SIMPLE DATA PROCESSING OF TRIPOTENTIAL APPARENT RESISTIVITY MEASUREMENTS AS AN AID TO THE INTERPRETATION OF SUBSURFACE STRUCTURE*

The advantages of the Wenner tripotential method (Carpenter 1955) for apparent resistivity profiling are described and two new data processing techniques introduced as an aid to the interpretation of apparent resistivity sections (pseudo-sections). These techniques were developed from model data computed using a two-dimensional finite difference method. Oscillatory components present in anomalies on tripotential profiles and related to electrode spacing are shown to be effectively removed by linear filtering that also simplifies their form and aids recognition. Furthermore, it is shown that the ratio of the beta- and gamma-apparent resistivities is a good indicator of resistivity variation, and is particularly sensitive to lateral change. Model data indicates that, over a wide range of conditions, enough subsurface information can be obtained by inspection of tripotential resistivity and ratio profiles, and from space sections to make possible a useful—and sometimes semi-quantitative—interpretation. A rationale for the general interpretation of tripotential data is developed. Field data are described from an area of weathered granite basement in Nigeria. A model of the subsurface is developed using parameters derived from the processed observations. The observed and calculated apparent resistivity space sections are very similar.     

TRANSFORMATION OF RESISTIVITY SOUNDING MEASUREMENTS OBTAINED IN ONE ELECTRODE CONFIGURATION TO ANOTHER CONFIGURATION BY MEANS OF DIGITAL LINEAR FILTERING*

The technique of digital linear filtering is used for transformation of apparent resistivity data from one electrode configuration into another. Usually filter spectra are determined via the discrete Fourier transforms of input and output functions: the filter characteristic is the quotient of the spectra of the output function and input function. In this paper, the transformation of the apparent resistivities is presented for four electrode configurations (Wenner, the two-electrode, Schlumberger, and dipole configurations). In our method, there is no need to use the discrete Fourier transform of the input and output functions in order to determine the filter spectrum for converting apparent resistivity in one electrode configuration to any other configuration. Sine responses for determination of the derivative of apparent resistivities are given in analytical form. If the filter spectrum for converting the apparent resistivity to the resistivity transform for one electrode configuration is known, the filter spectra for transforming the apparent resistivity to the resistivity transform for any electrode configurations can be calculated by using newly derived expressions.     

NUMERICAL INTERPRETATION OF RESISTIVITY SOUNDINGS OVER HORIZONTAL BEDS*

The digital computer technique described for interpreting resistivity soundings over a horizontally stratified earth requires two steps. First, the kernel function is evaluated numerically from the inverse Hankel transform of the observed apparent resistivity curve. Special attention is given to the inversion of resistivity data recorded over a section with a resistant basement. The second step consists in the least-squares estimation of layer resistivities and thicknesses from the kernel function. For the case of S or T-equivalent beds only one layer-parameter can be obtained, either the longitudinal conductance, or the transverse resistance respectively. Two examples given in the paper show that a wide tolerance is permitted for Choosing the starting values of the layering parameters in the successive approximation procedure. Another important feature for practical applications is good convergence of the iterations. The method is probably best suited for interpreting profiles of electrical soundings with the purpose of mapping approximately horizontal interfaces at depth.     

USE OF ELECTRICAL RESISTIVITY METHODS FOR THE STUDY OF COAL SEAMS IN PARTS OF THE RANIGANJ COALFIELD (INDIA)*

The surface resistivity method has been used to study a few exposed coal seams located in the northwestern part of the Raniganj Coalfield (belonging to the Damodar Valley Gondwana basin), India. Different electrode configurations, viz., Wenner, two-electrode and half-Schlumberger, have been used with different electrode spacings in horizontal profiling. The vertical distribution of resistivity has been studied using Schlumberger configuration at different locations along the profile. Laboratory studies of resistivity (at partial to full water saturation conditions) and porosity of different coal, shaly sandstone and sandstone samples of the survey area had already been carried out before the field survey. The results indicated the presence of a good resistivity contrast between the coal seams and the surrounding formations. The field results did not bear this out: the resistivity responses of the coal formations on the profiles and sounding curves are not as clear as one would expect for such high contents. The Wenner profiles show a broad resistivity anomaly over the coal seams. Two-electrode profiles are less noisy than Wenner profiles. Sharp peaks have been observed over the coal seams. The half-Schlumberger configuration seems the best: all the coal seams and their edges can be accurately outlined on the resistivity curves. Borehole data close to the profile have been used for correlating the field results. There is good agreement with vertical electrical soundings.     

THEORETICAL BROADSIDE RESISTIVITY PROFILES OVER AN OUTCROPPING DYKE

Theoretical broadside resistivity profiles over an outcropping dyke of infinite depth extent with three Wenner configurations (namely Alpha, Beta and Gamma), Schlumberger, and two-electrode configurations of various electrode spacings and for various reflection factors are presented. The broadside profiles qualitatively indicate that the shape of the anomaly is invariant with the electrode configurations. The various electrode configurations can be arranged in decreasing order of magnitude of anomalies as Beta Wenner, Alpha Wenner, Schlumberger, Gamma Wenner, and two-electrode. The broadside Wenner profiles also show larger anomalies compared to those in inline profiles.     

VERTICAL PROFILING OVER A MEDIUM OF CONTINUOUSLY VARYING RESISTIVITY*

An interpretation method is suggested for apparent resistivity profiles over a medium of continuously varying resistivity. The medium is replaced by an equivalent laminated system of constant resistivity in each layer and evaluated by superposition. The approximation facilitates detailed subsurface profiling as required for underground storage projects or water infiltration schemes.     

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.     

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.     

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.     

多极距地电阻率观测系统的分布式电极控制器研制

详述数字电极的系统构成、电路结构、通信协议和其他关键技术。该系统的通信网络结构基于RS-485现场总线,通过环境测试和台站试验,发现数字电极技术适用于多极距电阻率系统。     

A DIGITAL LINEAR FILTER FOR RESISTIVITY SOUNDING WITH A GENERALIZED ELECTRODE ARRAY*

This paper presents a digital linear filter which maps composite resistivity transforms to apparent resistivities for any four—electrode array over a horizontally layered earth. A filter is provided for each of three sampling rates; the choice of filter will depend on resistivity contrasts and computational facilities. Two methods of filter design are compared. The Wiener-Hopf least-squares method is preferable for low sampling rate filters. The Fourier transform method is more successful in producing a filter with a high sampling rate which can handle resistivity contrasts of 100 000: 1.     

激发极化法探测油气田——效果及异常模式探讨

本文是在20多个油气藏上作激发极化法找油气的试验结果。在华北的第三系油田,四川的中生界油气田,新疆的中生、古生界大逆掩断层带油田,以及华东的第三系油田上试验,普遍得到好的效果。各地区的充电率、电阻率及金属因数等参数的反应特点有差异,异常明显程度受盖层影响很大。该方法可以探测到埋深不小于3000m的油气藏,并在许多油气藏发现了具有共同特征的典型异常模式:它在浅部中心部位表现为高阻,高极化;两侧为低阻,低极化;深部表现为低阻,高极化;深浅两带之间为过渡带,异常无固定的特征。此模式可用以分辨油气藏异常,选择合适工作极距,以及研究引起异常的机制等。     

Apparent resistivity over a three layer earth with an inhomogeneous interstratum

Summary The theory of resistivity sounding on a three layer earth comprising an inhomogeneous interstratum has been presented. The electrical conductivity in the intermediate layer, embedded between two layers of uniform conductivity, is assumed to follow either generalised power law or exponential variation. A point source of current is placed on the surface. The electric potential functions on the ground surface have been obtained. The expressions for apparent resistivity over the above models for the Wenner and Schlumberger electrode configurations have been derived.     

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.     

I.P. AND RESISTIVITY MODEL STUDIES OVER THIN DYKES*

Induced polarization and resistivity model studies over thin dykes for varying resistivity contrasts, depth of burial, and dip angles show striking parallelism of the surface apparent resistivity contours with the boundary of the body. This effect may be utilized for the estimation of strike length of the body. Results show that intermediate values of the electrode spacing is satisfactory for detection under widely varying conditions of resistivity contrast and depth. The percentage frequency effect (P.F.E.) and the metal factor (M.F.) responses are found to be more sensitive to the variation in the depth of burial than the resistivity responses. Pseudosections for P.F.E. and M.F. are concentrated much closer to the body than the resistivity pseudo-sections.     

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.     

延庆台井下小极距地电阻率观测系统分析

随着经济建设的发展,地电阻率定点观测区环境被干扰严重影响观测质量,装置系统在地表布设的工作方式难以取得有效观测和持续发展,因此装置系统向井下深部布设受到人们关注。同时,地表大极距观测方式难以持续发展,也促使地电阻率定点观测向井下小极距观测方式发展。井下小极距观测相比地表大极距观测占地面积小,能较好地排除或减弱地表测区环境干扰对观测结果的影响,既能适应经济发展的需要,又能较好地为地震监测服务。2018年,在总结已建井下地电阻率台站布极方式和建设工艺的基础上,新建延庆台井下小极距地电阻率观测。本文重点分析了延庆台井下小极距地电阻率观测装置系统建设中的几个关键问题,如水平向和垂直向观测相结合、布极方式、电极制作和埋设深度等装置系统技术过程,以及水平向和垂直向观测装置系数的计算等。延庆台建设较好地获得了近全空间观测布设,从理论上解决了井下小极距地电阻率建设的难点,为将来要进行井下小极距地电阻率观测装置系统建设的台站提供参考。     

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 DIRECT INTERPRETATION OF RESISTIVITY OBSERVATIONS MADE WITH A WENNER ELECTRODE CONFIGURATION*

In a previous paper by the present author a method was developed for direct interpretation of resistivity observations made with a Schlumberger electrode configuration. This method consisted of two steps. The first of these was to derive the kernel function in the integral expression for the apparent resistivity from the observed data; the second step was to derive the resistivity stratification from this kernel function. The first of these two steps depends on the electrode configuration that has been used. In the present paper the above mentioned method is modified so as to make it apply to a Wenner electrode configuration. The procedure is indicated by which the method may be adapted to any other electrode configuration in which the distances between the electrodes are finite. The second step in the interpretation, i.e. the derivation of the resistivity stratification from the kernel function, is independent of the electrode configuration used, and therefore needs no further discussion in the present context.