Rapid inversion of data from 2D resistivity surveys with electrode displacements

Resistivity monitoring surveys are used to detect temporal changes in the subsurface using repeated measurements over the same site. The positions of the electrodes are typically measured at the start of the survey program and possibly at occasional later times. In areas with unstable ground, such as landslide‐prone slopes, the positions of the electrodes can be displaced by ground movements. If this occurs at times when the positions of the electrodes are not directly measured, they have to be estimated. This can be done by interpolation or, as in recent developments, from the resistivity data using new inverse methods. The smoothness‐constrained least squares optimisation method can be modified to include the electrode positions as additional unknown parameters. The Jacobian matrices with the sensitivity of the apparent resistivity measurements to changes in the electrode positions are then required by the optimisation method. In this paper, a fast adjoint‐equation method is used to calculate the Jacobian matrices required by the least squares method to reduce the calculation time. In areas with large near‐surface resistivity contrasts, the inversion routine sometimes cannot accurately distinguish between electrode displacements and subsurface resistivity variations. To overcome this problem, the model for the initial time‐lapse dataset (with accurately known electrode positions) is used as the starting model for the inversion of the later‐time dataset. This greatly improves the accuracy of the estimated electrode positions compared to the use of a homogeneous half‐space starting model. In areas where the movement of the electrodes is expected to occur in a fixed direction, the method of transformations can be used to include this information as an additional constraint in the optimisation routine.     

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.     

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.     

用有限差分法计算各向异性介质中多分量感应测井的响应

感应测井电阻率是砂泥岩储层中定量评价含油气性的主要参数之一,然而由于储层电各向异性的存在,传统的感应测井仪得到的电阻率主要响应地层的水平电阻率,比地层的垂直电阻率小,由此计算的含水饱和度偏高．多分量感应测井则可以通过不同方向的发射和接收,测量多个分量,弥补上述缺陷,为储层的含油气性评价提供准确信息．本文用交错网格有限差分法导出了主轴各向异性介质中Maxwell方程的离散化关系式,计算了三维各向异性介质中多分量感应测井的电磁响应．利用三层模型的数值模拟,分析了不同磁场分量对各向异性介质的响应特性,用多层模型和倾斜各向异性地层的响应计算检验了所编制的交错网格有限差分法程序．     

CARACTERES DE ĽONDE ELECTROMAGNETIQUE DE SURFACE ENGENDREE PAR UN DIPOLE MAGNETIQUE *

The electromagnetic field radiated from a magnetic dipole lying on the ground is considered, in the extremely low frequency range (DC to 20 000 Hertz). Theoretical and experimental data are given on the characteristics of the surface wave (vanishing wave) generated at the air-ground interface, in the case of an homogeneous subsurface. The case of a subsurface with electrical resistivity varying with depth is considered. It is shown how the above-mentioned characteristics may be applied in the quantitative investigation of the electrical resistivity of the subsurface as a function of depth, in a method using the measurements on the ground of all the components of the radiated field: horizontal electrical components, vertical and horizontal magnetic components.     

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.     

3-D Magnetotelluric Exploration of Tenerife Geothermal System (Canary Islands,Spain)

The resistivity structure of the Tenerife geothermal system has been determined by the 3-D inversion of data from different magnetotelluric surveys. In this paper, the ocean and topography effects on the magnetotelluric data were investigated by constructing a 3-D conceptual geoelectrical model of the island. The study showed that these effects should be taken into account in order to obtain a reliable subsurface model of the island. Data from 148 sites were used during three-dimensional inversion. The most interesting feature in the final geoelectrical model of the geothermal system is a low resistivity structure (<10 Ωm) above the resistive core of the system. The low resistivity structure has been interpreted as a hydrothermal clay alteration cap typically generated in the conventional geothermal systems. The resistivity model has been correlated with a recent seismic velocity model, showing that a low resistivity structure surrounds an area with high P wave velocity and medium–high resistivity. This medium–high resistivity area can be associated with a slowly solidified magma and, therefore, with a hotter part of the geothermal system.     

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.     

Stream bottom resistivity tomography to map ground water discharge

This study investigates the effectiveness of direct current electrical resistivity as a tool for assessing ground water/surface water interactions within streams. This research has shown that patterns of ground water discharge can be mapped at the meter scale, which is important for understanding stream water quality and ecosystem function. Underwater electrical resistivity surveys along a 107-m stream section within the Burd Run Watershed in South Central Pennsylvania identified three resistivity layers: a resistive (100 to 400 Ωm) surface layer corresponding to the streambed sediments, a conductive (20 to 100 Ωm) middle layer corresponding to residual clay sediments, and a resistive (100 to 450 Ωm) bottom layer corresponding to the carbonate bedrock. Tile probing to determine the depth to the bedrock and resistivity test box analysis of augered sediment samples confirmed these interpretations of the resistivity data. Ground water seeps occurred where the resistivity data showed that the residual clays were thinnest and bedrock was closest to the streambed. Plotting the difference in resistivity between two surveys, one conducted during low-stage and the other during high-stage stream conditions, showed changes in the conductivity of the pore fluids saturating the sediments. Under high-stream stage conditions, the top layer showed increased resistivity values for sections with surface water infiltration but showed nearly constant resistivity in sections with ground water seeps. This was expressed as difference values less than 50 Ωm in the area of the seeps and greater than 50 Ωm change for the streambed sediments saturated by surface water. Thus, electrical resistivity aided in characterizing ground water discharge zones by detecting variations in subsurface resistivity under high- and low-stream stage conditions as well as mapping subsurface heterogeneities that promote these exchanges.     

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.     

Gaussian character of the distribution of magnetotelluric results working in log-space

The distribution of individual values of the apparent resistivities given by two M-T soundings made over two different kinds of subsurface geology is described and computed. This distribution is Gaussian only if the logarithm of the resistivity values are used. Consequently, a statistical stability is obtained when the mean and standard deviation are calculated in log-space. Log-space is a mathematical space that may have one or more logarithmical dimensions; in this case two.     

Integrated geophysical and chemical study of saline water intrusion

Surface geophysical surveys provide an effective way to image the subsurface and the ground water zone without a large number of observation wells. DC resistivity sounding generally identifies the subsurface formations-the aquifer zone as well as the formations saturated with saline/brackish water. However, the method has serious ambiguities in distinguishing the geological formations of similar resistivities such as saline sand and saline clay, or water quality such as fresh or saline, in a low resistivity formation. In order to minimize the ambiguity and ascertain the efficacy of data integration techniques in ground water and saline contamination studies, a combined geophysical survey and periodic chemical analysis of ground water were carried out employing DC resistivity profiling, resistivity sounding, and shallow seismic refraction methods. By constraining resistivity interpretation with inputs from seismic refraction and chemical analysis, the data integration study proved to be a powerful method for identification of the subsurface formations, ground water zones, the subsurface saline/brackish water zones, and the probable mode and cause of saline water intrusion in an inland aquifer. A case study presented here illustrates these principles. Resistivity sounding alone had earlier failed to identify the different formations in the saline environment. Data integration and resistivity interpretation constrained by water quality analysis led to a new concept of minimum resistivity for ground water-bearing zones, which is the optimum value of resistivity of a subsurface formation in an area below which ground water contained in it is saline/brackish and unsuitable for drinking.     

Magnetotelluric sounding results in eastern Tibetan Plateau

The results of Zayü-Qingshuihe MT sounding profile carried out in eastern Tibetan Plateau are presented in this paper. Using 2-D RRI method, the resistivity distribution with depth is obtained along the profile. It is featured by the resistivity zones in the horizontal direction and layers in the vertical direction. The Bangong-Nujiang suture zone and Jinshajiang suture zone are both important electrical conductivity-separating zones in the plateau, and the former is a zone with relatively low resistivity while the latter is an electrical conductivity gradient zone. The highly electrical conductive bodies in the mid and lower crust of northern Qiangtang and Bayan Har Terrain might be caused by regional melting due to shear heating during the process of subduction in tectonic evolution.     

Subsurface DC resistivity mapping: approximate 1-D interpretation

Resistivity prospecting is the main tool used to investigate the shallow structure of the ground. A series of new techniques for determining the 2-D and 3-D geometry of the ground is now finding increasing use, but the light and simple Wenner prospecting technique remains a practical and efficient tool for rapidly mapping lateral variations in resistivity. When the resistivity changes are smooth, 1-D modelling can be used to interpret the data, and the criteria governing this approximation can be defined from synthetic data generated by a 3-D slab-model. For a Wenner array, two quadripole configurations can be used, Normal and Dipole-Dipole. For these two configurations the width of the transition zone, the apparent anisotropy effect and the precision of the resistivity values recovered from 1-D inversion differ. However the simultaneous inversion of both sets of data gives better results than for either configuration by itself. Two examples illustrate that in geological contexts where the thickness of the weathered zone causes the changes in the apparent resistivity value, this parameter can be recovered from 1-D inversion.     

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.     

Determining the origin of volcanic rocks in the mélange complex of Karangsambung based on the electrical resistivity imaging

An ENE-WSW-trending localized basalt-diabase outcrop along the SE margin of Luk Ulo Mélange Complex has been suggested as intrusive rocks cut through the Paleogene Totogan and Karangsambung formations. However, the absolute dating of the volcanics is older than the inferred relative age of the sedimentary formations, hence the in-situ intrusion theory is less likely. A subsurface imaging should delineate the possibility of the in-situ nature of volcanic rock by looking at the continuation of the rocks to the depth. In this study, we did a subsurface imaging by electrical resistivity method. The electrical resistivity surveys were conducted at 3 (three) lines across the ENE-WSW trend of the volcanic distribution. From those three measurements, we obtained three inversion models that present the distribution of the resistivity. We could differentiate between the high resistivity of volcanic rocks and the low resistivity of the clay-dominated sediments. Instead of the deep-rooted intrusions, the geometry of the volcanic rocks is concordant with the sedimentary strata. Since we do not observe any spatial continuity of the bodies, both laterally and vertically, the volcanic rocks might be part of broken intrusive rocks. Furthermore, the size and the sporadically distributed of the rocks also indicated that they are more likely as fragments during the olistostrome deposition, transported from its original location.     

The use of multi-electrode resistivity imaging in gravel prospecting

We investigated the potential of using a 24-electrode resistivity imaging apparatus for rapid reconnaissance surveys for natural-aggregate accumulation. The surveys were first calibrated at sites with known geometry of sand and gravel layers, which showed that subsurface accumulation of coarse material was accurately resolved with both 2- and 4-m electrode spacing. The inverted absolute resistivity of economically viable gravel deposits varied in the range of 300–1500 Ω m, depending on variation in ground-moisture levels. The exploration surveys were then conducted at seven sites where geomorphological analyses indicated a potential for gravel. Four of these sites, where subsurface resistivity did not exceed 30–40 Ω m, were found to have very little or no coarse material. The three remaining sites showed significant accumulations of high-resistivity material, two of which were subsequently augered for verification. The results of drilling demonstrated that resistivity images were an effective indicator of the presence of coarse material in the subsurface, allowing accurate determination of subsurface distribution and thickness of sand and gravel strata. The total volume of a deposit could easily be estimated from resistivity images. The absolute quality and economic value of the material, is, however, difficult to ascertain from resistivity images alone without drilling.     

Airborne VLF measurements and mapping of ground conductivity in Sweden

Airborne VLF data are routinely collected by The Geological Survey of Sweden (SGU) as part of its bedrock mapping programme. In this paper we demonstrate that the novel Tensor VLF technique developed at Uppsala University and SGU can provide useful qualitative and quantitative information about the electrical conductivity distribution in the upper few hundred meters. Single transmitter scalar VLF maps emphasize those conductive structures that have dominant strikes in the direction of the transmitter. The tensor tipper (essentially the vertical magnetic field from currents along the strike direction) calculated from multiple transmitters is dependent only upon the underlying conductivity structure. Transformation of the tipper into the peaker (the horizontal divergence) has proven to enhance the lateral resolution while the transformation to the apparent resistivity can be used to discriminate different rock types. Two case histories from the application of VLF data are presented in this study. Two dimensional structures can be quantitatively modelled by modern inversion methods developed originally for deep electromagnetic MT soundings. Direct inversion of the real and imaginary parts of the tipper provides more quantitative information about the subsurface resistivity distribution.     

垂直线电流源的三维电阻率成像

在油井注水和深井注浆的电法监测中,地表布设平面的电位测量网,而将钻井的钢套管作为线电流源来供电,据此可确定流体的运动方向和分布特征.数据处理中需解决垂直线电流源的三维电阻率反演.本文叙述了相应的反演理论和偏导数计算方法.在某油田的试验中,以生产井为电极圈的中心,每圈均匀布设18个电极,共6圈,在地表得到了108个电位数据,获得500～2 000m之间5个不同深度层的真电阻率分布图像,并对深度层为1 500～1 600m的图像进行了初步解释.结果表明,该方法可以对井下某深度层中的流体运动和分布可进行有效的监测.     

Evaluating ground water-sea water interactions via resistivity and seepage meters

We investigated submarine ground water discharge and salt water-fresh water interactions at two locations along the shoreline of the Upper Gulf of Thailand to evaluate mechanisms of water and material transport into the coastal zone. Our data set illustrates the value of using a combined approach consisting of automatic seepage meters to monitor flow rates while assessing the conductivity (salinity) of the subterranean fluids via remote resistivity measurements. Negative correlations between electric conductivities of fluids measured directly inside seepage meter chambers and the remotely assessed resistivities of subsurface pore water show that such measurements may evaluate the spatial distribution of flow rates as well as the subterranean water quality in the coastal zone. Combined seepage and resistivity measurements may thus provide a more complete understanding of coastal ground water dynamics.