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.     

3D inversion of DC data using artificial neural networks

In this paper, we investigate the applicability of artificial neural networks in inverting three-dimensional DC resistivity imaging data. The model used to produce synthetic data for training the artificial neural network (ANN) system was a homogeneous medium of resistivity 100 Ωm with an embedded anomalous body of resistivity 1000 Ωm. The different sizes for anomalous body were selected and their location was changed to different positions within the homogeneous model mesh elements. The 3D data set was generated using a finite element forward modeling code through standard 3D modeling software. We investigated different learning paradigms in the training process of the neural network. Resilient propagation was more efficient than any other paradigm. We studied the effect of the data type used on neural network inversion and found that the use of location and the apparent resistivity of data points as the input and corresponding true resistivity as the output of networks produces satisfactory results. We also investigated the effect of the training data pool volume on the inversion properties. We created several synthetic data sets to study the interpolation and extrapolation properties of the ANN. The range of 100–1000 Ωm was divided into six resistivity values as the background resistivity and different resistivity values were also used for the anomalous body. Results from numerous neural network tests indicate that the neural network possesses sufficient interpolation and extrapolation abilities with the selected volume of training data. The trained network was also applied on a real field dataset, collected by a pole-pole array using a square grid (8 ×8) with a 2-m electrode spacing. The inversion results demonstrate that the trained network was able to invert three-dimensional electrical resistivity imaging data. The interpreted results of neural network also agree with the known information about the investigation area.     

Field test to compare 3D imaging capabilities of three arrays in a site with high resistivity contrast regions

The applicability of three kinds of electrode configurations used to delineate a buried horizontal pipe was studied. A 3D resistivity imaging survey was carried out along eight parallel lines using pole-pole, pole-dipole, and dipole-dipole arrays with 1m minimum electrode spacings. Roll-along measurements were carried out to cover a rectangular grid. The 2D and 3D least squares algorithms based on the robust inversion method were used in the inversion of the apparent resistivity data sets. The 2D inversion of data sets could not delineate the orientation and dimension of the subsurface anomalies clearly. To obtain more accurate results, a 3D joint inversion of the pole-pole and pole-dipole data sets was performed, as well as of pole-pole and dipole-dipole data sets. In this case, both horizontal and vertical dimensions of subsurface structures were resolved. The resulting model obtained from each array was compared to those of joint inversion method. The result showed that the horizontal resolution does not improve so much as that in the vertical direction when joint inversion is applied.     

Practical techniques for 3D resistivity surveys and data inversion1

Techniques to reduce the time needed to carry out 3D resistivity surveys with a moderate number (25 to 100) of electrodes and the computing time required to interpret the data have been developed. The electrodes in a 3D survey are normally arranged in a square grid and the pole-pole array is used to make the potential measurements. The number of measurements required can be reduced to about one-third of the maximum possible number without seriously degrading the resolution of the resulting inversion model by making measurements along the horizontal, vertical and 45° diagonal rows of electrodes passing through the current electrode. The smoothness-constrained least-squares inversion method is used for the data interpretation. The computing time required by this technique can be greatly reduced by using a homogeneous half-space as the starting model so that the Jacobian matrix of partial derivatives can be calculated analytically. A quasi-Newton updating method is then used to estimate the partial derivatives for subsequent iterations. This inversion technique has been tested on synthetic and field data where a satisfactory model is obtained using a modest amount of computer time. On an 80486DX2/66 microcomputer, it takes about 20 minutes to invert the data from a 7 by 7 electrode survey grid. using the techniques described below, 3D resistivity surveys and data inversion can be carried out using commercially available field equipment and an inexpensive microcomputer.     

基于非结构网格的电阻率三维带地形反演

地表起伏地形在野外矿产资源勘察中不可避免,其对直流电阻率法勘探影响巨大.近年来,电阻率三维正演取得诸多进展,特别是应用非结构网格我们能够进行任意复杂地形和几何模型的电阻率三维数值模拟,但面向实际应用的起伏地形下电阻率三维反演依然困难.本文基于非结构化四面体网格,并考虑到应用GPS/GNSS时,区域地球物理调查中可非规则布设测网的实际特点,实现了任意地形(平坦或起伏)条件下、任意布设的偶极-偶极视电阻率数据的不完全Gauss-Newton三维反演.合成数据的反演结果表明了方法的有效性,可应用于复杂野外环境下的三维电法勘探.     

On the 3-D inversion of vertical electrical soundings: Application to the South Ismailia area—Cairo desert road, Cairo, Egypt

A code for 3-D resistivity modelling and inversion of vertical electrical soundings has been developed based on the finite-element technique and regularisation method. Synthetic data were used to test the effectiveness of the code and to examine the resolving capability of the Schlumberger array in investigating 3-D resistivity distributions. The code was applied to experimental data set constituted by 35 Schlumberger soundings collected near the Cairo city in order to study the subsurface resistivity distribution. The results have shown that valuable imaging of the subsurface resistivity distribution can be constructed even when the vertical electrical soundings are acquired in a sparse field data set.     

3D electrical resistivity inversion using prior spatial shape constraints

To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical data regarding the extent of a geological anomaly are important prior information. We propose the use of shape constraints in 3D electrical resistivity inversion, Three weighted orthogonal vectors （a normal and two tangent vectors） were used to control the resistivity differences at the boundaries of the anomaly. The spatial shape of the anomaly and the constraints on the boundaries of the anomaly are thus established. We incorporated the spatial shape constraints in the objective function of the 3D resistivity inversion and constructed the 3D resistivity inversion equation with spatial shape constraints. Subsequently, we used numerical modeling based on prior spatial shape data to constrain the direction vectors and weights of the 3D resistivity inversion. We established a reasonable range between the direction vectors and weights, and verified the feasibility and effectiveness of using spatial shape prior constraints in reducing excessive structures and the number of solutions. We applied the prior spatially shape-constrained inversion method to locate the aquifer at the Guangzhou subway. The spatial shape constraints were taken from ground penetrating radar data. The inversion results for the location and shape of the aquifer agree well with drilling data, and the number of inversion solutions is significantly reduced.     

Deep resistivity structure of the Dikili-Bergama region, west Anatolia, revealed by two- dimensional inversion of vertical electrical sounding data

Within the framework of the National Marine Geological and Geophysical Program, we re‐examined deep vertical electrical sounding (VES) data. The data, measured in 1968 by the General Directorate of Mineral Research and Exploration (MTA) of Turkey with the aim of exploring the deep resistivity structure of the Dikili–Bergama region, focus on the geothermal potential. The geoelectrical resistivity survey was conducted using a Schlumberger array with a maximum electrode half‐spacing of 4.5 km. The two‐dimensional (2D) inversion was utilized to interpret the VES data that were collected along 15‐ to 30‐km profiles. The 2D resistivity–depth cross‐sections obtained show very low resistivity values near the Dikili and Kaynarca hot springs. The 2D inversion results also indicate the presence of fault zones striking nearly N–S and E–W, and fault‐bounded graben‐horst structures that show promising potential for geothermal field resources. The 2D gravity model, which is in good agreement with the density variation of the region, supports the resistivity structure revealed by 2D inversion. The lithology information obtained from the borehole near Kaynarca also confirms the results of the resistivity interpretation and the density model.     

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.     

Three-dimensional forward modeling and inversion of borehole-to-surface electrical imaging with different power sources

Borehole-to-surface electrical imaging (BSEI) uses a line source and a point source to generate a stable electric field in the ground. In order to study the surface potential of anomalies, three-dimensional forward modeling of point and line sources was conducted by using the finite-difference method and the incomplete Cholesky conjugate gradient (ICCG) method. Then, the damping least square method was used in the 3D inversion of the formation resistivity data. Several geological models were considered in the forward modeling and inversion. The forward modeling results suggest that the potentials generated by the two sources have different surface signatures. The inversion data suggest that the low-resistivity anomaly is outlined better than the high-resistivity anomaly. Moreover, when the point source is under the anomaly, the resistivity anomaly boundaries are better outlined than when using a line source.     

Focused imaging of electrical resistivity data in archaeological prospecting

Electrical resistivity mapping and electrical resistivity profiling are powerful instruments for investigating archaeological structures. Interpretation of geoelectrical data is complicated by near-surface anomalies and the characteristics of the applied electrode arrays. Averaging Wenner α and Wenner β data as an alternative method of focused imaging is presented to overcome these problems. The mechanism of focused imaging is explained using the sensitivity distribution of the combined arrays. Various methods of imaging geoelectrical data are examined with synthetic and field data. In electrical resistivity mapping, inversion of the data is unnecessary when using focused imaging. In electrical resistivity profiling, focused imaging gives a first idea about the subsurface resistivity distribution without achieving the quality obtainable by inversion.     

Experimental study of ERT monitoring ability to measure solute dispersion

This paper reports experimental measurements performed to test the ability of electrical resistivity tomography (ERT) imaging to provide quantitative information about transport parameters in porous media such as the dispersivity α, the mixing front velocity u, and the retardation factor R(f) associated with the sorption or trapping of the tracers in the pore structure. The flow experiments are performed in a homogeneous porous column placed between two vertical set of electrodes. Ionic and dyed tracers are injected from the bottom of the porous media over its full width. Under such condition, the mixing front is homogeneous in the transverse direction and shows an S-shape variation in the flow direction. The transport parameters are inferred from the variation of the concentration curves and are compared with data obtained from video analysis of the dyed tracer front. The variations of the transport parameters obtained from an inversion performed by the Gauss-Newton method applied on smoothness-constrained least-squares are studied in detail. While u and R(f) show a relatively small dependence on the inversion procedure, α is strongly dependent on the choice of the inversion parameters. Comparison with the video observations allows for the optimization of the parameters; these parameters are found to be robust with respect to changes in the flow condition and conductivity contrast.     

Resistivity inversion of cross-hole and borehole-to-surface EM data using axially symmetric models1

We describe a least-squares inversion approach to estimating the subsurface resistivity structure from cross-hole or borehole-to-surface electromagnetic data. It is assumed that the resistivity distribution is symmetric about the axis of a borehole and that vertical magnetic dipoles are located on the borehole axis. The receivers are placed either in another borehole or on the earth's surface. The inversion scheme uses the finite-element and smoothness-constrained least-squares methods. The computational effort required to obtain partial derivatives is reduced considerably by using the reciprocity principle. Numerical simulations show that the reconstructions are generally in good agreement with the true structures when the assumption of an axisymmetric earth structure holds. An example involving the breakdown of this assumption, which can be obtained by interchanging the source and receiver boreholes, suggests that the inversion result may also be useful for locating a general 3D anomaly although artifacts are present.     

Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method1

A fast inversion technique for the interpretation of data from resistivity tomography surveys has been developed for operation on a microcomputer. This technique is based on the smoothness-constrained least-squares method and it produces a two-dimensional subsurface model from the apparent resistivity pseudosection. In the first iteration, a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. For subsequent iterations, a quasi-Newton method is used to estimate the partial derivatives which reduces the computer time and memory space required by about eight and twelve times, respectively, compared to the conventional least-squares method. Tests with a variety of computer models and data from field surveys show that this technique is insensitive to random noise and converges rapidly. This technique takes about one minute to invert a single data set on an 80486DX microcomputer.     

Inversion of DC resistivity data using neural networks

The inversion of geoelectrical resistivity data is a difficult task due to its non-linear nature. In this work, the neural network (NN) approach is studied to solve both 1D and 2D resistivity inverse problems. The efficiency of a widespread, supervised training network, the back-propagation technique and its applicability to the resistivity problem, is investigated. Several NN paradigms have been tried on a basis of trial-and-error for two types of data set. In the 1D problem, the batch back-propagation paradigm was efficient while another paradigm, called resilient propagation, was used in the 2D problem. The network was trained with synthetic examples and tested on another set of synthetic data as well as on the field data. The neural network gave a result highly correlated with that of conventional serial algorithms. It proved to be a fast, accurate and objective method for depth and resistivity estimation of both 1D and 2D DC resistivity data. The main advantage of using NN for resistivity inversion is that once the network has been trained it can perform the inversion of any vertical electrical sounding data set very rapidly.     

APPLYING 3D INVERSION OF SINGLE-PROFILE MAGNETOTELLURIC DATA TO IDENTIFY THE SHADE AND YUNONGXI FAULTS

Many synthetic model studies suggested that the best way to obtain good 3D interpretation results is to distribute the MT sites at a 2D grid array with regular site spacing over the target area. However, MT 3D inversion was very difficult about 10 years ago. A lot of MT data were collected along one profile and then interpreted with 2D inversion. How to apply the state-of-the-art 3D inversion technique to interpret the accumulated mass MT profiles data is an important topic. Some studies on 3D inversion of measured MT profile data suggested that 2D inversions usually had higher resolution for the subsurface than 3D inversions. Meanwhile, they often made their interpretation based on 2D inversion results, and 3D inversion results were only used to evaluate whether the overall resistivity structures were correct. Some researchers thought that 3D inversions could not resolute the local structure well, while 2D inversion results could agree with the surface geologic features much well and interpret the geologic structures easily. But in the present paper, we find that the result of 3D inversion is better than that of 2D inversion in identifying the location of the two local faults, the Shade Fault(SDF)and the Yunongxi Fault(YNXF), and the deep structures. In this paper, we first studied the electrical structure of SDF and YNXF based on a measured magnetotelluric(MT) profile data. Besides, from the point of identifying active faults, we compared the capacity of identifying deep existing faults between 2D inversion models and 3D models with different inversion parameters. The results show that both 2D and 3D inversion of the single-profile data could obtain reasonable and reliable electrical structures on a regional scale. Combining 2D and 3D models, and according to our present data, we find that both SDF and YNXF probably have cut completely the high resistivity layer in the upper crust and extended to the high conductivity layer in the middle crust. In terms of the deep geometry of the faults, at the profile's location, the SDF dips nearly vertically or dips southeast with high dip angle, and the YNXF dips southeast at depth. In addition, according to the results from our measured MT profile, we find that the 3D inversion of single-profile MT data has the capacity of identifying the location and deep geometry of local faults under present computing ability. Finally, this research suggests that appropriate cell size and reasonable smoothing parameters are important factors for the 3D inversion of single-profile MT data, more specifically, too coarse meshes or too large smoothing parameters on horizontal direction of 3D inversion may result in low resolution of 3D inversions that cannot identify the structure of faults. While, for vertical mesh size and data error thresholds, they have limited effect on identifying shallow tectonics as long as their changes are within a reasonable range. 3D inversion results also indicate that, to some extent, adding tippers to the 3D inversion of a MT profile can improve the model's constraint on the deep geometry of the outcropped faults.     

基于不等式约束的最小二乘法三维电阻率反演及其算法优化

基于光滑约束的最小二乘法是三维电阻率反演的主要方法,但该方法在某些情况下存在着多解性较强的问题,且普遍耗时较长,严重制约了三维反演方法的推广与发展.为改善上述问题,将表征模型参数变化范围的不等式约束作为先验信息引入最小二乘线性反演方法中,有效地改善了反演结果的精度,降低了反演的多解性问题.为了解决耗时较长的问题,基于预条件共轭梯度(PCG)算法和Cholesky分解法的特点提出了一套优化三维电阻率反演计算效率的计算方案.在该方案中,Cholesky分解法被用来求解敏感度矩阵计算中的多个点源场的正演问题,Cholesky分解法只需对总体系数矩阵进行一次分解,然后对不同的右端向量进行回代即可.将预条件共轭梯度法引入到三维电阻率反演方程的求解中,将雅可比迭代中的对角阵作为预处理矩阵,其具有求逆方便、无需内存空间的特点,有效地加快了收敛速度.对合成数据以及实测数据的反演算例表明,借助不等式约束和反演效率优化方案,最小二乘反演方法可得到较为精确的反演结果,有效地提高了反演计算效率,具有良好的推广前景.     

大斜度井和水平井井地三维电阻率数值模拟和联合反演

井地电阻率成像法利用井套管作电流源向井下供入大功率直流电流,在地表测量由地下介质的电性变化形成的电位分布,通过反演可得到地下介质的电阻率分布.针对大斜度井和水平井开展井地三维电阻率数值模拟和反演研究,对油田注水及压裂效果监测具有重要意义.基于井地电阻率成像法原理,采用有限差分法和不完全切勒斯基共轭梯度法进行了三维正演模拟,研究了大斜度井和水平井的井地电位响应特征.提出了采用层状约束阻尼最小二乘法由浅到深地进行大斜度井和水平井的多层联合反演,并对实际水平井井地电位各个层段数据进行了三维反演.模拟结果表明,倾斜线源和水平线源会对地面电位响应产生明显影响,在反演中需要考虑线源形态.实际水平井井地电位反演成像表明,考虑倾斜线源或者水平线源的联合反演得到了准确的水平井三维注水层成像图,得出注水层的真电阻率分布,能够判断注水运移方向.     

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.     

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.