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.     

APPROXIMATE RULES FOR THE COMPOSITION OF APPARENT RESISTIVITY SECTIONS *

Consideration is given to the form of apparent resistivity sections obtained by varying electrode array position and spacing over two dimensional features. Since basic solutions exist for horizontally layered media and for vertical or dipping single interfaces, simple rules are proposed whereby these solutions can be directly combined to give solutions for more complex sections. Substantial approximations may be involved as the rules do not fully allow for interactions between the constituents. The range of error incurred in application of the rules is explored, with particular reference to the square array system of resistivity measurement. The two extremes- of orientation of the square array with respect to the line of section are separately considered in this survey. Within appropriate limits, the rules appear extendable to a wide variety of simple structures for which rigorous solutions would be formidable. The rules are finally discussed in relation to practical applications.     

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.     

Research Note: The mean sensitivity depth of the electrical resistivity method

Until now, a simple formula to estimate the depth of investigation of the electrical resistivity method that takes into account the positions of all of the electrodes for a general four‐electrode array has not been available. While the depth sensitivity function of the method for a homogeneous infinite half‐space is well known, previous attempts to use it to characterize the depth of investigation have involved calculating its peak and median, both of which must be determined numerically for a general four‐electrode array. I will show that the mean of the sensitivity function, which has not been considered previously, does admit a very simple mathematical formula. I compare the mean depth with the median and peak sensitivity depths for some common arrays. The mean is always greater than or equal to the median that is always greater than the peak. All three measures give reasonable estimates to the depths of actual structures for most circumstances. I will further show that, for 1D soundings, the use of the mean sensitivity depth as the pseudo‐depth assigns an apparent resistivity to a given pseudo‐depth that is consistent between different arrays. One consequence of this is that smoother depth soundings are obtained as “clutches,” caused by a change in the depth sensitivity due to moving the potential electrodes, are effectively removed. I expect that the mean depth formula will be a useful “rule of thumb” for estimating the depth of investigation before the resistivity structure of the ground is known.     

ON THE COMPLETENESS OF DATA SETS WITH MULTIELECTRODE SYSTEMS FOR ELECTRICAL RESISTIVITY SURVEY

This paper describes how, using a surface linear array of equally spaced electrodes, potential data can be obtained for use in electrical resistivity imaging. The aim is to collect a complete data set which contains all linearly independent measurements of apparent resistivity on such an array using two-, three- or four-electrode configurations. From this primary data set, it is shown that any other value for apparent resistivity on the array can be synthesized through a process of superposition. Numerical tests show that such transformations are exact within the machine error for calculated data but that their use with real field data may lead to noise amplification.     

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.     

Practical techniques for 3D resistivity surveys and data inversion1

Techniques to reduce the time needed to carry out 3D resistivity surveys with a moderate number (25 to 100) of electrodes and the computing time required to interpret the data have been developed. The electrodes in a 3D survey are normally arranged in a square grid and the pole-pole array is used to make the potential measurements. The number of measurements required can be reduced to about one-third of the maximum possible number without seriously degrading the resolution of the resulting inversion model by making measurements along the horizontal, vertical and 45° diagonal rows of electrodes passing through the current electrode. The smoothness-constrained least-squares inversion method is used for the data interpretation. The computing time required by this technique can be greatly reduced by using a homogeneous half-space as the starting model so that the Jacobian matrix of partial derivatives can be calculated analytically. A quasi-Newton updating method is then used to estimate the partial derivatives for subsequent iterations. This inversion technique has been tested on synthetic and field data where a satisfactory model is obtained using a modest amount of computer time. On an 80486DX2/66 microcomputer, it takes about 20 minutes to invert the data from a 7 by 7 electrode survey grid. using the techniques described below, 3D resistivity surveys and data inversion can be carried out using commercially available field equipment and an inexpensive microcomputer.     

Pilot‐scale field validation of the long electrode electrical resistivity tomography method

A validation experiment, carried out in a scaled field setting, was attempted for the long electrode electrical resistivity tomography method in order to demonstrate the performance of the technique in imaging a simple buried target. The experiment was an approximately 1/17 scale mock‐up of a region encompassing a buried nuclear waste tank on the Hanford site. The target of focus was constructed by manually forming a simulated plume within the vadose zone using a tank waste simulant. The long electrode results were compared to results from conventional point electrodes on the surface and buried within the survey domain. Using a pole‐pole array, both point and long electrode imaging techniques identified the lateral extents of the pre‐formed plume with reasonable fidelity but the long electrode method was handicapped in reconstructing vertical boundaries. The pole‐dipole and dipole‐dipole arrays were also tested with the long electrode method and were shown to have the least favourable target properties, including the position of the reconstructed plume relative to the known plume and the intensity of false positive targets. The poor performance of the pole‐dipole and dipole‐dipole arrays was attributed to an inexhaustive and non‐optimal coverage of data at key electrodes, as well as an increased noise for electrode combinations with high geometric factors. However, when comparing the model resolution matrix among the different acquisition strategies, the pole‐dipole and dipole‐dipole arrays using long electrodes were shown to have significantly higher average and maximum values within the matrix than any pole‐pole array. The model resolution describes how well the inversion model resolves the subsurface. Given the model resolution performance of the pole‐dipole and dipole‐dipole arrays, it may be worth investing in tools to understand the optimum subset of randomly distributed electrode pairs to produce maximum performance from the inversion model.     

A SOLUTION OF THE DIPPING INTERFACE PROBLEM USING THE SQUARE ARRAY RESISTIVITY TECHNIQUE*

Apparent resistivity measurements with the square array technique in the vicinity of a dipping interface have the advantage over collinear array methods that they are less dependent on orientation of the array. In order to exploit this, existing potential solutions for the dipping interface problem have been adapted for the computation of apparent resistivities over such a feature using a square array. Comprehensive interpretation techniques covering this problem are given and the limitations imposed by residual array orientation effects are discussed.     

基于数字电极技术的电法测量系统

本文分析了电阻率层析成像系统的阵列电极的特征和现代地震勘探采集系统的数字检波器技术,提出了基于数字电极的电法测量系统设计,这种设计将实现电法测量的一次创新;然后较为详细讨论了数字电极的电路结构、系统的总体设计、控制通信网络拓扑结构和其他关键技术,该系统的通信网络结构基于DeviceNet现场总线;最后描述了该系统的功能特点,它不仅用于电阻率、激发极化、相位以及复电阻率的等多种方法,而且可用于时间域或频率域中的2D、3D电法勘探,并同时测量多种装置的数据,实现拟地震方式的勘探.     

电阻率测井响应的积分方程解法

从电流守恒条件出发,得到了两个积分方程.其中第一个和在1964年提出的相同,它的未知函数是边界面上的隐电流源分布密度;第二个积分方程的未知函数则是电位函数本身. 在的文章以及本文作者的另一篇文章中,供电电极和测量电极都被当成点电极处理.用这种方法来处理电位电极系和梯度电极系已不够准确,用来处理三侧向或双侧向等具有大电极的电极系则完全无能为力. 测井中所用的电极系是包着金属外皮的绝缘心棒,金属外皮就是电极.本文提出了处理这种电极系的方法.结果表明,第二个积分方程在处理这种电极系时有明显优点.     

A TUNNEL RESOLUTION INVESTIGATION USING AN AUTOMATED RESISTIVITY TANK ANALOG*

The examination of apparent resistivity space sections over two-dimensional targets requires the accumulation of large amounts of data, if the resistivity field is to be adequately described. Whilst such data may be obtained from an intensive sounding traverse in the field, it is desirable for interpretation purposes to be able to generate such space sections for a range of model variations. Within their limitations, tank analogs can be used to provide such interpretation material, but the collection of data can itself be time-consuming. In this paper, an account is given of the development of an automated tank analog, where an entire space section can be scanned and the output obtained in paper tape format for later processing on a digital computer. The resistance measurement accuracy attained is comparable with normal field measurement accuracy. A practical example of the use of this analog in investigating the problem of resolving and discriminating between two horizontal cylindrical tunnels is given. This problem is basic to an understanding of the minimum size and disposition of targets which can be observed on a space section. The square array has been used in this example because of its good resolution properties in general prospecting rather than its particular suitability for the targets investigated. The directional response of the array is also illustrated and discussed.     

Cross‐hole resistivity tomography using different electrode configurations

This paper investigates the relative merits and effectiveness of cross‐hole resistivity tomography using different electrode configurations for four popular electrode arrays: pole–pole, pole–bipole, bipole–pole and bipole–bipole. By examination of two synthetic models (a dipping conductive strip and a dislocated fault), it is shown that besides the popular pole–pole array, some specified three‐ and four‐electrode configurations, such as pole–bipole AM–N, bipole–pole AM–B and bipole–bipole AM–BN with their multispacing cross‐hole profiling and scanning surveys, are useful for cross‐hole resistivity tomography. These configurations, compared with the pole–pole array, may reduce or eliminate the effect of remote electrodes (systematic error) and yield satisfactory images with 20% noise‐contaminated data. It is also shown that the configurations which have either both current electrodes or both potential electrodes in the same borehole, i.e. pole–bipole A–MN, bipole–pole AB–M and bipole–bipole AB–MN, have a singularity problem in data acquisition, namely low readings of the potential or potential difference in cross‐hole surveying, so that the data are easily obscured by background noise and yield images inferior to those from other configurations.     

深埋电极的地电阻率观测研究

首先研究了四极观测系统装置系数与电极埋深的关系;然后给出了点电流源在3层地壳模型的地表和第二层时,电源所在层的电位的解析表达式;最后将天津宝坻地区的电性结构简化成一个3层模型,计算给出了当地表层和基岩中的电阻率出现变化时,在地表和基岩上层开展四极地电阻率观测结果与供电极距和深度的关系.     

多同性源阵列电阻率法隧道超前探测方法与物理模拟试验研究

直流电阻率法以其对含水构造响应敏感且适应性强的特点,是隧道施工期超前地质预报的常用方法.针对目前定点源三极观测方式易受到测线附近旁侧异常干扰与聚焦观测方式探测距离过短无法三维成像的问题,提出了一种基于多同性源阵列电阻率的隧道超前探测新方法,利用环形布置的多同性源供电压制隧道掌子面后方的异常体的干扰,同时增强掌子面前方远处异常体的敏感度,阵列电极测量可为含水构造的三维反演成像提供三维数据.首先,开展了含水构造超前探测的数值正演模拟,发现多同性源方法的视电阻率纵向微分曲线极小值以及与横轴的交点位置可对异常体位置进行定性判断,探讨了多同性源方法对后方及侧向异常干扰的响应特征及识别方法.其次,将电阻率光滑约束与轨迹光滑策略引入蚁群反演算法,提出了一种最小二乘方法与改进蚁群算法相结合的混合反演算法,反演数值算例表明混合反演算法能够实现含水构造的三维成像,较好地反演出不同距离的含水构造位置,并使其边界较为清晰.为了验证多同性源探测方法的探测效果开展了物理模型试验,多同性源阵列电阻率法能较好的反映含水构造的存在,与实际含水构造的位置较为相符.     

RESOLUTION OF RESISTIVITY TOMOGRAPHY INFERRED FROM NUMERICAL SIMULATION1

Some factors affecting the resolution and accuracy of resistivity tomography are examined using numerical simulation. The inversion method used is based on smoothness-constrained least-squares and finite-element methods. An appropriate block discretization is obtained by dividing the target region into square blocks of size equal to half the minimum electrode spacing. While the effect of the damping factor on the resolution is significant, the resolution is not very sensitive to Gaussian noise as long as the damping factor is properly chosen, according to the noise level. The issue of choosing an optimum electrode array should be considered at the planning stage of a survey. When the instrumental accuracy is high, the dipole-dipole array is more suitable for resolving complex structures than the pole-pole array. The pole-dipole array gives somewhat less resolution than the dipole-dipole array but yields greater signal strength; thus, the pole-dipole array may be a good compromise between resolution and signal strength. The effect of an inhomogeneity located outside the target region may be very small if block discretization is done so as to represent the resistivity variations in both the target and outside regions.     

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.     

平凉台井下地电阻率观测影响系数分析

根据地电阻率影响系数理论,以平凉台4层电性结构为例,分析了井下对称四极地电阻率观测影响系数随深度和极距的变化。结果表明:对于固定的观测极距,影响系数与电极埋深之间的关系复杂;通过计算各层影响系数的大小,认为平凉台井下观测对地表及浅层干扰有较好的抑制作用,其分析结果可为在类似台址电性结构中实施井下地电阻率观测时选择电极埋深和供电极距提供参考。     

The effect of subsurface pipes on apparent‐resistivity measurements

Subsurface conducting pipes can be either a target or a noise source in geophysical surveying. Their effect as a noise source in resistivity imaging can be so severe as to render the geophysical data uninterpretable. A method is developed here for identifying, locating and removing the effects of subsurface conducting pipes from image data, thus revealing the background resistivity structure.
A previously known analytic solution for the potential distribution produced by current injection in a uniform half‐space containing an infinitely long conducting cylinder is used to calculate apparent resistivities corresponding to electrode arrays on the surface of the half‐space. Most results concern the Wenner array and an examination is made of the effects produced by varying the electrode spacing and the depth, size and orientation of the pipe with respect to the array. A method is developed for locating pipes in resistivity image data by cross‐correlation of the analytic solution with the measured field data. Pipe effects are then removed by multiplying each datum point in the measurements by the reciprocal of the corresponding value in the analytic solution. The success of the method is demonstrated by applications to synthetic data sets involving one or two pipes embedded in non‐uniform half‐spaces.
In further examples, the method is applied to some measured resistivity images from an ex‐industrial site (a former oil distribution terminal), where an electromagnetic survey had previously revealed a labyrinth of underground pipes. The method is shown to be successful in removing the effects of the pipes to reveal the underlying geology.