Analysis and application of a non-conventional underwater geoelectrical method in Lake Geneva,Switzerland

The electrical method presented is used for determining the resistivity of lake-bottom sediments and is based on the d.c. electrical sounding principles. The electrode array, called the fishing rod (FR), is of pole-pole type and is orientated vertically on a line perpendicular to the surface of the water. The technique is used for mapping resistivity anomalies located deep underwater. This paper presents an analysis of the resolution capabilities of the FR method and the results of a case study carried out in Lake Geneva, where measurements were interpreted using a one-dimensional (1D) multilayer earth model. The analysis of the uncertainty in the model parameters of a 1D multilayer earth model is carried out using the covariance matrix of the linearized inversion problem. The results of the analyses show that when the thickness and resistivity of the water layer is known, the resistivity of the sediment layer is well determined under most circumstances. The thickness of the sediment layer is well determined when resistivity contrasts are not too low. In Lake Geneva the FR method has been used to study an old depression with a resistive channel. This application shows the efficiency of the method compared with conventional electrical methods, where water depth becomes a limiting factor. The use of an automated iterative inversion scheme in this particular case is advantageous, as a joint interpretation of the three different data sets measured with the FR method can be carried out. Finally, the result of the inversion is compared with the trial-and-error interpretations of a previous study.     

The use of non-conventional CPTe data in determination of 3-D electrical resistivity distribution

The spatial distribution of the electrical resistivity data provides useful information for investigating and modeling the fluid transport processes. 3D electrical resistivity distribution provides information about water flow and changes in electrical resistivity of the pore fluid.Therefore, to assist in understanding and modeling of the fluid transport process, 3D spatial distribution of the electrical resistivity data with the corresponded 3D geological section were mapped and interpreted in the test site located in western Germany. A process of deriving electrical resistivity values from the mechanical and radioactive parameters of cone penetration tests (CPT) and geological information of boreholes was presented. A reliable method which gives accurate resistivity values in cases of near surface sediments was introduced. Then a field test was executed where the calculated resistivity values were compared with the measured CPTe resistivity data. The CPTe (cone penetration test with electrical extension) data were also used in correlating to the ERT (electrical resistivity tomography) data. Consequently, obtained dense CPT surveys give us the possibility to determine a high resolution resistivity distribution of the investigated area.     

水平多层大地上垂直磁偶极频率测深的全波视电阻率

本文根据视电阻率定义的原则,以及用不同的场量定义的视电阻率效果不同这一事实,提出一种新的全波视电阻率定义.在全区同时用均匀大地上电磁场的三个分量来分区定义祝电阻率.在远区视电阻率由磁场的水平分量求出,在近区由磁场的垂直分量或其实分量定义,而在过渡区则由电场的水平分量确定.用这种方法定义的视电阻率为电磁响应的单值函数,它随频率变化的曲线显著改善,能直观地反映地层电阻率随深度的变化,数值比较接近地层的真电阻率值,假极值效应明显压低.在计算中用切比雪夫多项式分段拟合均匀大地电磁响应的反函数,并给出一套系数,由此算出的视电阻率误差小于1％.     

3D resistivity inversion using 2D measurements of the electric field

Field and 'noisy' synthetic measurements of electric-field components have been inverted into 3D resistivities by smoothness-constrained inversion. Values of electrical field can incorporate changes in polarity of the measured potential differences seen when 2D electrode arrays are used with heterogeneous 'geology', without utilizing negative apparent resistivities or singular geometrical factors. Using both the X - and Y -components of the electric field as measurements resulted in faster convergence of the smoothness-constrained inversion compared with using one component alone. Geological structure and resistivity were reconstructed as well as, or better than, comparable published examples based on traditional measurement types. A 2D electrode grid (20 × 10), incorporating 12 current-source electrodes, was used for both the practical and numerical experiments; this resulted in 366 measurements being made for each current-electrode configuration. Consequently, when using this array for practical field surveys, 366 measurements could be acquired simultaneously, making the upper limit on the speed of acquisition an order of magnitude faster than a comparable conventional pole–dipole survey. Other practical advantages accrue from the closely spaced potential dipoles being insensitive to common-mode noise (e.g. telluric) and only 7% of the electrodes (i.e. those used as current sources) being susceptible to recently reported electrode charge-up effects.     

Use of four-electrode arrays in three-dimensional electrical resistivity imaging survey

The objective of this paper is to investigate the applicability of four-electrode arrays in 3D electrical resistivity imaging survey. A 3D resistivity imaging survey was carried out along fourteen parallel lines using dipole-dipole, Wenner-Schlumberger, and Wenner arrays with 2 m minimum electrode spacings. Roll-along measurements using a line spacing of 1 m were carried out covering a grid of 20 × 14 electrodes. The 3D least squares algorithm, based on the robust inversion method, was used in the inversion of the 3D apparent resistivity data sets. The results show that the 3D electrical resistivity imaging survey using the Wenner-Schlumberger and the dipole-dipole arrays, or the Wenner and the dipole-dipole arrays, in combination with an appropriate 3D inversion method, can be highly useful when the site conditions do not allow using the pole-pole or pole-dipole arrays.     

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.     

Real-Time Geoelectric Monitoring of Seepage into Sand and Clay Layer

The migration of groundwater in rock and soil can appear as abnormalities in geoelectric fields. It is therefore important to study the characteristics of seepage in porous media by measuring the geoelectric field signatures. In this study, a physical model with layers of sand and clay was constructed and an electrical resistivity meter was used to examine the changes in the geoelectric field parameters during the infiltration process. The results show that the infiltration could be detected based on the geoelectric signatures including temporal changes through the spontaneous potential, excitation currents, and apparent resistivity. Specifically, the spontaneous potential was reduced by 100 to 200 mV when the water reaches an electrode. During the second water injection in the experiment, the measured spontaneous potential of all the electrodes recovered to the previous extreme values that range from −200 to −550 mV, thus indicating a “memory” effect. With stepwise changes in the excitation current, it was possible to determine the seepage velocity in sand and clay layer. The apparent resistivity is reduced to less than 400 Ωm when the infiltration reaches the electrodes. These results indicate the potential for real-time monitoring of water flow.     

电测井中电流参数对地层的分辨能力分析

常规电测井一般通过测量供电电极的电流和测量电极之间的电位差来计算围岩的视电阻率并划分地层界面,而忽略了对电流参数的利用。本文基于欧姆定律,通过供电电极电流的变化定性分析其周围岩矿石电阻的变化,进而用电流强度变化曲线识别地层属性。理论分析和试验结果表明,供电电极电流大小取决于电极的接触电阻,而视电阻率大小取决两个测量电极之间或供电与测量电极之间介质的电阻率总和,因此,电流比视电阻率对地层的灵敏度要高一些。绘制电流强度测井曲线可以准确划分地层层位,确定地层厚度,且不增加成本。     

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.     

层状介质中膨胀球模拟力源的应力——应变场与视电阻率的关系

本文研究了三层介质中膨胀球模拟震源的应力、应变场以及由这个应力、应变场产生的电阻率变化量和地表视电阻率变化的关系。结果表明,对于一定强度的“震源”,在地电装置探测范围内的应力场随具有不同弹性参数的层位有显著的变化;而应变场却看不出有明显的突变;由地表视电阻率变化量的计算结果揭示了地电异常受台站介质电性结构与力学结构的综合影响。因此作为预报地震的地电阻率法一方面要寻找具有高电阻率——应变灵敏度岩层的台址,另一方面台址的视电阻率变化对各层真电阻率变化要具有好的响应。     

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.     

Three-dimensional numerical modeling of full-space transient electromagnetic responses of water in goaf

The full-space transient electromagnetic response of water-filled goaves in coal mines were numerically modeled. Traditional numerical modeling methods cannot be used to simulate the underground full-space transient electromagnetic field. We used multiple transmitting loops instead of the traditional single transmitting loop to load the transmitting loop into Cartesian grids. We improved the method for calculating the z-component of the magnetic field based on the characteristics of full space. Then, we established the fullspace 3D geoelectrical model using geological data for coalmines. In addition, the transient electromagnetic responses of water-filled goaves of variable shape at different locations were simulated by using the finite-difference time-domain (FDTD) method. Moreover, we evaluated the apparent resistivity results. The numerical modeling results suggested that the resistivity differences between the coal seam and its roof and floor greatly affect the distribution of apparent resistivity, resulting in nearly circular contours with the roadway head at the center. The actual distribution of apparent resistivity for different geoelectrical models of water in goaves was consistent with the models. However, when the goaf water was located in one side, a false low-resistivity anomaly would appear on the other side owing to the full-space effect but the response was much weaker. Finally, the modeling results were subsequently confirmed by drilling, suggesting that the proposed method was effective.     

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.     

Method to obtain standard pseudosections from pseudo pole-dipole arrays

This study deals with electrical resistivity tomography data and it is addressed at obtaining, from linear combinations of data, other datasets not directly measured. The method presented here allows performing the fieldwork systematically, without deciding the type of the more suitable common electrode array (e.g. Wenner, Wenner-Schlumberger, dipole-dipole or multiple-gradient) until or even after the interpretation time. The electrode configuration used by this method is denoted as pseudo pole-dipole array, because it is based on the standard pole-dipole one, but avoiding the disadvantage of locating the remote electrode far away from the profile (to “infinity”). The pseudo pole-dipole datasets can be acquired with common equipment using standard pole-dipole recording sequences. Once the desired datasets have been calculated, they can be inverted using standard interpretation software. The procedure used allows a data quality control to be introduced that is similar to the one based on normal and reciprocal measurements. To assess the method we considered noise-contaminated model responses as well as field data. It has been applied to build dipole-dipole and Wenner-Schlumberger datasets. Results show the suitability of both, the proposed method and the quality control.     

Non-linear inversion of resistivity profiling data for some regular geometrical bodies1

The inversion of resistivity profiling data involves estimation of the spatial distribution of resistivities and thicknesses of rock layers from the apparent resistivity data values measured in the field as a function of electrode separation. The drawbacks of using traditional curve-matching techniques to solve this inverse problem have been overcome by iterative linear techniques but these require good starting models even if the shape of the causative body is asssumed known. In spite of the recent developments in inversion techniques, no robust method exists for the inversion of resistivity profiling data for the simple model of dikes and spheres which are the classical models of geophysical prospecting. We apply three different non-linear inversion schemes to invert synthetic resistivity profiling data for the classical models embedded in a uniform matrix of contrasting resistivity. The three non-linear algorithms used are called the Metropolis simulated annealing (SA), very fast simulated annealing (VFSA) and a genetic algorithm (GA). We compare the performance of the three algorithms using synthetic data for an outcropping vertical dike model. Although all three methods were successful in obtaining optimal solutions for arbitrary starting models, VFSA proved to be computationally the most efficient.     

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.     

线源三维井地电法异常边界增强及地形校正技术

基于非结构网格有限元方法开展了三维复杂地电模型的线源井地电法的高效正演模拟研究,探讨了通过求取电场响应导数来刻画目标体边界范围、采用差异场地形校正技术来消除地形影响等措施对井地电法成像的效果和精度的影响。并通过对比与解析解,验证了本文数值解算法的有效性。模型计算结果表明：积水巷道的空间位置和走向均会引起视电阻率的显著变化,视电阻率变化率的极值准确且清晰地指示了巷道边界的位置;电位的归一化总水平导数极大地提高了井地电法对目标体复杂边界位置的识别能力;地形对井地电场分布的影响也很大,其视电阻率响应与地形形状近似呈对称关系,利用差异场技术能有效地削弱地形对井地电法高精度成像的影响。     

唐山7.8级强震前震中周围形变电阻率的下降异常

1976年7月28日唐山7.8级强震前,北京、天津、唐山地区已布设14个形变电阻率观测台站,其中9个台,震前2-3年内记录到形变电阻率长趋势下降异常,这9个台围绕震中形成一个半长轴可达150公里的异常区.位于震中区的两个台还记录到临震前2-3个月内的加速下降异常.根据现场条件下地表浅部岩（土）层受压时,视电阻率下降的实验结果,认为在震中周围较大的区域内,震前浅部岩（土）层被压密,其压缩线应变的数量级约为3×10^-5.这一认识得到唐山震前地面基线实测资料的支持.     

Two-dimensional joint inversion of radiomagnetotelluric and direct current resistivity data

An algorithm for the two-dimensional (2D) joint inversion of radiomagnetotelluric and direct current resistivity data was developed. This algorithm can be used for the 2D inversion of apparent resistivity data sets collected by multi-electrode direct current resistivity systems for various classical electrode arrays (Wenner, Schlumberger, dipole-diplole, pole-dipole) and radiomagnetotelluric measurements jointly. We use a finite difference technique to solve the Helmoltz and Poisson equations for radiomagnetotelluric and direct current resistivity methods respectively. A regularized inversion with a smoothness constrained stabilizer was employed to invert both data sets. The radiomagnetotelluric method is not particularly sensitive when attempting to resolve near-surface resistivity blocks because it uses a limited range of frequencies. On the other hand, the direct current resistivity method can resolve these near-surface blocks with relatively greater accuracy. Initially, individual and joint inversions of synthetic radiomagnetotelluric and direct current resistivity data were compared and we demonstrated that the joint inversion result based on this synthetic data simulates the real model more accurately than the inversion results of each individual method. The developed 2D joint inversion algorithm was also applied on a field data set observed across an active fault located close to the city of Kerpen in Germany. The location and depth of this fault were successfully determined by the 2D joint inversion of the radiomagnetotelluric and direct current resistivity data. This inversion result from the field data further validated the synthetic data inversion results.     

单轴压力下有补给水岩石电阻率变化各向异性研究

将两种规格的长方体水饱和花岗岩标本，以标本一个面的中心点为中心，对称布置成互成４５°角的４条对称四极法电阻率测线。标本电极面和相邻面的一小部分用防水环氧胶密封，使标本在装有水的承压水箱中，沿标本长轴方向受压，观测标本视电阻率随压力的变化。实验结果为：（１）有补给水实验与无补给水实验，电阻率变化整体形态相似，即电阻率随压力的变化先上升，后下降，但有补给水实验的电阻率下降幅度要大一些。（２）电阻率变化出现明显的方向性，可以用电阻率变化最大的各向异性主轴方向表示；实验中，用４条测线、４种组合（每３条测线组合可以确定１个视电阻率变化各向异性主轴方向）方法确定的４个电阻率变化各向异性主轴方向基本一致。（３）加压期间，电阻率各向异性主轴方向随压力增加发生变化，这种变化不是渐变和乱变，而是有规律的跃变，即整个实验过程，多数标本只跃变１—３次，每次跃变形成一个主方向，在主方向内，角度变化不大。（４）有补给水岩石电阻率变化整体形态与美国Ｂｒａｃｅ等（１９６８）所作的围压和孔隙压的岩石电阻率变化形态相似。