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.     

坑道直流电阻率测深异常研究

电阻率测深数据可利用抗道的四个面和四个角得到。但由于受到坑道本身和体积效应影响,坑道内电阻率测深资料解释的困难很大。本文用有限单元法对坑道内的直流电阻率测深进行数值模拟计算。首先给出坑道中正常电位的取值,并利用有限单元异常电位计算法对坑道内电阻率测深进行正演计算。结果表明,在异常体断面尺寸、埋深及所用电极距与坑道截面尺寸相差不大时,坑道面上的测深断面反映的基本是本坑道面外侧地质体的信息,对其他位置的地质体没有明显反映,坑道角断面则反映的是相邻两个坑道面外侧地质体的综合信息。     

Rapid inversion of data from 2D resistivity surveys with electrode displacements

Resistivity monitoring surveys are used to detect temporal changes in the subsurface using repeated measurements over the same site. The positions of the electrodes are typically measured at the start of the survey program and possibly at occasional later times. In areas with unstable ground, such as landslide‐prone slopes, the positions of the electrodes can be displaced by ground movements. If this occurs at times when the positions of the electrodes are not directly measured, they have to be estimated. This can be done by interpolation or, as in recent developments, from the resistivity data using new inverse methods. The smoothness‐constrained least squares optimisation method can be modified to include the electrode positions as additional unknown parameters. The Jacobian matrices with the sensitivity of the apparent resistivity measurements to changes in the electrode positions are then required by the optimisation method. In this paper, a fast adjoint‐equation method is used to calculate the Jacobian matrices required by the least squares method to reduce the calculation time. In areas with large near‐surface resistivity contrasts, the inversion routine sometimes cannot accurately distinguish between electrode displacements and subsurface resistivity variations. To overcome this problem, the model for the initial time‐lapse dataset (with accurately known electrode positions) is used as the starting model for the inversion of the later‐time dataset. This greatly improves the accuracy of the estimated electrode positions compared to the use of a homogeneous half‐space starting model. In areas where the movement of the electrodes is expected to occur in a fixed direction, the method of transformations can be used to include this information as an additional constraint in the optimisation routine.     

STUDYING THE INTERCONNECTION OF GROUND AND SURFACE WATERS IN REPRESENTATIVE BASINS UNDER THE PROGRAMME OF THE INTERNATIONAL HYDROLOGICAL DECADE

Abstract

Four geoelectrical soundings were measured with a combination of Schlumberger and azimuthal or equatorial dipole electrode arrays on a Carboniferous limestone basin of the Condroz area, Belgium. The measuring technique is briefly outlined as well as the interpretation procedure, which follows a closed-loop scheme with control of calculated model curves. Some general problems of interpretation of geoelectrical sounding curves are tackled, as far as they have a practical bearing on the treatment of Condroz soundings.

The problem of determining the very high resistivity of limestone is approached through ARCHIE's formula, an empirical relation between the bulk rock resistivity, the porosity and the electrolyte resistivity. An evaluation of the latter two parameters, combined with electrical horizontal conductance measurements directly made on resistivity sounding curves, offers a possibility for fast determination of the total water storage in a limestone aquifer. Such storage determinations could be applied whenever an aquifer shows up as a conductive layer interbedded between two highly resistant layers (e.g. nonsaturated limestone and compact, non-fractured limestone).     

ULTRA DEEP SCHLUMBERGER SOUNDING AND CRUSTAL CONDUCTIVITY STRUCTURE IN SOUTH AFRICA*

A second deep Schlumberger sounding has been carried out in South Africa, this time using a newly completed power transmission line, not yet in sevice, as emission line. The maximum current electrode separation attained was 600 km. The sounding was situated on a shield area with a thin cover of sedimentary rocks (Karroo System) overlying the archaean granite. The center was chosen near to the village of Dealesville. It is shown that lateral effects at large AB spacings are unlikely, but due to numerous dolerite intrusions in the sediments surface electrode effects must be guarded against; thus AB positions were chosen by geologists. Because of a low signal/noise ratio at large AB spacings the measurements were treated statistically; in particular, the elimination of non-random events improved the measuring accuracy. Although a thin conducting layer at the base of the sedimentary succession decreased the resolution of the sounding curve, the results, which were interpreted with the aid of a computer, show positively that

• (a). the crust is multi-layered with a highly resistant portion having a minimum resistivity of 15000 ohm.m and
• (b). a good, thick conductor appears as the final layer.

The Dealesville results are in complete agreement with those obtained from the first deep Schlumberger sounding at Pofadder (Van Zijl 1969) except that the transverse resistance of the lowermost resistant crust is about 100% larger at Pofadder due probably to a second period of metamorphism. Both electrical studies support the view of a dehydrated lower crust (granulite facies).     

用有限元法正演京津唐地区二维构造的大地电磁测深资料

本文阐述在大地电磁测深工作中,用有限单元法,模拟计算京津唐地区二维地质构造的大地电磁响应。 文章前部分,论述了用有限单元法正演二维大地电磁测深曲线的原理及其数学公式推导。文章后部分,根据两条测线实测的大地电磁测深结果并结合其它地球物理探测资料,给出了两个二维剖面模型,并计算了两种极化的视电阻率曲线。两条实测剖面分别是横切唐山地震带的马兰峪—柏各庄剖面及横过北京地区北北东构造走向的文化营—王辛庄剖面     

Combined straightforward inversion of resistivity and induced polarization (time-domain) sounding data

It is proposed that the Straightforward Inversion Scheme (SIS) developed by the authors for 1D inversion of resistivity sounding and magneto-telluric sounding data can also be used in similar fashion for time-domain induced polarization sounding data. The necessary formulations based on dynamic dipole theory are presented. It is shown that by using induced polarization potential, measured at the instant when steady state current is switched off, an equation can be developed for apparent ‘chargeability–resistivity’ which is similar to the one for apparent resistivity. The two data sets of apparent resistivity and apparent chargeability–resistivity can be inverted in a combined manner, using SIS for a common uniform thickness layer earth model to estimate the respective subsurface distributions of resistivity and chargeability–resistivity. The quotient of the two profiles will give the sought after chargeability profile. A brief outline of SIS is provided for completeness. Three theoretical models are included to confirm the efficacy of SIS software by inverting only the synthetic resistivity sounding data. Then one synthetic data set based on a geological model and three field data sets (combination of resistivity and IP soundings) from diverse geological and geographical regions are included as validation of the proposal. It is hoped that the proposed scheme would complement the resistivity interpretation with special reference to shaly sand formations.     

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 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.     

电偶源频率电磁测深中的静位移现象及视电阻率曲线的畸变

以电偶源频率电磁测深 (FEMS)二维数字模拟为例 ,从理论上简略讨论了波区定义的 5种视电阻率的变化特征及静位移现象 ,定性分析了表面局部水平非均匀体对视电阻率曲线畸变的影响 .     

A STUDY ON THE DIRECT INTERPRETATION OF DIPOLE SOUNDING RESISTIVITY MEASUREMENTS OVER LAYERED EARTH *

Dipole sounding resistivity measurements over layered earth can be interpreted directly by adapting the procedure given by Koefoed (1968) for Schlumberger system. To carry out the first step of the interpretation leading to the determination of the raised kernel function, partial resistivity functions for the dipole method are derived and given in the form of standard curves. The second step involving the derivation of layering parameters from the kernel being independent of the electrode configurations remains unaltered. The applicability and limitations of the method are discussed.     

晋冀蒙交界及附近地区小极距井下地电阻率观测装置设计

为提升2022年北京冬奥会期间地电阻率测项的震情保障能力,将对晋冀蒙交界及附近区域的宝昌、集宁、阳原、大同、代县、临汾、通州和平谷8个台站在原有观测基础上增加具有全空间性质的小极距井下地电阻率观测。本文根据台站钻孔岩芯剖面和电测深数据反演测区水平层状电性结构,利用介质对地电阻率观测的影响系数方法,计算影响系数随极距和埋深的变化,选择合适的极距和埋深,使浅层介质对地电阻率观测的影响尽可能小,使目标层位对观测的贡献尽可能大,减少浅层介质对观测的影响。由此得出了各台站观测极距及埋深等装置系数,在此基础上完成了8个台站观测装置的方案设计。     

MATRIX METHOD FOR THE TRANSFORMATION OF RESISTIVITY SOUNDING DATA OF ONE ELECTRODE CONFIGURATION TO THAT OF ANOTHER CONFIGURATION1

Matrix equations are derived to transform the resistivity sounding data obtained in one type of a four-electrode array to the corresponding resistivity sounding data that would be obtained using a different four-electrode array. These expressions are based primarily on recent work in which we have established a linear relation between the apparent resistivity and the kernel function by using a powerful exponential approximation for the kernel function. It is shown that the resistivity sounding data of two different four-electrode arrays have a linear relation through an essentially non-singular matrix operator and, as such, one is derivable from the other for a one-dimensional model and it can also be extended to two-dimensions. Some numerical examples considering synthetic data are presented which demonstrates the efficiency of the method in such transformations. Two published field examples are also considered for transformation giving a reliable interpretation.     

THE INFLUENCE OF LATERAL INHOMOGENEITIES ON THE DIPOLE METHODS*

The theory of electrical dipole soundings proved that this method can produce resistivity measurements, which are comparable with those obtained by electrical soundings of the Wenner or Schlumberger type. Their main advantage is the use of short cable lengths, which is important if the depth of penetration should be large. A considerable disadvantage of the dipole method is the great sensitivity to lateral discontinuities. Though these have an influence on the Schlumberger arrangement as well, they can disturb a dipole sounding to such an extent than an interpretation based on a horizontal layer case is no more possible. There are six different dipole arrays, which differ from each other with respect to the angle enclosed by the two dipole orientations-the current dipole AB and the measuring dipole MN. The theoretical comparison of the dipole arrays with the Schlumberger array concerning their sensitivity to lateral discontinuities is a useful basis for the choice of the most suitable configuration. Considering geological subsurface conditions the right choice of a dipole array can give an optimal result, i.e. a dipole sounding for which the sensitivity to lateral discontinuities is as small as possible under the given circumstances.     

三维坑道直流聚焦法超前探测的电极组合研究

在坑道超前探测方法中,直流电阻率法原理和操作简单,应用前景广阔,其中侧向聚焦电阻率法应用在测井中已经成为一种常用方法.本文研究了三维坑道直流聚焦法电极组合,首先计算分析了两个同性点电源的电流分布规律,指出由于电流的相互排斥作用,电流密度在这两个点电源的中垂线下一定深度处产生最大值,这个深度与这两个点源之间的距离成正比.基于上述原理,设计出三种电极组合：四点电源、五点电源和九点电源布极方式.其次,用三维有限单元数值模拟的方法计算了上述三种电极系的空间电位分布,得出九点电源方式对电流聚束效果较好,而且当主电极电流小于屏蔽电极电流时效果最好.     

SENSITIVITY ANALYSIS OF MAGNETOTELLURIC MEASUREMENTS IN RELATION TO STATIC EFFECTS1

The relation between the horizontal profiles of the subsurface resistivity and surface magnetotelluric data can be described by the input and output of a moving-average filter. The impulse response of this spatial filter, which characterizes the averaging process of the magnetotelluric measurements, is given by the sensitivity profile. Thus, the sensitivity analysis can provide insight into the characteristics of the measurements and hence the mechanism of the static effects. The sensitivity analysis presented here consists of constructing the vertical section of the sensitivity distribution using the finite-element method and then Fourier transforming the selected horizontal profiles. When the dipole is assumed for measuring the electric field, the static effects can be explained by the high-pass filter characteristics for the near-surface. When the electrode separation is taken into account, the sensitivity can be obtained by averaging the sensitivities for the dipoles over the horizontal distance equal to the electrode separation. Therefore, the higher-frequency components at each depth decrease with increasing electrode separation. Thus, although the static effects can be reduced simply by increasing the electrode separation, information on the resistivity variation at depth is also lost. However, such an adverse effect can be reduced by making the EMAP-type measurements followed by the spatial filtering of the profile data using the tapered weighting function.     

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.     

水下激发极化测深异常特征研究

利用有限单元法对水下激发极化测深进行数值模拟以研究其异常特征和适用条件.水下的电阻率测深和激电测深均可对水底地质体进行近距离探测,提高探测分辨率.而水底地形对视电阻率测深的影响很大.水底极化体有限元正演模拟的结果表明,水底地形对激发极化测深结果没有影响.采用水下激发极化法进行地质体探测是可行、有效的.通过计算不同水体和水底岩石电阻率对视极化率幅值的影响发现,水体电阻率是影响水下极化率测深的主要因素.由于海水的电阻率过低,观测视极化率异常微弱而不适合开展水下激电工作.     

Behavior of electric potential fields over random conductivity,layered earth models

Solutions are derived for the potential distributions over one-layer and two-layer random conductivity earth models for the direct current resistivity method. Monopole and Wenner arrays are considered. It is shown that the random potential due to a spatially stationary Gaussian random conductivity is also Gaussian but not spatially stationary. The ensemble and sample statistics of the random kernel and apparent resistivity are examined. Representative curves of these functions are presented to show the effects of a random conductivity profile on them. It is shown that the effect of the random nature of the conductivity profile on an apparent resistivity sounding curve is greatest for small electrode spacings.