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.     

Grounded-source transientE-field modeling of a shallow resistive layer with 3-D inhomogeneity

There is growing interest in the use of transient electromagnetic (TEM) sounding for shallow geotechnical, environmental and groundwater investigations. Two commonly used transmitterreceiver configurations for TEM sounding are 1) loop-loop or its variation, in-loop configuration and 2) wire-loop configuration. The less common configuration of a horizontal electric dipole (HED) transmitter and receiver is treated in this study and called wire-wire configuration.Two important problems of shallow investigation in hard and soft rocks respectively are, defining 1) a fractured/fissured zone of medium resistivity, sandwiched between an overlying surface weathered rock of low resistivity and an underlying fresh compact rock of high resistivity and 2) a body of resistive sand buried in conductive clay. Lateral change in the middle layer resistivity is modeled by including a 3-D body of anomalous resistivity. The effect of perturbing the resistivity of the 3-D inclusion and the host middle layer for the wire-wire configuration is compared with that of the commonly used loop-loop configuration. The wire-wire configuration is found more sensitive to the model perturbations than the loop-loop configuration.1-D inversion of synthetic 1-D data sets for the wire-wire configuration finds resolution and estimation errors to be less than 10 percent for all the model parameters. For 3-D models, 1-D inversion results give a resolution error of 10 percent or less for the depth to, resistivity and thickness of, the 3-D inclusion. The estimate is within 10 percent of the true value for the first parameter but 40 percent for the other two. Resolution as well as estimation of the basement resistivity is always very poor.Using the wire-wire configuration, it is theoretically possible to define a buried resistive layer and any lateral change in its resistivity, subject to the above limitations of 1-D inversion. However, the basement resistivity cannot be estimated with reasonable accuracy in the presence of a lateral inhomogeneity in the overlying layer.     

Assessment of the reliability of 2D inversion of apparent resistivity data

The reliability of inversion of apparent resistivity pseudosection data to determine accurately the true resistivity distribution over 2D structures has been investigated, using a common inversion scheme based on a smoothness‐constrained non‐linear least‐squares optimization, for the Wenner array. This involved calculation of synthetic apparent resistivity pseudosection data, which were then inverted and the model estimated from the inversion was compared with the original 2D model. The models examined include (i) horizontal layering, (ii) a vertical fault, (iii) a low‐resistivity fill within a high‐resistivity basement, and (iv) an upfaulted basement block beneath a conductive overburden. Over vertical structures, the resistivity models obtained from inversion are usually much sharper than the measured data. However, the inverted resistivities can be smaller than the lowest, or greater than the highest, true model resistivity. The substantial reduction generally recorded in the data misfit during the least‐squares inversion of 2D apparent resistivity data is not always accompanied by any noticeable reduction in the model misfit. Conversely, the model misfit may, for all practical purposes, remain invariant for successive iterations. It can also increase with the iteration number, especially where the resistivity contrast at the bedrock interface exceeds a factor of about 10; in such instances, the optimum model estimated from inversion is attained at a very low iteration number. The largest model misfit is encountered in the zone adjacent to a contact where there is a large change in the resistivity contrast. It is concluded that smooth inversion can provide only an approximate guide to the true geometry and true formation resistivity.     

ELECTRICAL SOUNDING OF A HALF SPACE WHOSE RESISTIVITY OR ITS INVERSE FUNCTION VARIES LINEARLY WITH DEPTH*

The solution for the potential distribution about a point source of current placed at the surface of a continuous half-space is obtained for two cases: (1) the resistivity increases linearly with depth; (2) the conductivity increases linearly with depth. In each case, an expression for the apparent resistivity is established and master curves are presented for both the Wenner and the Schlumberger configurations. The results can be used in the interpretation of electrical sounding data in specified geologic situations. Furthermore, they may be used as a first step in the development of solutions for the more complex electric sounding problems.     

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.     

基于地电场响应的地裂缝模拟试验

在应用网络并行电法技术的基础上,建立有基底潜山的物理模型,对注水条件下模型土体开裂过程中的地电场响应进行测量。试验结果表明,土体中电位、电流和电阻率的变化与土体含水量密切相关,随着土体中含水量的改变,自然电位、一次场电位、激励电流和视电阻率发生急剧变化;网络分布式并行电法反演信息表明在视电阻率曲率值较大位置容易产生不均匀沉降和裂缝,不均匀沉降的程度越大,地裂缝的长度、宽度、深度也越大。     

Some considerations on electrical resistivity imaging for characterization of waterbed sediments

The paper focuses on defining the performance and limits of ERI in the detection and sedimentary characterization of near-bottom thin layers. The analysis of the resolution of floating and submerged cables, and the effect of the accuracy of a priori information (resistivity and thickness) in the data inversion, is based on theory, models and actual data. Theoretical models show that the actual reconstruction of the near water-bottom sediments, in terms of geometry and resistivity, can be obtained only with the submerged cable, however, the data, unlike that acquired with the floating cable, require a priori information on water resistivity and thickness for the data inversion. Theoretical forward models based on wrong a priori water thickness and resistivity information influence the inverted model in different ways, depending on the under- and over-estimation of water resistivity and thickness, and the resistivity contrast of the water–solid layer; however a water–solid resistivity contrast of less than 2 and within 10% of error in water resistivity has no effect. Overestimating water resistivity depicts a ground similar to the actual ground in terms of resistivity, more so than the underestimation of water resistivity. Moreover, the data inversion is less influenced by water parameter error in the case of low resistivity contrast in the water–solid layer, than it is for high resistivity contrast. Wenner and Schlumberger arrays give comparable results, while a dipole–dipole array seems to be more sensitive to the accuracy of apparent resistivity measurements and a priori information on water.The theoretical considerations were validated by actual data acquired with a submerged cable on the Tiber River. The study has shown that if highly accurate measurements are made of water thickness and resistivity, then electrical resistivity imaging from the submerged cable can be used in addition to, or even to substitute, seismic data for the reconstruction of the features and sedimentary characterization of near-bed sediments where seismic data fail to give a suitable resolution.     

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.     

Improvement to resistivity pseudosection modelling by removal of near-surface inhomogeneity effects: application to a soil system in south Cameroon*

Near-surface inhomogeneities (NSIs) can lead to severe problems in the interpretation of apparent resistivity pseudosections because their effects significantly complicate the image aspect. In order to carry out a more efficient and reliable interpretation process, these problematic features should be removed from field data. We describe a filtering scheme using two-sided half-Schlumberger array data. The scheme was tested on synthetic data, generated from a simple 2D resistivity model contaminated by NSIs, and is shown to be suitable for eliminating such contaminations from apparent resistivity data. Furthermore, the original model without NSIs can be recovered satisfactorily from the inversion of filtered apparent resistivity data. The algorithm is also applied efficiently to a real data set collected at Nsimi, in southern Cameroon, along a 200-m shallow depth profile crossing a complex transitional zone. For this case, the filtering scheme provides accurate structural and behavioural interpretations of both the geometry of the major soil constituents and the groundwater partitioning.     

The use of reference models from a priori data to guide 2D inversion of electrical resistivity tomography data

Clay-rich till plains cover much of the UK. Such sites are attractive locations for landfills, since clay aquitards lower the risk of landfill leachate entering groundwater. However, such tills often contain sand and gravel bodies that can act as leachate flow routes. Such bodies may not be detected by conventional site investigation techniques such as drilling boreholes and trial pitting. A method of guided inversion, where a priori data are used to construct structural reference models for use in inverting electrical resistivity tomography data, was proposed as a tool to improve the detection of sand and gravel bodies within clay-rich till sequences.
Following a successful 2D guided inversion synthetic modelling study, a field study was undertaken. Wenner 2D electrical resistivity tomography lines, resistivity cone penetrometry bores and electromagnetic induction ground resistivity data were collected over a site on the East Yorkshire coast, England, where sand and gravel lenses were known to exist from cliff exposures. A number of equally valid geoelectrical models were constructed using the electromagnetic and resistivity cone data. These were used as structural reference models in the inversion of the resistivity tomography data. Blind inversion using an homogenous reference model was also carried out for comparison.
It was shown for the first time that the best solution model produced by 2D inversion of one data set with a range of structural reference models could be determined by using the l ₂ model misfit between the solution models and associated reference models (reference misfit) as a proxy for the l ₂ misfit between the solution models and the synthetic model or 'best-guess' geoelectrical model (true misfit). The 2D methodology developed here is applicable in clay-rich till plains containing sand and gravel bodies throughout the UK.     

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.     

Delineation of a quick clay zone at Smørgrav,Norway, with electromagnetic methods under geotechnical constraints

In many coastal areas of North America and Scandinavia, post-glacial clay sediments have emerged above sea level due to iso-static uplift. These clays are often destabilised by fresh water leaching and transformed to so-called quick clays as at the investigated area at Smørgrav, Norway. Slight mechanical disturbances of these materials may trigger landslides. Since the leaching increases the electrical resistivity of quick clay as compared to normal marine clay, the application of electromagnetic (EM) methods is of particular interest in the study of quick clay structures.For the first time, single and joint inversions of direct-current resistivity (DCR), radiomagnetotelluric (RMT) and controlled-source audiomagnetotelluric (CSAMT) data were applied to delineate a zone of quick clay. The resulting 2-D models of electrical resistivity correlate excellently with previously published data from a ground conductivity metre and resistivity logs from two resistivity cone penetration tests (RCPT) into marine clay and quick clay. The RCPT log into the central part of the quick clay identifies the electrical resistivity of the quick clay structure to lie between 10 and 80 Ω m. In combination with the 2-D inversion models, it becomes possible to delineate the vertical and horizontal extent of the quick clay zone. As compared to the inversions of single data sets, the joint inversion model exhibits sharper resistivity contrasts and its resistivity values are more characteristic of the expected geology. In our preferred joint inversion model, there is a clear demarcation between dry soil, marine clay, quick clay and bedrock, which consists of alum shale and limestone.     

用双侧向测井响应求取地层参数的Newton－SVD反演方法

针对测井中经常遇到的完全非均匀的地层模型，利用深、浅双侧向测井的视电阻率曲线作为约束条件，给出了反演侵入半径ｒ_ｉ、原状地层电阻率Ｒ_ｔ、上（下）围岩电阻率Ｒ_{ｓｕ（Ｒｓｄ）的Ｎｅｗｔｏｎ－ＳＶＤ反演方法．数值模拟表明这一方法是可行的，经实际资料处理．说明该方法实用．}     

Recent developments in the direct-current geoelectrical imaging method

There have been major improvements in instrumentation, field survey design and data inversion techniques for the geoelectrical method over the past 25 years. Multi-electrode and multi-channel systems have made it possible to conduct large 2-D, 3-D and even 4-D surveys efficiently to resolve complex geological structures that were not possible with traditional 1-D surveys. Continued developments in computer technology, as well as fast data inversion techniques and software, have made it possible to carry out the interpretation on commonly available microcomputers. Multi-dimensional geoelectrical surveys are now widely used in environmental, engineering, hydrological and mining applications. 3-D surveys play an increasingly important role in very complex areas where 2-D models suffer from artifacts due to off-line structures. Large areas on land and water can be surveyed rapidly with computerized dynamic towed resistivity acquisition systems. The use of existing metallic wells as long electrodes has improved the detection of targets in areas where they are masked by subsurface infrastructure. A number of PC controlled monitoring systems are also available to measure and detect temporal changes in the subsurface. There have been significant advancements in techniques to automatically generate optimized electrodes array configurations that have better resolution and depth of investigation than traditional arrays. Other areas of active development include the translation of electrical values into geological parameters such as clay and moisture content, new types of sensors, estimation of fluid or ground movement from time-lapse images and joint inversion techniques. In this paper, we investigate the recent developments in geoelectrical imaging and provide a brief look into the future of where the science may be heading.     

DIGITAL LINEAR FILTER FOR COMPUTING TYPE CURVES FOR THE TWO-ELECTRODE SYSTEM OF RESISTIVITY SOUNDING*

In this paper a technique for computing type curves for the two-electrode resistivity soundings is presented. It is shown that the apparent resistivity due to the system can be represented by a convolution integral. Thus, it is possible to apply the principle of digital linear filtering and compute the desired type-curves. The filter function required for the purpose is found to be identical with that used to compute the EM sounding curves for the two coplanar horizontal loop system. It is further shown that from the two-electrode apparent-resistivity expression one can easily derive the apparent resistivities for other configurations. A comparison of depths of investigation for various systems reveals that the two-electrode system has greater depth of investigation than other conventional systems. This is also supported by the field example presented in the end, which illustrates the relative performance of the two-electrode system vis-a-vis the Wenner system.     

2D电阻率正反演成像在水平和垂直模型上的异常响应研究

2D电阻率成像技术近年来被广泛应用于工程、水文、环境和矿产等领域，在实际应用中它具有多种的装置类型，不同的装置类型对特定的地质情况有不同的应用效果.本文通过采用Wenner、Wenner-Schlumberger和dipole-dipole三种排列装置在一个水平和一个垂直模型上正演模拟和块反演，揭示了不同的排列装置在水平结构和垂直结构的异常响应，并对高阻体和低阻体进行了模拟.结果显示当采用Wenner,Wenner-Schlumberger和dipole-dipole数据采集技术时，不同的模型结构异常响应有明显的不同，三种排列类型对地下低阻体的分辨能力均高于高阻体，Wenner装置和dipole-dipole装置分别对水平层状结构和垂直结构有较好的分辨力，wenner-Schlumberger装置对水平层状结构有好的分辨力，对垂直结构有中等的分辨能力.     

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.     

Electrical imaging of lateritic weathering mantles over granitic and metamorphic basement of eastern Senegal, West Africa

The electrical properties of several tens of metres of lateritic weathering mantle were investigated by using electrical resistivity tomography (ERT) in two basement areas of eastern Senegal. The field survey was conducted along two profiles providing continuous coverage. Colour-modulated pseudosections of apparent resistivity vs. pseudo-depth were plotted for all survey lines, giving an approximate image of the subsurface structure. In the area underlain by granitic basement, the pseudosection suggests a very inhomogeneous weathered layer in which the apparent resistivity changes more rapidly than thickness. In the second area, underlain by schists, the lateral changes in electrical properties are less pronounced than those of the granitic area. Interpretation of 2D Wenner resistivity data yielded considerable detail about the regolith, even without pit information. In both areas, the near-surface topsoil comprising undersaturated lateritic material is highly resistive. The intermediate layer with low resistivities (e.g., 20–100 Ωm) contains clays including small quantities of water. The third, highly resistive layer reflects the granitic basement. Comparison of ERT survey results with pit information shows general agreement and suggests that ERT can be used as a fast and efficient exploration tool to map the thick lateritic weathering mantle in tropical basement areas with hard rock geology.     

Laterally constrained inversion of helicopter-borne frequency-domain electromagnetic data

Helicopter-borne frequency-domain electromagnetic (HEM) surveys are used for fast high-resolution, three-dimensional resistivity mapping. Standard interpretation tools are often based on layered earth inversion procedures which, in general, explain the HEM data sufficiently. As a HEM system is moved while measuring, noise on the data is a common problem. Generally, noisy data will be smoothed prior to inversion using appropriate low-pass filters and consequently information may be lost.For the first time the laterally constrained inversion (LCI) technique has been applied to HEM data combined with the automatic generation of dynamic starting models. The latter is important because it takes the penetration depth of the electromagnetic fields, which can heavily vary in survey areas with different geological settings, into account. The LCI technique, which has been applied to diverse airborne and ground geophysical data sets, has proven to be able to improve the HEM inversion results of layered earth structures. Although single-site 1-D inversion is generally faster and — in case of strong lateral resistivity variations — more flexible, LCI produces resistivity — depth sections which are nearly identical to those derived from noise-free data.The LCI results are compared with standard single-site Marquardt–Levenberg inversion procedures on the basis of synthetic data as well as field data. The model chosen for the generation of synthetic data represents a layered earth structure having an inhomogeneous top layer in order to study the influence of shallow resistivity variations on the resolution of deep horizontal conductors in one-dimensional inversion results. The field data example comprises a wide resistivity range in a sedimentary as well as hard-rock environment.If a sufficient resistivity contrast between air and subsurface exists, the LCI technique is also very useful in correcting for incorrect system altitude measurements by using the altitude as a constrained inversion parameter.     

边界元法在地电预报地震中的研究与应用

在以往地电预报地震研究及电法勘探研究中，二维、三维点电源层状横向非均匀介质条件下的数值模拟方法存在着不少困难问题。利用边界单元法可使得该类二、三维问题中难处理的问题变得较为简单易行。本文综合分析叙述了边界元法在这类地电断面结构下的理论研究及其在地电预报地震中的应用情况。探讨了地电学在地震预报研究中的理论及实际应用前景。