THEORETICAL ANALYSIS OF APPARENT RESISTIVITY OVER A DYKE OF ARBITRARY SHAPE*

This paper deals with the apparent resistivity as observed on the surface due to a dyke of arbitrary shape. In order to give a closed analytical solution it has been necessary to assume that the dyke is either perfectly conductive or resistive relative to the enclosing medium. Furthermore we have considered an infinite line source instead of a conventional point current source; however a simple integral transform is given to transform the point-source-data into the line-source-data. So the present study is equally useful where line sources are inconvenient to handle. Besides considering the conventional method of electrical surveying (bipole method) where the source and sink are separated by a finite distance, we have considered a new variation (unipole method) where the source and sink are separated by an infinite distance, and the source is split into two separate sources each of half strength. A series of apparent resistivity curves for both methods are presented for different parameters of the dyke. The usefulness of these curves lies mainly in the fact that they may provide the necessary guide-lines for semi-quantitative interpretation of the observed data.     

A fracture study by using bipole–bipole cross-well logging

Electrical Resistivity Tomography (ERT) can provide images of subsurface electrical structure between two boreholes. Data quality control is a key issue before ERT inversion. However, there is no effective data quality control method on an ERT survey. In this paper, a method called common current gather for a bipole–bipole array (CCGbb) was proposed to check ERT data quality in a rapid way. Synthetic models were conducted to compare the response difference between pole–pole array and bipole–bipole array. A field work at granite area was tested to verify the applicability of the proposed CCGbb method. From the results of this study, we suggested that conducting CCGbb before ERT inversion and a cross-borehole tracer test for both field data quality control and possible water conducting fractures (WCFs) delineation.     

Quantitative interpretation of self potential anomalies of some specific geometric bodies

Summary Some direct and quantitative methods of SP anomalies caused by some specific geometric bodies have been developed in this paper. The models of current sources which have been considered are i) single pole, ii) a doublet, iii) a pair of single point poles separated by a horizontal distance, iv) single finite line pole, v) single infinite line pole and vi) two similar double infinite vertical line poles separated by a horizontal distance.     

电阻率层析成像和激电测深对栾川铅锌矿的联合勘探

在栾川铅锌矿的物探工作中，采用了电阻率层析成像和激电测深两种方法，电阻率层析成像法采用温纳装置或偶极装置，电极数量和极距视情况而定，主要调查工作区内隐伏构造情况，激电测深采用对称四极测深法，最小AB／2距为3M，最大AB／2距为500M，主要研究激电测深参数的变化规律，对于含矿构造而言，激电参数呈异常高值反映，视极化率在15－40％，两种方法的联合应用，具有快速而准确的特点，在探矿工作中取得了良好的效果。     

Interpretation of self-potential anomalies of some simple geometric bodies

Summary An entirely new procedure for interpreting selfpotential anomalies of spheres, rods and dipping sheets is presented. The anomaly of a sphere is divided into two parts — the anomaly of odd symmetry and the anomaly of even symmetry — from which the depth can be obtained by fitting them with the master curves. The self-potential anomalies of a finite rod are transformed to the anomalies of a veritcal sheet, for which standard curves are presented. The case of a sheet was divided into three parts; (a) finite line of poles; (b) infinite double line of poles and (c) finite double line of poles. For the first case logarithmic curves were prepared and presented; by their comparison with the field profile, different parameters can be obtained. In the second case, a geometrical construction is provided to obtain the various values. In the third case, the anomalies of finite sheet (finite double line of poles) are transformed into those due to an infinite double line of poles for interpretation.     

3D modelling and sensitivity in DC resistivity using charge density

A three‐dimensional (3D) electrical resistivity modelling code is developed to interpret surface and subsurface data. Based on the integral equation, it calculates the charge density caused by conductivity gradients at each interface of the mesh, allowing the estimation of the potential everywhere without the need to interpolate between nodes. Modelling generates a huge matrix, made up of Green's functions, which is stored by using the method of pyramidal compression. The potential is compared with the analytical and the numerical solutions obtained by finite‐difference codes for two models: the two‐layer case and the vertical contact case. The integral method is more accurate around the source point and at the limits of the domain for the potential calculation using a pole‐pole array. A technique is proposed to calculate the sensitivity (Jacobian) and Hessian matrices in 3D. The sensitivity is based on the derivative with respect to the block conductivity of the potential computed using the integral equation; it is only necessary to compute the electrical field at the source location. A direct extension of this technique allows the determination of the second derivatives. The technique is compared with the analytical solutions and with the calculation of the sensitivity according to the method using the inner product of the current densities calculated at the source and receiver points. Results are very accurate when the Green's function that includes the source image is used. The calculation of the three components of the electric field on the interfaces of the mesh is carried out simultaneously and quickly, using matrix compression.     

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.     

Internal waves and temperature fronts on slopes

Time series measurements from an array of temperature miniloggers in a line at constant depth along the sloping boundary of a lake are used to describe the ‘internal surf zone” where internal waves interact with the sloping boundary. More small positive temperature time derivatives are recorded than negative, but there are more large negative values than positive, giving the overall distribution of temperature time derivatives a small negative skewness. This is consistent with the internal wave dynamics; fronts form during the up-slope phase of the motion, bringing cold water up the slope, and the return flow may become unstable, leading to small advecting billows and weak warm fronts. The data are analysed to detect ‘events’, periods in which the temperature derivatives exceed a set threshold. The speed and distance travelled by ‘events’ are described. The motion along the slope may be a consequence of (a) instabilities advected by the flow (b) internal waves propagating along-slope or (c) internal waves approaching the slope from oblique directions. The propagation of several of the observed ‘events’ can only be explained by (c), evidence that the internal surf zone has some, but possibly not all, the characteristics of the conventional ‘surface wave’ surf zone, with waves steepening as they approach the slope at oblique angles.     

Geotectonic bipolarity, evidence from the pattern of active oceanic ridges bordering the Pacific and African plates

Active oceanic ridges are part of the global system of diverging plate boundaries encircling the Earth. They represent weak zones of the lithosphere. They are isostatically equilibrated. The system as a whole is considered to be well adapted to the present field of plate driving forces. The search for regularities in the pattern of active oceanic ridges may, therefore, provide valuable information as to the large-scale characteristics of structures and processes in the Earth’s mantle. Two large belts of active oceanic ridges are envisaged: (1) The semi-circular belt bordering the Pacific plate which extends from South of Tasmania to Northwest of Vancouver Island over a length of 20,000 km. It appears to encircle a center P1 in the central Pacific region. (2) The circum-African belt bordering the African plate which extends from the Azores to the Gulf of Aden over a length of 24,000 km. It appears to encircle a center A1 in central Africa. The attempt is made to determine the position of these centers. Extent and position of the ridge systems are described by 34 fixed points. Points R01–R20 mark the circum-African ridge system, points R21-R34 the Pacific ridge system. A least-squares adjustment is used to determine the optimum position of the centers P1 and A1. Center P1 of the Pacific ridge system is located at 169.8°W/2.6°S. Center A1 of the circum-African ridge system is located at 11.6°E/2.4°N. The location error of the centers is less than 2.8°. In view of the great extent of the ridge systems, and considering the fact that the location of P1 and A1 is based on independent data sets, the nearly antipodal and equatorial position of the centers is remarkable. The newly defined centers P1 and A1 are located close to the Pacific pole P, at 170°W/0°N, and the African pole A, at 10°E/0°N. Within the limits of error the center P1 coincides with pole P, the center A1 with pole A. Originally, these poles were introduced in order to describe a fundamental hemispherical symmetry which is apparent in the evolution of the Earth’s lithosphere during the last 180 Ma. The new results confirm the unique position of poles P and A in the global tectonic framework.     

Temperature profiles in the earth of importance to deep electrical conductivity models

Deep in the Earth, the electrical conductivity of geological material is extremely dependent on temperature. The knowledge of temperature is thus essential for any interpretation of magnetotelluric data in projecting lithospheric structural models. The measured values of the terrestrial heat flow, radiogenic heat production and thermal conductivity of rocks allow the extrapolation of surface observations to a greater depth and the calculation of the temperature field within the lithosphere. Various methods of deep temperature calculations are presented and discussed. Characteristic geotherms are proposed for major tectonic provinces of Europe and it is shown that the existing temperatures on the crust-upper mantle boundary may vary in a broad interval of 350–1,000°C. The present work is completed with a survey of the temperature dependence of electrical conductivity for selected crustal and upper mantle rocks within the interval 200–1,000°C. It is shown how the knowledge of the temperature field can be used in the evaluation of the deep electrical conductivity pattern by converting the conductivity-versustemperature data into the conductivity-versus-depth data.     

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.     

Measurement of shallow shear wave velocities at a rock site using the ReMi technique

Shallow shear wave velocities beneath a rock site are characterized using the refraction microtremor (ReMi) technique developed by Louie [Faster, better: shear-wave velocity to 100 m depth from ReMi arrays. Bull Seism Soc Am 2001; 91: 347–64]. Ground motion from a passing train enabled capture of energy propagating parallel to the recording array. This allowed evaluation of the variation of the minimum phase-velocity of the dispersion curve envelope and better estimation of the true minimum velocity beneath the site. We use a new method to image and evaluate the dispersion curve envelope via power–slowness profiles through the slowness–frequency plots introduced by Louie [Faster, better: shear-wave velocity to 100 m depth from ReMi arrays. Bull Seism Soc Am 2001; 91: 347–64]. Data illustrated the frequency dependency of dispersion curve uncertainties, with greater uncertainty occurring at low frequencies. These uncertainties map directly into uncertainty of the inverted velocity–depth profile. Above 100 m depth velocities are well constrained with 10% variability. Variability is greatly reduced when the energy propagation is along the geophone array. Greater velocity variation is observed below 100 m depth.     

3-D Non-linear Travel-time Tomography: Imaging High Contrast Velocity Anomalies

In this paper we present an approach for 3-D travel-time tomography, which works well in reconstructing high contrast velocity anomalies in both location and strength. It uses a revised ‘irregular’ approach to the shortest-path method as the ray tracer and a damped minimum norm, and constrained least-squares CG approach as the inversion solver. In ray tracing, the advantages of the revised ‘irregular’ over the ‘regular’ approach are that the secondary nodes introduced on the cell surfaces significantly improve accuracy of computed travel times, without dramatically increasing the total number of cells and nodes; the tri-linear velocity function defined across the cell guarantees accurate ray tracing in a high velocity contrast medium; and the capacity to calculate a relatively large 3-D model, due to the fast run speed (at least one order of magnitude over the ‘regular’ approach) and less number of total nodes. The introduction of ‘soft’ and ‘hard’ bounds into the inversion process changes the conditioning and makes the solution meaningful in a physical sense. Thus the artifacts caused by noise and high velocity contrasts are substantially suppressed and the image quality is considerably improved, making the solution realistic with noisy or inconsistent travel-time data. Several numerical tests indicate that we can obtain good quality images even for high velocity contrast anomalies (say more than 20%) in the target region. This means the inversion algorithm is an efficient and effective procedure. Meanwhile, the inversion procedure is not very sensitive to the quality of the travel-time data, which is promising for practical usage.     

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.     

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.     

Determination of depths to centroids of three-dimensional sources of potential-field anomalies with examples from environmental and geologic applications

A method is developed for determining the depth to the centroid (the geometric center) of ‘semi-compact' sources. The method, called the anomaly attenuation rate (AAR) method, involves computing radial averages of AARs with increasing distances from a range of assumed source centers. For well-isolated magnetic anomalies from ‘semi-compact' sources, the theoretical AARs range from 2 (close to the sources) to 3 (in the far-field region); the corresponding theoretical range of AARs for gravity anomalies is 1 to 2. When the estimated source centroid is incorrect, the AARs either exceed or fall short of the theoretical values. The levelling-off of the far-field AARs near their theoretical maximum values indicates the upper (deeper) bound of the centroid location. Similarly, near-field AARs lower than the theoretical minimum indicate the lower (shallower) bound of the centroid location. It is not always possible to determine usable upper and lower bounds of the centroids because the method depends on characteristics of sources/anomalies and the noise level of the data. For the environmental magnetic examples considered in this study, the determined deeper bounds were within 4% of the true centroid-to-observation distance. For the case of the gravity anomaly from the Bloomfield Pluton, Missouri, USA, determination of only the shallower bound of the centroid location (7 km) was possible. This estimate agrees closely with the centroid of a previously determined three-dimensional model of the Bloomfield Pluton. For satellite magnetic anomalies, the method is appropriate only for high-amplitude, near-circular anomalies due to the inherent low signal-to-noise ratio of satellite magnetic anomalies. Model studies indicate that the AAR method is able to place depths within ±20–30 km of actual center locations from a 400-km observation altitude. Thus, the method may be able to discriminate between upper crustal, lower crustal, and mantle magnetic sources. The results from the prominent Kentucky anomaly are relatively well-resolved (centroid depth 30 km below the Earth's surface). For the Kiruna Magsat anomaly, the deleterious effects from neighboring anomalies make a determination difficult (possible depth could be between 20 and 30 km). The centroid depths are deeper for the Kursk anomaly (40–50 km). These depths may indicate that magnetic anomalies from the near-surface Kursk iron formations (a known contributor) and deep crustal magnetic sources could combine to form the Kursk Magsat anomaly.     

2.5D direct‐current resistivity forward modelling and inversion by finite‐element–infinite‐element coupled method

To reduce the numerical errors arising from the improper enforcement of the artificial boundary conditions on the distant surface that encloses the underground part of the subsurface, we present a finite‐element–infinite‐element coupled method to significantly reduce the computation time and memory cost in the 2.5D direct‐current resistivity inversion. We first present the boundary value problem of the secondary potential. Then, a new type of infinite element is analysed and applied to replace the conventionally used mixed boundary condition on the distant boundary. In the internal domain, a standard finite‐element method is used to derive the final system of linear equations. With a novel shape function for infinite elements at the subsurface boundary, the final system matrix is sparse, symmetric, and independent of source electrodes. Through lower upper decomposition, the multi‐pole potentials can be swiftly obtained by simple back‐substitutions. We embed the newly developed forward solution to the inversion procedure. To compute the sensitivity matrix, we adopt the efficient adjoint equation approach to further reduce the computation cost. Finally, several synthetic examples are tested to show the efficiency of inversion.     

Polar ionic conductivity profile in fair weather conditions. Terrestrial test of the Huygens/Hasi-PWA instrument aboard the Comas Sola balloon

The permittivity wave and altimetry (PWA) instrument is a part of the CASSINI/HUYGENS HASI experiment and was designed to determine the electrical parameters of the atmosphere of Titan in 2004. In December 1995, a balloon campaign was conducted in León, Spain, to test the HASI onboard hardware and software using a HUYGENS probe mock-up in an electromagnetic-disturbance-free environment (mainly from power emission lines at 50 Hz). This work is concerned with the measurements of small ion polar conductivities and DC fields using the PWA relaxation probes (RP). The two RP electrodes were periodically set to ±5 V relative to the conductive surface of the mock-up and allowed to discharge in the surrounding atmosphere. The polar components of conductivity are calculated from the discharge time, and the DC field from the floating potential differences once the electrodes reach equilibrium. In spite of some observed effects, such as mock-up charging or oscillations in the measurement of potential, the conductivity measurements are coherent and in good agreement with the obtained results in other experiments. The conductivity data were collected in ‘fair-weather’ conditions, up to 30 km during a 4-h flight, every 72 s, giving an altitude resolution better than 400 m. We also discuss the DC field data that do not lead, in presence of charging effects, to a straightforward measurement of the natural DC field. The Comas Solá balloon flight, first real test of the PWA experiment in the terrestrial atmosphere, confirmed the validity of the ionic conductivity measurements but raised the problem of a reliable interpretation of the DC field.     

Out‐of‐plane effects in 2D borehole‐to‐surface resistivity tomography and applications in mineral exploration

In this paper, we discuss the effects of anomalous out‐of‐plane bodies in two‐dimensional (2D) borehole‐to‐surface electrical resistivity tomography with numerical resistivity modelling and synthetic inversion tests. The results of the two groups of synthetic resistivity model tests illustrate that anomalous bodies out of the plane of interest have an effect on two‐dimensional inversion and that the degree of influence of out‐of‐plane body on inverted images varies. The different influences are derived from two cases. One case is different resistivity models with the same electrode array, and the other case is the same resistivity model with different electrode arrays. Qualitative interpretation based on the inversion tests shows that we cannot find a reasonable electrode array to determine the best inverse solution and reveal the subsurface resistivity distribution for all types of geoelectrical models. Because of the three‐dimensional effect arising from neighbouring anomalous bodies, the qualitative interpretation of inverted images from the two‐dimensional inversion of electrical resistivity tomography data without prior information can be misleading. Two‐dimensional inversion with drilling data can decrease the three‐dimensional effect. We employed two‐ and three‐dimensional borehole‐to‐surface electrical resistivity tomography methods with a pole–pole array and a bipole–bipole array for mineral exploration at Abag Banner and Hexigten Banner in Inner Mongolia, China. Different inverse schemes were carried out for different cases. The subsurface resistivity distribution obtained from the two‐dimensional inversion of the field electrical resistivity tomography data with sufficient prior information, such as drilling data and other non‐electrical data, can better describe the actual geological situation. When there is not enough prior information to carry out constrained two‐dimensional inversion, the three‐dimensional electrical resistivity tomography survey is the better choice.     

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.