation of lateral resistivity variations and the reduced dependence on orientation makes possible the recasting of interpretation data in an orientationally invariant form with a consequent drastic reduction in the number of type curves required for a particular problem.     

Apparent resistivity of azimuthal anisotropy layered media

Introduction The method of apparent resistivity with direct current (DC) measurement, adopted from geophysical exploration, is one of the most important precursory approaches in earthquake prediction, in which the geo-electric constitutive model is illustrated by the scalar theory Archies law and correspondingly a set of calculation methods for apparent resistivity of layered media has been established (QIAN, et al, 1985; YAO, 1989). But this is not consistent with the fact that in earthqu…     

1920年海原8.5级地震震中区地电阻率各向异性研究

通过海原8.5级地震震中区环行电测深研究,发现在断层破碎带有明显的电阻率各向异性,垂直断层走向呈现明显的高电性,断层走向呈现明显的低电性.根据电性差异讨论了断层地表的变形特征.研究结果表明：环形电测深工作,对研究地面附近地层物性变化有重要意义.     

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.     

The effectiveness of azimuthal apparent-resistivity measurements as a method for determining fracture strike orientations

Azimuthal apparent-resistivity measurements are made for the purpose of determining the strike direction of subvertical fracture sets. Data are collected about a common centre, with an electrode array expanded along a sufficient number of azimuths to define the variation of apparent resistivity with orientation. The apparent resistivities for any one electrode spacing are then plotted in a polar diagram. If the data form an ellipse, this is often interpreted as reflecting aligned, subvertical fracturing. However, it is also possible for heterogeneity within the rockmass to manifest itself, at the scale of the measurement, as a variation of apparent resistivity with azimuth. It is recommended that the offset Wenner array is used for all measurements and that a parameter is introduced, the homogeneity index, which defines whether the variations due to homogeneous anisotropy, such as subvertical fracturing, are greater than those due to inhomogeneity. This simple parameter, which is the quotient of two standard deviations, is valid for both single-peaked and multiple-peaked ellipses. A four-stage scheme for the interpretation of azimuthal data is suggested and a consistent set of quantitative measures is recommended. These will allow data, collected by different workers over different lithologies, to be compared. There are a number of geological situations which can give rise to anisotropy within the rockmass and great care is needed when interpreting azimuthal data in terms of aligned fracturing. Numerical modelling of the response to a buried channel of a rotated offset Wenner array demonstrates that elliptical data are generated by such a linear feature. Depending on the location of the array with respect to the channel, these data are either indistinguishable from those generated by aligned fracturing, or can be recognized by application of the homogeneity index. In the case where the response can be identified as being due to a channel, diagnostic information can be derived on the location and strike of the channel.     

ESTIMATION OF TEMPORAL CHANGES IN SOIL MOISTURE USING RESISTIVITY METHOD

The temporal variation in a soil moisture profile can be studied using resistivity sounding data acquired at different times. The layered earth model based estimation of soil moisture from apparent resistivity data is a two-step non-linear inversion. Firstly, the apparent resistivity data are inverted to derive the layer resistivity variations and thicknesses and, secondly, the moisture content is estimated from these layer resistivity variations using a calibration equation. The soil moisture–resistivity problem was studied using the one-dimensional formulation of resistivity problem. A generalized geoelectric earth model was considered to simulate the soil moisture distribution and its temporal variation in the unsaturated zone. An algorithm (RESMOS) for the interpretation of the apparent resistivity data in terms of soil moisture variations through this two-step inversion process is reported.     

Anisotropy Versus Heterogeneity in Continental Solid Earth Electromagnetic Studies: Fundamental Response Characteristics and Implications for Physicochemical State

Electrical anisotropy, the effect of current density in a medium being a function of the orientation of the electric field, is being recognized increasingly as an important effect in explaining Earth electromagnetic observations. A consideration of anisotropy, however, in most cases is an admission of spatial aliasing in earth structure, wherein the averaging volume of diffusive EM fields may be greater than the characteristic dimensions of a family of oriented structures, thus leading to a response which is equivalent to a bulk anisotropic medium. Even for two-dimensional geometries, there can be strong non-parallelism of principal axes of vertical magnetic field relative to the impedance over broad areas, as well as impedance phase variations which leave normal quadrants, if there are multiple directions of anisotropy or anisotropy strike distinct from bulk geometric (2D) strike. This paper concentrates on experience with regional field studies in continental settings where bulk anisotropy is apparent. Upper crustal anisotropy may result from preferred orientations of fracture porosity, or lithologic layering, or oriented heterogeneity. Lower crustal anisotropy may result from preferred orientations of fluidized/melt-bearing or graphitized shear zones, but does not necessarily reflect current state of stress per se. In the upper mantle, the prior causes all may act in pertinent domains, but added to these is the possibility of strong electrical anisotropy due to hydrous defects within shear-aligned olivine crystals (solid-state conduction). Several field examples from continental MT investigations will be discussed, which roughly fall into active transpressional, active transtensional, and fossil transpressional regimes. A general challenge in interpreting data with apparent anisotropic effects is to establish the tradeoff between heterogeneity and anisotropy in the inversion of EM responses.     

裂隙非均匀分布岩石中的电位及视电阻率计算

计算了在均匀高阻介质中含有低阻裂隙的岩石的电场分布，并由此推导出裂隙非均匀分布的岩石中视电阻率的计算公式．结果表明，裂隙的埋深、规模、走向（平行或垂直视电阻率测线）以及真电阻率等，对视电阻率的观测和计算结果都有不同程度的影响．本文结果对视电阻率法用于地震分析预报提供了一种有效的计算方法．      

利用对称四极横向剖面法探测走滑断层的应用

从走滑断层难以探测的实际出发,讨论了其物性特征;通过对低阻板模型的物理模拟、数值模拟以及对实地观测资料的分析,研究了对称四极纵、横向剖面法视电阻率曲线的变化特征和差异. 结果表明,横向剖面法相对纵向剖面法异常幅度明显增加,可对地震活动断层进行更为有效的探测和定位. 这一研究为走滑断层探测提供了新的思路. 同时,利用对称四极横向剖面法可以解决走滑断层难以探测这一技术难题.      

强地震附近视电阻率各向异性变化的原因

讨论了强地震、孕震晚期阶段、震源区及附近介质的物理变化过程,证明了视电阻率变化最显著的方向与最大加载方向之间的正交关系,建立了真、视电阻率各向异性变化与裂隙率ν、骨架电阻率ρ_o、饱水裂隙电阻率ρ_f的本构关系,解释了视电阻率各向异性变化的原因.研究认为：在强地震孕震晚期阶段,在震源区及附近地壳近地表的较深部,介质微裂隙发育,其走向沿最大主压应力方位优势取向,低阻水充填微裂隙,导电通道连通,引起最大主压应力方向真电阻率变化最显著的真各向异性变化,从而产生垂直主压应力方向视电阻率变化最显著的视各向异性变化,低阻水在其物理过程中起了显著作用.     

Application of Schlumberger transverse profiling method to detecting a strike fault

Because it is difficult to detect a strike fault, its physical properties are discussed in this paper. Using physical simulation, numerical modeling and the in situ data, the differences between the apparent resistivity of low resistivity model obtained by transverse profiling method （TPM） whose electrode array is vertical to the profile and those by longitudinal profiling method （LPM） whose electrode array is parallel to the profile are analyzed, respectively. Our results show that the former has much marked amplitudes of anomaly. Therefore, TPM can be used to detect a strike fault more effectively and locate it more precisely, and is expected to be a new approach for detecting a sliding fault.     

A SIMPLE METHOD OF INTERPRETATION OF RESISTIVITY SOUNDING DATA USING EXPONENTIAL APPROXIMATION OF THE KERNEL FUNCTION*

A simple unified equation of apparent resistivity for a general four-electrode array is developed. The main idea is the analytical integration of the Stefanescu expression for potential over a layered earth by writing an exponential approximation for the kernel function. Finally a matrix equation is developed to estimate the kernel function from observed apparent resistivity values. The general equation automatically reduces to the particular configuration once the electrode separations are modified suitably. Examples for Schlumberger and Wenner configurations are numerically calculated to estimate the precision of the method. Good results in a short execution time are obtained, irrespective of the shape of the apparent resistivity curve. Finally, the full interpretation of one theoretical resistivity curve and two field resistivity curves is demonstrated. The more stable ridge-regression estimation method is used in the identification of layer parameters from the kernel function.