Electric field data in inductive source electromagnetic surveys

Measurement of the electric field data due to an inductive loop source in a controlled source electromagnetic survey is not common, because electric field data, usually involving grounded electrodes, are expensive to acquire and difficult to interpret. With the recently developed capability of versatile three‐dimensional inversion, we revisit the idea of measuring electric field in a large ground loop survey for mineral exploration. The three‐dimensional modelling and inversion approach helps us quantitatively understand the detectability and recoverability of the proposed survey configuration. Our detectability study using forward modelling shows that the relative anomaly (percentage difference) in electric field does not decay with a lower induction number, but the conventional magnetic field data (dB/dt) does. Our recoverability study examines how much and what kind of information can be extracted from electric field data for the reconstruction of a three‐dimensional model. Synthetic inversions show the following observations. (i) Electric field data are good at locating lateral discontinuity, whereas dB/dt has better depth resolution. (ii) Electric field is less sensitive to the background conductivity and, thus, is prone to misinterpretation because of a bad initial model in inversion. We recommend warm‐starting the electric field inversion with an initial model from a separate dB/dt inversion. (iii) Electric field data may be severely contaminated by near‐surface heterogeneity, but an inversion can recover the deep target concealed by the geologic noise. (iv) Even one line of single‐component electric field data can greatly improve the horizontal resolution in a dB/dt inversion. Finally, we investigate a field dataset of both electric field and dB/dt measurements at a uranium deposit. The field example confirms that the electric field and magnetic field data contain independent information that is crucial in the accurate recovery of subsurface conductivity. Our synthetic and field examples demonstrate the benefit of acquiring electric field data along with magnetic field data in an inductive source survey.     

Estimating magnetic dike parameters using a non‐linear constrained inversion technique: an example from the Särna area,west central Sweden

In this paper, we describe a non‐linear constrained inversion technique for 2D interpretation of high resolution magnetic field data along flight lines using a simple dike model. We first estimate the strike direction of a quasi 2D structure based on the eigenvector corresponding to the minimum eigenvalue of the pseudogravity gradient tensor derived from gridded, low‐pass filtered magnetic field anomalies, assuming that the magnetization direction is known. Then the measured magnetic field can be transformed into the strike coordinate system and all magnetic dike parameters – horizontal position, depth to the top, dip angle, width and susceptibility contrast – can be estimated by non‐linear least squares inversion of the high resolution magnetic field data along the flight lines. We use the Levenberg‐Marquardt algorithm together with the trust‐region‐reflective method enabling users to define inequality constraints on model parameters such that the estimated parameters are always in a trust region. Assuming that the maximum of the calculated g_zz (vertical gradient of the pseudogravity field) is approximately located above the causative body, data points enclosed by a window, along the profile, centred at the maximum of g_zz are used in the inversion scheme for estimating the dike parameters. The size of the window is increased until it exceeds a predefined limit. Then the solution corresponding to the minimum data fit error is chosen as the most reliable one. Using synthetic data we study the effect of random noise and interfering sources on the estimated models and we apply our method to a new aeromagnetic data set from the Särna area, west central Sweden including constraints from laboratory measurements on rock samples from the area.     

地电观测中电磁干扰源定位方法研究

本文提出了一种地表偶极源干扰影响模型和动态枚举定位求解方法.该方法基于均匀电流场和点源电流场模型,由地表偶极源对不同测点的影响幅度和测点位置求解偶极源位置,并给出了仿真计算结果.利用该方法结合高邮地震台人工干扰源试验观测数据进行计算,计算结果将干扰源定位于30 m范围内的小区域, 较好地验证了本文模型和定位求解方法的正确性.该研究可为地电观测台站周边工农业漏电干扰源的定位和查找提供有效参考.      

Analogue model measurements for a horizontal magnetic dipole embedded within a conducting medium

The validity of an analogue model method employing a horizontal magnetic dipole source situated within a conducting layer for the cases of a poorly conducting model earth and a highly conducting model ocean is studied by comparing model magnetic field measurements with theoretical calculations. The model is then used to study one example for each case; the response of a conducting cylinder simulating an ore body embedded in the earth, and the response of a conducting wedge simulating a shelving ocean.     

Monitoring subsurface changes over time with cross-well electromagnetic tomographyt1

A fast imaging technique is developed to deduce the spatial conductivity distribution in the earth from low-frequency (> 1 MHz) cross-well electromagnetic measurements. A sinusoidally oscillating, vertically orientated, magnetic dipole employed as a source, and it is assumed that the scattering bodies are azimuthally symmetric about the source dipole axis. The use of this model geometry reduces the 3D vector problem to a more manageable 2D scalar form. Additional efficiency is obtained by using the Born series approximation which is derived from nonlinear integral equations that account for the scattered magnetic fields generated by inhomogeneities embedded in a layered earth. Stabilization of the inversion problem is accomplished through the use of bounding constraints and a regularization method which results in a smooth model that fits the data to the desired noise level. The applicability of cross-well electromagnetics for imaging and monitoring changes caused by subsurface processes has been tested by simulating plumes of conductive fluid with 2D models. The images that result from inverting these synthetic data indicate that the vertical resolution of the method is better than the horizontal, increasing the noise decreases the image resolution, and incorporating a priori knowledge in the form of positivity constraints improves the results. Although higher operating frequencies are usually associated with better resolution, frequencies as low as 100 Hz can produce acceptable images in simulated oilfield environments. The imaging scheme has been applied to data collected during a salt-water injection experiment at the Richmond Field Station test site in Richmond, California. Both the data and the resulting images clearly reveal the presence of the plume and indicate that it is migrating towards the north-northwest rather than spreading symmetrically about the injection well. Applying the imaging code to synthetic data generated by a 3D sheet model verifies the interpretation of these results.     

Numerical modelling of resolution and sensitivity of ERT in horizontal boreholes

Resistivity in horizontal boreholes can give useful detailed information about the geological conditions for construction in rock, i.e. in front of a tunnel bore machine. This paper is an attempt to identify a suitable methodology for an effective measuring routine for this type of geophysical measurements under actual construction site conditions.Prior to any measurements numerical modelling was done in order to evaluate the resolution of different electrode arrays. Four different arrays were tested; dipole–pole, cross-hole dipole–dipole, cross-hole pole–tripole and multiple gradient array. Additionally the resolution of a combination of cross-hole dipole–dipole and multiple gradient was assessed. The 2D sensitivity patterns for various arrangements of the cross-hole dipole–dipole and multiple gradient array were examined. The sensitivity towards inaccurate borehole geometry and the influence of water in the boreholes were also investigated. Based on the model study the cross-hole dipole–dipole array, multiple gradient array and a combination of these were found to give the best result and therefore were used for test measurements in horizontal boreholes. The boreholes were 28.5 m long and drilled 6.5 m apart. Prototypes of semi-rigid borehole cables made it possible to insert multi electrode cables in an efficient way, allowing fast measurement routines. These measurements were then studied to determine their accuracy and applicability. The results showed a high resistivity rock mass at the site. A transition from high resistivity to slightly lower resistivity coincides well with a change in lithology from gneiss-granite to gneiss. It is likely that the shotcrete on the tunnel wall is seen as a low resistivity zone.The measurements are a valuable tool, but further development of the cables and streamlining of measuring routines have to be performed before the resistivity tomography can be used routinely in pilot holes during construction in rocks.     

海底表面磁源瞬变响应建模及海水影响分析

根据电磁场理论,推导了磁偶源和接收点均位于海水中时层状海底模型的频域电磁场响应一般表达式,并通过此式,得到了海水为均匀半空间和有限海水深度两种情况下,垂直磁偶极装置、中心回线和重叠回线分别置于均匀半空间海底表面时的瞬变电磁响应（磁场和感应电压）表达式. 这些表达式将瞬变响应和海底的电导率等参数有机联系在一起,为海底瞬变电磁法的正演计算和反演解释提供了理论基础. 仿真计算表明,海水的存在不仅使得瞬变响应曲线形态发生变化,而且影响其对海底电导率的分辨能力.     

Analysis of source location errors for a magnetic dipole buried in a laterally inhomogeneous conducting earth

Summary A numerical model is used to simulate a vertical magnetic dipole (VMD), with time harmonic excitation, buried under a segmented overburden. Results are presented in terms of readily measured field quantities. Of special interest are the ellipticities of the magnetic field in the vertical and horizontal planes. These turn out to be very sensitive to the lateral variation of the conductivity structure. Other parameters, such as the vertical magnetic field on the surface, are much less influenced. It is suggested that the combination of such measurements should lead to an optimum system for source location in application to mine rescue operations.     

磁偶极子梯度张量的几何不变量及其应用

磁梯度张量系统姿态的变化将影响梯度场测量和数据解释的精度,使得具有坐标变换不变性特点的张量不变量成为磁梯度张量数据解释的研究热点.本文在对磁偶极子产生的磁梯度张量进行特征值分析的基础上得到了:测量点与磁偶极子位置形成的位置矢量、磁偶极子磁矩矢量与绝对值最小的特征值对应的特征向量垂直;位置矢量和磁矩矢量与最大及最小特征值对应的特征向量共面,且两矢量间的夹角可由磁梯度张量矩阵的特征值表示.最后,将本文所得磁偶极子梯度张量的几何不变量用于磁性目标的跟踪中,取得了较好的实时跟踪效果.     

Detecting small-scale targets by the 2D inversion of two-sided three-electrode data: application to an archaeological survey

The detecting capabilities of some electrical arrays for the estimation of position, size and depth of small-scale targets were examined in view of the results obtained from 2D inversions of apparent-resistivity data. The two-sided three-electrode apparent-resistivity data are obtained by the application of left- and right-hand pole–dipole arrays that also permit the computation of four-electrode and dipole–dipole apparent-resistivity values without actually measuring them. Synthetic apparent-resistivity data sets of the dipole–dipole, four-electrode and two-sided three-electrode arrays are calculated for models that simulate buried tombs. The results of two-dimensional inversions are compared with regard to the resolution in detecting the exact location, size and depth of the target, showing some advantage for the two-sided three-electrode array. A field application was carried out in the archaeological site known as Alaca Hoyuk, a religious temple area of the Hittite period. The two-dimensional inversion of the two-sided three-electrode apparent-resistivity data has led to locating a part of the city wall and a buried small room. The validity of the interpretation has been checked against the results of subsequent archaeological excavations.     

瞬变电磁快速成像解释系统研究

为了提高瞬变电磁测深法对地探测的垂向分辨能力,文中研究了磁偶源瞬变电磁法快速成像的方法.详细讨论了电磁波与地震波在介质中的传播规律,分析了磁偶源瞬变电磁场在远区的响应特性.根据磁偶源瞬变电磁场与反射地震波的传播规律的相似性,提出了TEM资料拟地震快速成像解释的思路.理论模型正、反演计算结果表明方法理论是可行的,野外实测资料处理结果进一步说明了该方法是有效的.     

磁总场异常垂直梯度三维相关成像

本文提出了磁总场异常垂直梯度三维相关成像方法,用于成像地下等效磁源分布.它首先将地下待成像空间划分为三维规则网格,然后直接计算每个网格节点磁偶板子在观测面理论磁总场异常垂直梯度与实测磁总场异常垂直梯度的互相关,其相关系数值表征等效磁偶极子分布(即磁偶极子发生的概率).理论长方体组合模型数据和实际某矿区磁测资料试验结果表明本文方法计算得到的相关系数值能基本反映地下的磁源分布,且分辨率明显高于磁总场异常三维相关成像的分辨率,也高于基于熵滤波分离异常的磁总场异常三维相关成像的分辨率.     

Data assimilation for distributed hydrological catchment modeling via ensemble Kalman filter

Catchment scale hydrological models are critical decision support tools for water resources management and environment remediation. However, the reliability of hydrological models is inevitably affected by limited measurements and imperfect models. Data assimilation techniques combine complementary information from measurements and models to enhance the model reliability and reduce predictive uncertainties. As a sequential data assimilation technique, the ensemble Kalman filter (EnKF) has been extensively studied in the earth sciences for assimilating in-situ measurements and remote sensing data. Although the EnKF has been demonstrated in land surface data assimilations, there are no systematic studies to investigate its performance in distributed modeling with high dimensional states and parameters. In this paper, we present an assessment on the EnKF with state augmentation for combined state-parameter estimation on the basis of a physical-based hydrological model, Soil and Water Assessment Tool (SWAT). Through synthetic simulation experiments, the capability of the EnKF is demonstrated by assimilating the runoff and other measurements, and its sensitivities are analyzed with respect to the error specification, the initial realization and the ensemble size. It is found that the EnKF provides an efficient approach for obtaining a set of acceptable model parameters and satisfactory runoff, soil water content and evapotranspiration estimations. The EnKF performance could be improved after augmenting with other complementary data, such as soil water content and evapotranspiration from remote sensing retrieval. Sensitivity studies demonstrate the importance of consistent error specification and the potential with small ensemble size in the data assimilation system.     

Comparison of the time-domain electromagnetic field from an infinitesimal point charge and dipole source

An electromagnetic field is generated through the accelerating movement of two equal but opposite charges of a single dipole. An electromagnetic field can also be generated by a time-varying infinitesimal point charge. In this study, a comparison between the electromagnetic fields of an infinitesimal point charge and a dipole has been presented. First, the time-domain potential function of a point source in a 3D conductive medium is derived. Then the electric and magnetic fields in a 3D homogeneous lossless space are derived via the relation between the potential and field. The field differences between the infinitesimal point charge and the dipole in the step-off time, far-source, and near-source zones are analyzed, and the accuracy of the solutions from these sources is investigated. It is also shown that the field of the infinitesimal point charge in the near-source zone is different from that of the dipole, whereas the far-source zone fields of these two sources are identical. The comparison of real and simulated data shows that the infinitesimal point charge represents the real source better than the dipole source.     

Evolutionary computation-based approach for model error correction and calibration

Calibration is typically used for improving the predictability of mechanistic simulation models by adjusting a set of model parameters and fitting model predictions to observations. Calibration does not, however, account for or correct potential misspecifications in the model structure, limiting the accuracy of modeled predictions. This paper presents a new approach that addresses both parameter error and model structural error to improve the predictive capabilities of a model. The new approach simultaneously conducts a numeric search for model parameter estimation and a symbolic (regression) search to determine a function to correct misspecifications in model equations. It is based on an evolutionary computation approach that integrates genetic algorithm and genetic programming operators. While this new approach is designed generically and can be applied to a broad array of mechanistic models, it is demonstrated for an illustrative case study involving water quality modeling and prediction. Results based on extensive testing and evaluation, show that the new procedure performs consistently well in fitting a set of training data as well as predicting a set of validation data, and outperforms a calibration procedure and an empirical model fitting procedure.     

二维激电中梯数据磁类比拟合反演研究

本文通过柯尔-柯尔模型研究地下不同几何参数的极化椭球体在地表的中梯双频激电响应,从而了解不同产状极化体产生极化率的特征,便于后期交互建模。由理论推导可知,任何具有激发极化特征的地质体在地表产生的激电异常都可近似为一个地下电偶极子的三维空间积分,这个积分形式与磁场正演计算公式一致,这意味着我们可以用解释磁法异常的方法解释激电异常,即磁类比法。只要根据先验信息实时改变模型,使激电正演得到的曲线与实测激电曲线逼近,当拟合差小于均方误差时,我们将最后一次模型近似看作是真实模型,由此获得地下极化体的顶埋深、倾角和几何大小等空间参数。实测数据测试表明,这种磁类比人机交互方法加入矿体的一些已知信息后,其拟合反演结果比自动反演更具合理性。      

Multi‐method virtual electromagnetic experiments for developing suitable monitoring designs: A fictitious CO2 sequestration scenario in Northern Germany

We present a numerical study for 3D time‐lapse electromagnetic monitoring of a fictitious CO₂ sequestration using the geometry of a real geological site and a suite of suitable electromagnetic methods with different source/receiver configurations and different sensitivity patterns. All available geological information is processed and directly implemented into the computational domain, which is discretized by unstructured tetrahedral grids. We thus demonstrate the performance capability of our numerical simulation techniques. The scenario considers a CO₂ injection in approximately 1100 m depth. The expected changes in conductivity were inferred from preceding laboratory measurements. A resistive anomaly is caused within the conductive brines of the undisturbed reservoir horizon. The resistive nature of the anomaly is enhanced by the CO₂ dissolution regime, which prevails in the high‐salinity environment. Due to the physicochemical properties of CO₂, the affected portion of the subsurface is laterally widespread but very thin. We combine controlled‐source electromagnetics, borehole transient electromagnetics, and the direct‐current resistivity method to perform a virtual experiment with the aim of scrutinizing a set of source/receiver configurations with respect to coverage, resolution, and detectability of the anomalous CO₂ plume prior to the field survey. Our simulation studies are carried out using the 3D codes developed in our working group. They are all based on linear and higher order Lagrange and Nédélec finite‐element formulations on unstructured grids, providing the necessary flexibility with respect to the complex real‐world geometry. We provide different strategies for addressing the accuracy of numerical simulations in the case of arbitrary structures. The presented computations demonstrate the expected great advantage of positioning transmitters or receivers close to the target. For direct‐current geoelectrics, 50% change in electric potential may be detected even at the Earth's surface. Monitoring with inductive methods is also promising. For a well‐positioned surface transmitter, more than 10% difference in the vertical electric field is predicted for a receiver located 200 m above the target. Our borehole transient electromagnetics results demonstrate that traditional transient electromagnetics with a vertical magnetic dipole source is not well suited for monitoring a thin horizontal resistive target. This is due to the mainly horizontal current system, which is induced by a vertical magnetic dipole.     

A multifactor analysis of parameters controlling solar wind ion flux correlations using an artificial neural network technique

Solar wind plasma and magnetic field observations from multiple spacecraft can be used to separate temporal and spatial variations and to determine the accuracy of predictions of solar wind conditions near Earth based on distant-spacecraft measurements. The study of correlations between the ion fluxes measured by three spatially separated spacecraft (IMP 8, WIND and INTERBALL-1) was one of the first steps in this direction. This paper describes a complex multifactor analysis of different physical, geometrical, and statistical parameters that control such correlations (considered separately and in combination). A linear-regression and an artificial neural network techniques are used for this analysis. The analysis is applied to an extensive array of correlation coefficients for the ion flux in the solar wind and provides estimates of the relative significance of the factors that control these correlation coefficients. The study shows that the most influential parameters are the solar wind density and the standard deviations of solar wind density, solar wind velocity and interplanetary magnetic field. This set of parameters permits us to develop a sufficiently accurate (with a relative error of less than a few per cent) quantitative model for the correlation between the ion fluxes measured on two spatially separated spacecraft.     

Electromagnetic analogue model measurements and finite-difference numerical calculations of the response of a conducting slab to three different source fields

This work compares experimental analogue model measurements and finite-difference numerical calculations of the electric and magnetic fields for a highly conducting slab embedded in a poorly conducting host earth for three different source field configurations. Measurements and calculations were carried out for a uniform source, a sheet current source with a y exp(?ay) current intensity distribution, and a horizontal magnetic dipole source. The results indicate reasonable agreement with some exceptions between the analogue and numerical methods. The source field is found to have an important effect on the field anomalies at the interface of the highly conducting slab and the poorly conducting host medium.     

基于最小反演拟合差的重磁场源深度计算方法

以等效源及位场物性反演为基础,本文提出一种新的求取重磁场源深度的方法.该方法将一层等效源以一定的间隔从浅部向深部移动,并将等效源作为初始模型进行反演,当反演拟合差最小时,停止反演,此时的等效源底深即为所求场源的中心深度.由于仅需要反演一层等效源,比传统的物性反演计算时间大大减少,并且不需要进行深度加权约束.理论模型数据处理结果表明该方法能够获得较准确的场源深度:以长宽比为7.5的薄板模型为例,深度计算误差约为1个点距(25 m);以长宽比为0.5~1.5的厚板模型为例,深度计算误差小于1个点距(25m).将该方法应用于实测航磁梯度数据,计算的磁源中心深度在200~250m之间,钻井资料显示该异常由埋藏深度在200~300m的闪长岩引起,计算结果与钻井资料较吻合.