Ray-based amplitude tomography for crosshole georadar data: a numerical assessment

Analyses of travel times and amplitudes of crosshole georadar data provide estimates of the electromagnetic velocity and attenuation of the probed media. Whereas inversions of travel times are well established and robust, ray-based inversions of amplitudes depend critically on the complex directive properties of the georadar antennae. We investigate the variations of radiation patterns in the presence of water-filled boreholes and/or changes of electrical material properties in the vicinity of the transmitters or receivers. To assess the implications of such complicating factors for ray-based georadar amplitude tomography, we generate crosshole georadar data for a suite of canonical models using a finite difference time domain (FDTD) solution of Maxwell's equations in cylindrical coordinates. The emitting dipole-type antenna is approximated by an infinitesimal vertical electric dipole, whereas a corresponding receiving antenna is emulated by recording the vertical component of the transmitted electric field. Inversions of the amplitudes of these synthetic data demonstrate that the presence of water-filled boreholes as well as changes in the material properties along the boreholes may cause substantial artifacts in the estimated attenuation structure. Furthermore, our results indicate that ray-based amplitude tomography of crosshole georadar data is unable to constrain absolute values of attenuation. Despite these inherent limitations, the method is surprisingly robust at detecting and constraining relative changes in attenuation. In particular, we find the method to be highly effective for locating conductivity contrasts that are not associated with corresponding changes in dielectric permittivity, and hence, cannot be located by travel time tomography alone.     

A radio magnetotelluric study to evaluate the extents of a limestone quarry in Estonia

Electromagnetic signals from distant radio transmitters in the frequency range 15–250 kHz were measured to model an electrical resistivity structure beneath 7 profiles in the vicinity of the Karinu limestone quarry in Estonia with the aim to map the extent of the economically exploitable limestone. The resistivity models from a 2D inversion of determinant resistivity and phase values using an Occam type of regularization contained reasonably accurate information about the geometry, namely depth to the top and the bottom of the target high‐resistivity limestone. The resistivity models correlated well with existing geological evidences as well as information from closely located boreholes. However, the sharp lithological boundaries seen in the boreholes were not resolved exactly in the resistivity models. This is probably because of the smoothing regularization used in the inversion process. Combined use of borehole data together with resistivity models resulted in two major geological interpretations; a) towards the western part of the existing limestone quarry there is a NNW to NS striking fault, covered by post‐glacial sediments, b) a potential cost‐effective exploitable area containing high quality highly resistive limestone is located south of the existing quarry. This case study shows the applicability of the reasonably fast radio magnetotelluric (RMT) method for the exploration of near‐surface resources.     

Non-linear three-dimensional inversion of cross-well electrical measurements

Cross-well electrical measurement as known in the oil industry is a method for determining the electrical conductivity distribution between boreholes from the electrostatic field measurements in the boreholes. We discuss the reconstruction of the conductivity distribution of a three-dimensional domain. The measured secondary electric potential field is represented in terms of an integral equation for the vector electric field. This integral equation is taken as the starting point to develop a non-linear inversion method, the so-called contrast source inversion (CSI) method. The CSI method considers the inverse scattering problem as an inverse source problem in which the unknown contrast source (the product of the total electric field and the conductivity contrast) in the object domain is reconstructed by minimizing the object and data error using a conjugate-gradient step, after which the conductivity contrast is updated by minimizing only the error in the object. This method has been tested on a number of numerical examples using the synthetic 'measured' data with and without noise. Numerical tests indicate that the inversion method yields a reasonably good reconstruction result, and is fairly insensitive to added random noise.     

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.     

Magnetic resonance sounding applied to aquifer characterization

Magnetic resonance sounding (MRS) is distinguished from other geophysical tools used for ground water investigation by the fact that it measures a magnetic resonance signal generated directly from subsurface water molecules. An alternating current pulse energizes a wire loop on the ground surface and the MRS signal is generated; subsurface water is indicated, with a high degree of reliability, by nonzero amplitude readings. Measurements with varied pulse magnitudes then reveal the depth and thickness of water saturated layers. The hydraulic conductivity of aquifers can also be estimated using boreholes for calibration. MRS can be used for both predicting the yield of water supply wells and for interpolation between boreholes, thereby reducing the number of holes required for hydrogeological modeling. An example of the practical application of MRS combined with two-dimensional electrical imaging, in the Kerbernez and Kerien catchments area of France, demonstrates the efficiency of the technique.     

The application of an indirect electromagnetic geothermometer to temperature extrapolation in depth

We study the feasibility of the application of an indirect EM geothermometer, developed recently, to the temperature extrapolation in depth using magnetotelluric data collected in the seismically active northern Tien Shan faulted area (Bishkek Geodynamic Test Site, Kyrgyzstan) and Hengill geothermal zone (Iceland). The approach used is based on the artificial neural network technique, which does not imply the prior knowledge of the electrical conductivity mechanisms on the one hand and provides temperature estimates based on the analysis of the implicit conductivity-temperature relations, on the other.
The samples for neuronet teaching consisted in the well temperature records and electrical conductivity values determined for the same depths from the magnetotelluric data measured in the vicinities of eight boreholes in each testing area. The testing of the taught neuronets was carried out using the temperature records not involved in the teaching process. The results indicate that the temperature extrapolation accuracy essentially depends on the ratio between the well length and the extrapolation depth. In particular, in extrapolation to a depth twice as large as the well depth the relative error is 5–6% and in case of threefold excess, the error is around 20%. This result makes it possible to increase significantly the depth of indirect temperature estimation in the Earth's interior (in particular, for geothermal exploration) based on the available temperature logs.
The practical application of an indirect electromagnetic geothermometer could provide the following facilities: 1) more exact temperature estimation in the extrapolation mode; 2) remote temperature estimates in the boreholes in areas characterized by extreme conditions for conventional geothermometers.     

Improved Monte Carlo inversion of surface wave data

Inversion of surface wave data suffers from solution non‐uniqueness and is hence strongly biased by the initial model. The Monte Carlo approach can handle this non‐uniqueness by evidencing the local minima but it is inefficient for high dimensionality problems and makes use of subjective criteria, such as misfit thresholds, to interpret the results. If a smart sampling of the model parameter space, which exploits scale properties of the modal curves, is introduced the method becomes more efficient and with respect to traditional global search methods it avoids the subjective use of control parameters that are barely related to the physical problem. The results are interpreted drawing inference by means of a statistical test that selects an ensemble of feasible shear wave velocity models according to data quality and model parameterization. Tests on synthetic data demonstrate that the application of scale properties concentrates the sampling of model parameter space in high probability density zones and makes it poorly sensitive to the initial boundary of the model parameters. Tests on synthetic and field data, where boreholes are available, prove that the statistical test selects final results that are consistent with the true model and which are sensitive to data quality. The implemented strategies make the Monte Carlo inversion efficient for practical applications and able to effectively retrieve subsoil models even in complex and challenging situations such as velocity inversions.     

Geomorphology of the Alluvial Sediments and Bedrock in an Intermontane Basin: Application of Variogram Modeling to Electrical Resistivity Soundings

The study describes a methodology used to integrate legacy resistivity data with limited geological data in order to build three-dimensional models of the near subsurface. Variogram analysis and inversion techniques more typically found in the petroleum industry are applied to a set of 1D resistivity data taken from electrical surveys conducted in the 1980s. Through careful integration with limited geological data collected from boreholes and outcrops, the resultant model can be visualized in three dimensions to depict alluvium layers as lithological and structural units within the bedrock. By tuning the variogram parameters to account for directionality, it is possible to visualize the individual lithofacies and geomorphological features in the subsurface. In this study, an electrical resistivity data set collected as part of a groundwater study in an area of the Peshawar basin in Pakistan has been re-examined. Additional lithological logs from boreholes throughout the area have been combined with local outcrop information to calibrate the data. Tectonic activity during the Himalayan orogeny has caused uplift in the area and generated significant faulting in the bedrock resulting in the formation of depressions which are identified by low resistivity values representing clays. Paleo-streams have reworked these clays which have been eroded and replaced by gravel–sand facies along paleo-channels. It is concluded that the sediments have been deposited as prograding fan-shaped bodies and lacustrine deposits with interlayered gravel–sand and clay–silt facies. The Naranji area aquifer system has thus been formed as a result of local tectonic activity with fluvial erosion and deposition and is characterized by coarse sediments with high electrical resistivities.     

Modelling the stress-strain behaviour of saturated rocks undergoing triaxial deformation using complex electrical conductivity measurements

Measurement of complex electrical conductivity as a function of frequency is an extremely sensitive probe for changes in pore and crack volume, crack connectivity, and crack surface topography. Such measurements have been made as a function of pore fluid chemistry, hydrostatic confining pressure, as well as uniaxial and triaxial deformation. This paper will; (1) describe the effects of triaxial deformation on the complex electrical conductivity of saturated porous rocks, (2) use the electrical data to model the mechanical stress-strain behaviour, and (3) compare the modelled behaviour with the stress-strain behaviour measured during the deformation. Experimental conductivity data tracks how the rock undergoes compaction with progressive loss of crack volume, followed by dilatation due to new crack formation, growth of existing cracks, crack interlinkage, and finally failure, as axial strain is increased. We have used the complex electrical data to produce a direction-sensitive (anisotropic) crack damage parameter, and used it to calculate the effective Young's modulus by employing the models of Walsh and Bruner. Comparison of the synthetic stress-strain curves so produced, with the experimentally derived stress-strain curves shows good agreement, particularly for undrained tests. This modelling is an improvement on similar curves produced using isotropic crack damage parameters derived from acoustic emission data. The improvement is likely to be due to the directional sensitivity of the electrical conductivity measurement, and its ability to discriminate between the formation of isolated cracks, and those cracks that contribute to the inter-connected crack space i.e. those cracks upon which transport properties of the rock such as electrical conductivity, and mechanical properties depend most critically during triaxial deformation.     

带地形的大地电磁各向异性二维模拟及实例对比分析

带地形的大地电磁二维正演数值模拟多数基于电性各向同性理论,由于地球内部电性各向异性现象的普遍存在,基于电性各向异性理论研究地形起伏情况下大地电磁二维正演数值模拟就显得非常迫切.本文首先由麦克斯韦方程出发,引入张量电导率,求得一组关于平行走向的电场分量Ex和磁场分量Hx的二阶偏微分方程,使用有限差分法求解出Ex和Hx的近似解,并以此求得其他场分量;其次,引入地形因素,改变变量在网格节点中的排列方式,选择交错排列方式从而给有限差分系数矩阵的最大带宽分配合理的存储空间;最后,使用Weaver的方法解决TM模式下,在地-空分界面垂直于构造走向的一些区域存在不同电导率的问题.通过对带地形的二维电性各向异性结构做正演模拟,研究地形因素对大地电磁响应的影响;以电性各向异性理论为基础,将地形因素引入对实测大地电磁资料的处理中,通过做二维正演拟合和未引入地形因素的结果做对比,说明电性各向异性现象的普遍存在,认识地形因素对观测大地电磁场的影响,为今后分析解释实测大地电磁资料包含地形因素和电性各向异性情况提供理论基础和技术指导.     

Comparison of formation and fluid-column logs in a heterogeneous basalt aquifer

Deep observation boreholes in the vicinity of active production wells in Honolulu, Hawaii, exhibit the anomalous condition that fluid-column electrical conductivity logs and apparent profiles of pore-water electrical conductivity derived from induction conductivity logs are nearly identical if a formation factor of 12.5 is assumed. This condition is documented in three boreholes where fluid-column logs clearly indicate the presence of strong borehole flow induced by withdrawal from partially penetrating water-supply wells. This result appears to contradict the basic principles of conductivity-log interpretation. Flow conditions in one of these boreholes was investigated in detail by obtaining flow profiles under two water production conditions using the electromagnetic flowmeter. The flow-log interpretation demonstrates that the fluid-column log resembles the induction log because the amount of inflow to the borehole increases systematically upward through the transition zone between deeper salt water and shallower fresh water. This condition allows the properties of the fluid column to approximate the properties of water entering the borehole as soon as the upflow stream encounters that producing zone. Because this condition occurs in all three boreholes investigated, the similarity of induction and fluid-column logs is probably not a coincidence, and may relate to aquifer response under the influence of pumping from production wells.     

Geophysical techniques to aquifer locating and monitoring for industrial zones in North Hanoi, Vietnam

Geophysical methods were applied for hydrogeological targets in many countries including Vietnam. This paper presents results of using complex geophysical techniques as well as 2D electrical resistivity imaging (ERI), vertical electrical sounding (VES), very low frequency (VLF), and seismic refraction for geological structure investigation for locating the aquifers and assessing the hydrogeological conditions for groundwater potential in industrial zones of North Hanoi, Vietnam. The locations of two aquifers are determined by their depth and thickness on the basis of resistivity and seismic velocity values which were proved by stratifications of three boreholes to 40–60 m of depth on the study area. There are connections from surface water to shallow aquifer by hydraulic windows, as follows from VLF data. The deeper aquifer can be considered as a potential groundwater supply, but the water level is descending in time, as shown by hydrological monitoring. However, with careful use and by reducing sources of pollution, groundwater can continue to be an important natural resource for future.     

Characterisation of glacial sediments using geophysical methods for groundwater source protection

A sequence of glacial and alluvial deposits overlying the Cretaceous Chalk in Eastern England was characterised using two geophysical techniques: electrical resistivity imaging and electromagnetic (EM) induction. Extensive geological data were available from trenching and boreholes. Synthetic modelling of the electrical resistivity imaging technique was undertaken to identify its limitations and to optimise survey design. The EM induction method provided a quick and cost-effective reconnaissance technique for identifying large-scale lateral variation in lithology, and for siting resistivity profiles and further boreholes. The resistivity imaging technique provided detailed information on the vertical continuity of permeable units, and was able to identify permeable pathways through the sequence. Certain limitations in detecting thin sand or gravel layers underlying electrically conductive clay were seen in both the synthetic and field data. Nevertheless, the study shows that knowledge of these limitations allows interpretation for the purpose of groundwater vulnerability assessment, given that an appropriate amount of invasive investigation has been conducted.     

Characterisation of glacial sediments using geophysical methods for groundwater source protection

A sequence of glacial and alluvial deposits overlying the Cretaceous Chalk in Eastern England was characterised using two geophysical techniques: electrical resistivity imaging and electromagnetic (EM) induction. Extensive geological data were available from trenching and boreholes. Synthetic modelling of the electrical resistivity imaging technique was undertaken to identify its limitations and to optimise survey design. The EM induction method provided a quick and cost-effective reconnaissance technique for identifying large-scale lateral variation in lithology, and for siting resistivity profiles and further boreholes. The resistivity imaging technique provided detailed information on the vertical continuity of permeable units, and was able to identify permeable pathways through the sequence. Certain limitations in detecting thin sand or gravel layers underlying electrically conductive clay were seen in both the synthetic and field data. Nevertheless, the study shows that knowledge of these limitations allows interpretation for the purpose of groundwater vulnerability assessment, given that an appropriate amount of invasive investigation has been conducted.     

大地电磁测深二维反演方法求解复杂电性结构问题的适应性研究

为探讨二维反演方法在三维电性结构中的适应性问题,本研究中设计了一系列的二维/三维正演模型进行实验计算,分析了三维高阻/低阻异常体对模型响应的畸变作用,并从反演模式选择和数据旋转方向两个方面进行模型二维反演的对比分析,与三维反演的结果进行了比较,最后采用了实测数据进一步进行了二维和三维反演的比较实验.实验和研究结果表明,在剖面选择方面,在剖面方向与垂直主构造方向相差不大的情况下,截取剖面方向,将电性主轴旋转到垂直剖面方向的二维反演结果与垂直主构造方向的反演结果都可以较好地还原正演模型,在大的构造的反映上并无太大差异.在地下为二维或近三维条件时,正演模型的主要结构都可以较好地被二维和三维反演解析出来.二维的反演结果可能甚至会比三维的反演结果的边界更清晰,更精确.然而,对于具有较强的三维结构的模型而言,其二维反演结果与原始模型可能仍然存在较大差异,其中TM+TP或TM模式的二维反演结果相对更接近原始模型,而TE模式的结果往往会有较大误差,需要在解释时特别注意以免得出错误结论.     

大地电磁法三维快速松弛反演

实现大地电磁法快速三维反演的关键在于找到快速计算灵敏度矩阵的方案. 本文在对大地电磁三维张量阻抗表达式进行深入分析的基础上，获得了三维快速松弛反演算法的灵敏度函数表达式，解决了三维快速松弛反演的核心问题；为了减小反演解的多解性，针对三维问题定义了最小构造函数，实现了求最小构造的三维快速松弛反演算法. 对二维棱柱体、三维棱柱体理论模型的大地电磁合成数据进行了反演试算，反演结果与理论模型相吻合. 对日本Kayabe地区实测资料进行了XY模式反演，反演得到的地电模型较好地反映了地热资源的分布. 反演试算结果表明大地电磁三维快速松弛反演具有计算速度快、结果稳定可靠等特点；使三维快速松弛反演在普通微机上得以实现.     

Simple Electrical Logging Technique for Base Metal Exploration

—It is well known that electrical logs of boreholes can play a signi|fi|cant role in base metal exploration in identifying mineralised zones, especially when there is core loss or the borehole diameter is small or if drilling is by percussion. However, electrical logging is not widely utilised because of the additional burden on finances and time.¶A simple electrical logging technique, based on a pole-pole (hole-to-surface) configuration with one borehole electrode and nearly akin to the single point method, for S.P., resistivity and I.P. parameters, is presented. It is shown that it has the resolution of the single point method and the penetration of a very long normal sonde which is helpful for detection. Besides these features, the main advantage of this technique is that it can be easily carried out using ground I.P. (time domain) equipment.¶The electrical logs obtained in different base metal belts in Rajasthan, India, employing this technique and using ground I.P. equipment in connection with mise-à-la-masse surveys, illustrate the above features. A comparison with logs recorded by means of multi-electrode drill hole I.P. equipment of Scintrex, Canada, substantiates the same.     

Image processing of 2D resistivity data for imaging faults

A methodology to locate automatically limits or boundaries between different geological bodies in 2D electrical tomography is proposed, using a crest line extraction process in gradient images. This method is applied on several synthetic models and on field data set acquired on three experimental sites during the European project PALEOSIS where trenches were dug. The results presented in this work are valid for electrical tomographies data collected with a Wenner-alpha array and computed with an l₁ norm (blocky inversion) as optimization method. For the synthetic cases, three geometric contexts are modelled: a vertical and a dipping fault juxtaposing two different geological formations and a step-like structure. A superficial layer can cover each geological structure. In these three situations, the method locates the synthetic faults and layer boundaries, and determines fault displacement but with several limitations. The estimated fault positions correlate exactly with the synthetic ones if a conductive (or no superficial) layer overlies the studied structure. When a resistive layer with a thickness of 6 m covers the model, faults are positioned with a maximum error of 1 m. Moreover, when a resistive and/or a thick top layer is present, the resolution significantly decreases for the fault displacement estimation (error up to 150%). The tests with the synthetic models for surveys using the Wenner-alpha array indicate that the proposed methodology is best suited to vertical and horizontal contacts. Application of the methodology to real data sets shows that a lateral resistivity contrast of 1:5–1:10 leads to exact faults location. A fault contact with a resistivity contrast of 1:0.75 and overlaid by a resistive layer with a thickness of 1 m gives an error location ranging from 1 to 3 m. Moreover, no result is obtained for a contact with very low contrasts (1:0.85) overlaid by a resistive soil. The method shows poor results when vertical gradients are greater than horizontal ones. This kind of image processing technique should be systematically used for improving the objectiveness of tomography interpretation when looking for limits between geological objects.     

Predicting horizontal velocities from well data

The Imperial College borehole test site consists of four boreholes with depths lying between 260 and 280 m. The boreholes intersect several cyclical sequences of sandstones, mudstones and limestones. The formations are highly laminated and ultrasonic measurements on preserved core have shown that the mudstones are intrinsically anisotropic. Little or no anisotropy is associated with the sandstones and limestones. A scheme is proposed to predict synthetic vertical and horizontal P- and S-wave logs. Combining (an)isotropic effective medium theories, the Gassmann equation and Backus averaging, the scheme extends previous sand-shale models to transversely isotropic rock formations. The model assumes that the anisotropy is due to layering and due to the preferred horizontal orientation of the clay minerals, pores and cracks within the mudstones. The pores and cracks within the sandstones and limestones are randomly orientated. After fitting the model to the ultrasonic data to obtain the unknown parameters, the model successfully predicts the sonic log and the direct arrival times from a cross-hole survey.     

A Bayesian trans-dimensional approach for the fusion of multiple geophysical datasets

We propose a Bayesian fusion approach to integrate multiple geophysical datasets with different coverage and sensitivity. The fusion strategy is based on the capability of various geophysical methods to provide enough resolution to identify either subsurface material parameters or subsurface structure, or both. We focus on electrical resistivity as the target material parameter and electrical resistivity tomography (ERT), electromagnetic induction (EMI), and ground penetrating radar (GPR) as the set of geophysical methods. However, extending the approach to different sets of geophysical parameters and methods is straightforward. Different geophysical datasets are entered into a trans-dimensional Markov chain Monte Carlo (McMC) search-based joint inversion algorithm. The trans-dimensional property of the McMC algorithm allows dynamic parameterisation of the model space, which in turn helps to avoid bias of the post-inversion results towards a particular model. Given that we are attempting to develop an approach that has practical potential, we discretize the subsurface into an array of one-dimensional earth-models. Accordingly, the ERT data that are collected by using two-dimensional acquisition geometry are re-casted to a set of equivalent vertical electric soundings. Different data are inverted either individually or jointly to estimate one-dimensional subsurface models at discrete locations. We use Shannon's information measure to quantify the information obtained from the inversion of different combinations of geophysical datasets. Information from multiple methods is brought together via introducing joint likelihood function and/or constraining the prior information. A Bayesian maximum entropy approach is used for spatial fusion of spatially dispersed estimated one-dimensional models and mapping of the target parameter. We illustrate the approach with a synthetic dataset and then apply it to a field dataset. We show that the proposed fusion strategy is successful not only in enhancing the subsurface information but also as a survey design tool to identify the appropriate combination of the geophysical tools and show whether application of an individual method for further investigation of a specific site is beneficial.