一维时域磁场与频域电场联合反演方法研究

多方法、多参数的联合是地球物理反演的一个重要的发展方向.本文中,在水平电偶极发射下,频率域利用快速汉克尔变换法计算一维水平层状大地的水平电场响应,时间域利用G-S变换计算垂直磁场对时间的导数值.设计了四个简单模型进行对比,正演计算表明时域磁场对低阻体反映极为灵敏,对高阻体反映不灵敏;而频域电场对低阻体及高阻体反映都比较...     

井地电位测量系统的三维正演

针对井地电位测量系统的正演数值模拟问题,首先介绍了该系统的正演基本理论,然后采用"镜像"法,推导了垂直有限长线电流源在无限大半均匀介质中任意深度时的正常电位解析式,并在此基础上,推导了相应的装置系数和混合边界条件公式.结合有限差分法,实现了正演模型的求解计算.数值模拟中,采用不同的正常电位公式,混合边界条件公式和装置系数公式,分别建立了均匀介质模型、高阻异常体模型和低阻异常体模型,并对异常体正演响应的异常特征和分布规律进行了对比分析.结果表明,所推导的公式模拟异常体电位响应更准确,为后续更精确的反演和解释现场测量数据奠定了基础.     

高密度电阻率法对不同电极排列的分辨率响应研究

高密度电阻率法不同电极排列以及异常体尺寸和位置关系对探测结果有不同的分辨率响应,探明不同电极排列对分辨率的响应,对于科学合理地解析地电信息所揭示的地下构造具有重要的指导意义.通过Ansys中APDL命令流的方式对不同排列方式以及异常体尺寸进行模拟,分析了α、β以及γ等电极排列对水平异常体、竖直异常体以及异常体尺寸与其相邻位置的关系对分辨率的影响.研究表明,温纳电极排列的电极信号强,而且对竖直方向具有较好的敏感性.偶极排列对水平方向具有较好的敏感性,但其信号强度较弱.异常体水平排列时,异常体之间的距离大于其尺寸,能较好的分辨出其位置关系;竖直排列时,高密度电法难以探测出其异常体之间的信息.T比值参数结合了β、γ排列信息,对地下信息具有更清晰的分辨率,但T比值参数对于竖直方向,分辨率较低.     

大地电磁测深垂直剖面响应分析

类比过源虚界面法,根据无源区电磁波在层状介质中传播时场的分布特点,计算大地电磁视电阻率的垂直分布情况.建立水平层状模型,从Helmoltz方程出发,根据分界面处阻抗的连续性,推导层状模型任意深度处的阻抗,计算多个频率的视电阻率发现,随着频率的增高,所得视电阻率曲线划分地层能力越强.此外计算了多个频率薄层厚度不同时的视电阻率,对比可知高频时视电阻率曲线对低阻薄层的分辨能力最佳,对高阻薄层的分辨能力较差,这对研究地下水平层状介质垂直电性变化具有重要意义.     

大地电磁局部畸变异常特征三维数值模拟研究

局部畸变问题曾经困扰大地电磁资料反演解释几十年,大地电磁三维数值模拟技术的发展为剖析局部畸变特点和得到可靠的反演成像结果提供了技术基础。本文采用三维数值模拟成像方法对典型三维局部畸变模型进行模拟分析。三维数值模拟结果显示:电场分量垂直电性分界面的极化模式视电阻率曲线(对应二维情况下TM模式)在穿越低阻异常体界面时,曲线会先上移后下移,而在穿越高阻异常体界面时,曲线会先下移后上移,这与电性分界面处积累面电荷产生的二次电场有关。三维模型中XY模式、YX模式视电阻率和相位在三维异常体附近的水平变化是呈现近似垂向对称的,该现象与电场垂直跨越电性界面时视电阻率的变化规律是吻合的,当测线分别沿X方向和Y方向展布时,三维情况下的XY和YX模式分别对应二维情况下的TM模式。低阻小异常体对区域构造响应的畸变影响比高阻小异常体要严重。低阻小异常体对二维区域响应的两种极化模式视电阻率和相位都有非常明显的畸变影响,相比较而言对TE模式的畸变要大于TM模式,因此我们在做二维反演解释时,可优先考虑拟合TM模式数据。位于小异常体中心上方测点的三维畸变响应虽然与对应真实二维区域响应的差异比较大,但可以等效于某种二维模型响应,这种由局部畸变造成的假二维响应在实际野外数据的解释中是需要注意的。      

瞬变电磁横磁场响应特征与探测能力分析

瞬变电磁法是重建地下电阻率等电性结构的重要方法.传统磁性源和电性源瞬变电磁法主要观测横电极化场,横电极化场仅对良导目标敏感,对高阻目标的分辨能力有限.横磁极化场对高阻目标具有较强的分辨能力,但未得到有效利用.双线源瞬变电磁法可以增强观测电场中横磁极化场的占比,但对该方法的响应特征和分辨能力缺乏系统性的研究.为此,本文以双线源为例开展瞬变电磁横磁场响应特征与分辨能力分析.双线源瞬变电磁水平电场的响应强度要小于传统接地导线源,在发射源的中垂线上,层状大地模型的响应为零,观测的水平电场响应只能由地下的三维目标体产生.分别提取双线源和传统接地导线源激发电磁场中的横磁场和横电场,双线源瞬变电磁场中的横磁场占比要大于传统接地导线源,特别是在中晚期,横磁场远大于横电场,横磁场占比得到明显增强.通过均方根差和三维数值模拟的计算,双线源瞬变电磁水平电场显示出相较于传统接地导线源更强的高阻目标分辨能力,特别是在赤道向,水平电场对高阻目标分辨能力的增强效果更加明显.     

大地电磁倾子资料的三维正演研究

在实际复杂的三维地电条件下,倾子作为大地电磁法的重要解释参数之一,其正演模拟和响应分析对提高大地电磁法的探测精度具有重要作用.本文在简要阐述大地电磁三维正演基本理论的基础上,利用交错网格有限差分法开展了大地电磁三维倾子正演模拟研究,首先正演模拟单个低、高阻两种地电模型的倾子响应,结果表明倾子资料能够较好反映地下异常体的空间分布;在此基础上,设计了含有两个低(高)阻异常体和低阻垂直断层的复杂组合模型并计算了其三维倾子响应,结果表明,倾子具有对复杂的地电结构良好的空间分辨率,且倾子响应既保留了模型中每单个异常体的倾子响应形态,又表现出了异常体之间相互作用的整体响应情况,进一步加深了对倾子的响应特征和规律、以及倾子资料对异常体边界的识别能力的认识,为倾子资料从定性解释向定量解释发展提供参考和依据.     

钻井-地表电极联合电阻率观测装置的异常特征研究

本文利用有限单元法对多种钻井-地表电极联合电阻率观测装置在球体、直立板和水平板体等典型地质体模型上的异常响应进行正演计算,并分析其异常特征和分布规律.计算结果表明利用井中和地表电极的联合观测方式进行地下介质探测,可在兼顾地质体的水平分辨能力的同时,提高电阻率测深在垂向上分辨率.就水平分辨率而言,四极（偶极）装置对地质体的水平定位能力最强,井-地三极装置次之,地-井三极的分辨能力最差.就垂向分辨能力来说,各种观测装置的分辨率相差不大.     

逆Laplace变换新算法及其在时间域电磁响应计算中的应用

时间域电磁响应的正演计算多是由频率域响应经逆Laplace变换而得到.逆Laplace变换的计算精度和效率是时间域电磁响应计算中方法选择的重要指标.论文分析了几种逆Laplace变换的算法机制,并优选出Talbot算法计算了水平电偶源层状模型的时间域电磁响应.逆Laplace变换常用的算法有折线法、数字滤波算法和Gaver-Stehfest算法(简称G-S算法).折线法需要精细地确定分割步长以提高精度,数字滤波算法系数很多,适应频率范围受计算问题所限,而G-S算法受计算机字长和问题对象的影响大.本文在64位计算平台中计算比较了G-S算法、Euler算法和Talbot算法的节点数对于精度的影响,发现Talbot算法受节点数影响小,计算精度高,适应频率范围宽.最后利用21点Talbot算法计算了水平电偶源轴向偶极装置均匀大地模型径向电场的阶跃响应和冲激响应,计算精度及响应时间范围均优于G-S算法.计算了水平电偶源赤道偶极装置均匀大地模型垂直磁场的阶跃响应和冲激响应,冲激响应峰值时刻对于电阻率的变化响应灵敏,与轴向偶极径向电场响应能力相当,但垂直磁场随收发距增大,衰减较快.根据层状模型阶跃响应晚期渐近值计算的视电阻率,水平电偶源轴向偶极径向电场有能力发现大埋深高阻或低阻薄层,收发距应大于中间目标层埋深的5~6倍方可完整探测,类似的,采用水平电偶源赤道偶极装置测量垂直磁场也能达到与之相当的探测能力.计算结果证实了21点Talbot算法适应不同地电模型、不同观测方式的时间域电磁响应计算.     

AMT 、TEM 、VES地层响应特征模拟分析及其联合反演探讨

通过正演模拟方式分析音频大地电磁法(AMT)、中心回线瞬变电磁法(TEM)、直流电测深法(VES)对地层的响应特征,结果表明:TEM、AMT对地层的响应特征类似,即对低阻层反应灵敏,而对高阻层的分辩能力较差;VES对高阻层及低阻层的分辩能力相当,相对于TEM、AMT,VES对低阻层的分辩能力差,而对高阻层的分辨能力较高.基于AMT或TEM与VES对地层的响应具有互补的特点,探讨了对AMT或TEM与VES数据进行的联合反演.结果表明,AMT或TEM与VES进行联合反演,相比单一方法进行反演,结果能得到明显的改善.     

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.     

不同电极阵列联合反演在古墓探测中的应用

电阻率层析成像是一种广泛应用在水文、考古和地质等浅地表勘探领域的地球物理方法。为了增强电阻率层析成像的分辨率、应对复杂的地质问题,本文提出基于雅可比矩阵的不同电极阵列直流电阻率数据的加权联合反演算法,并以温纳和偶极-偶极电极阵列数据为例,在理论模型和古墓探测的野外实例中测试该算法的有效性。结果表明,加权联合反演结果的横向和纵向分辨率都优于单一电极阵列的反演结果,并在实例中缓解“U形”电极阵列的固有缺陷、减少反演模糊性、更好地约束墓室宽度的反演结果。      

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.     

Physical Modeling Results on Modified Pseudo-depth Sections in Exploration of Highly Resistive Targets – II

-- This work extends the results that Apparao et al. (1997a) obtained for a vertical resistive sheet to the case of inclined resistive sheet models for different electrode arrays. It is found that the depth of investigation (DI) remains the same as that for the vertical target. Using this DI, modified pseudo-depth sections have been constructed over sheet models at different inclinations. It is noted that, for the Wenner array, the maximum anomaly contours fall directly over the target cross section. For dipole-dipole and three-electrode arrays, these contours fall on the up-dip side of the dipping target, with the maximum anomaly contour matching the depth level of the top of the target. It is also observed that the target cross section is at a distance of about 0.33L (L/3) from the maximum anomaly value/contour position for the three-electrode array and 0.25L (L/4) for the dipole-dipole system. These features are identifiable in the individual profiles and may help field geophysicists in the recognition and location of dipping target bodies.     

Method to obtain standard pseudosections from pseudo pole-dipole arrays

This study deals with electrical resistivity tomography data and it is addressed at obtaining, from linear combinations of data, other datasets not directly measured. The method presented here allows performing the fieldwork systematically, without deciding the type of the more suitable common electrode array (e.g. Wenner, Wenner-Schlumberger, dipole-dipole or multiple-gradient) until or even after the interpretation time. The electrode configuration used by this method is denoted as pseudo pole-dipole array, because it is based on the standard pole-dipole one, but avoiding the disadvantage of locating the remote electrode far away from the profile (to “infinity”). The pseudo pole-dipole datasets can be acquired with common equipment using standard pole-dipole recording sequences. Once the desired datasets have been calculated, they can be inverted using standard interpretation software. The procedure used allows a data quality control to be introduced that is similar to the one based on normal and reciprocal measurements. To assess the method we considered noise-contaminated model responses as well as field data. It has been applied to build dipole-dipole and Wenner-Schlumberger datasets. Results show the suitability of both, the proposed method and the quality control.     

利用高密度电阻率法确定滑坡面的正演研究

高密度电法探测是滑坡面探测的有效手段,适宜 的现场工作方案和相应的资料解译模型,是获取 可靠探测成果的前提。本文针对高密度电法勘探 中常用的四类电极排列方式,即维纳、施伦贝谢、 偶极、二极,利用有限元的方法二维正演模拟建 立了均质土坡滑面、软弱夹层滑面、堆积层滑面、 构造破碎带滑面的标准地电模型剖面;明确了进 行不同类型滑坡工程地质调查时不同电测装置的 探测能力和视电阻率异常模式;提出复杂地质条 件下斜坡问题探测数据有效处理的设计比值参数 方法。最后给出若干利用高密度电阻率法进行滑 坡工程地质调查的典型实例。     

多同性源阵列电阻率法隧道超前探测方法与物理模拟试验研究

直流电阻率法以其对含水构造响应敏感且适应性强的特点,是隧道施工期超前地质预报的常用方法.针对目前定点源三极观测方式易受到测线附近旁侧异常干扰与聚焦观测方式探测距离过短无法三维成像的问题,提出了一种基于多同性源阵列电阻率的隧道超前探测新方法,利用环形布置的多同性源供电压制隧道掌子面后方的异常体的干扰,同时增强掌子面前方远处异常体的敏感度,阵列电极测量可为含水构造的三维反演成像提供三维数据.首先,开展了含水构造超前探测的数值正演模拟,发现多同性源方法的视电阻率纵向微分曲线极小值以及与横轴的交点位置可对异常体位置进行定性判断,探讨了多同性源方法对后方及侧向异常干扰的响应特征及识别方法.其次,将电阻率光滑约束与轨迹光滑策略引入蚁群反演算法,提出了一种最小二乘方法与改进蚁群算法相结合的混合反演算法,反演数值算例表明混合反演算法能够实现含水构造的三维成像,较好地反演出不同距离的含水构造位置,并使其边界较为清晰.为了验证多同性源探测方法的探测效果开展了物理模型试验,多同性源阵列电阻率法能较好的反映含水构造的存在,与实际含水构造的位置较为相符.     

Two‐dimensional joint inversions of cross‐hole resistivity data and resolution analysis of combined arrays

In this study, a new two‐dimensional inversion algorithm was developed for the inversion of cross‐hole direct current resistivity measurements. In the last decades, various array optimisation methods were suggested for resistivity tomography. However, researchers have still collected data by using classical electrode arrays in most cross‐hole applications. Therefore, we investigated the accuracy of both the individual and the joint inversion of the classical cross‐hole arrays by using both synthetic and field data with the developed algorithm. We showed that the joint inversion of bipole–bipole, pole–bipole, bipole–pole, and pole–tripole electrode arrays gives inverse solutions that are closer to the real model than the individual inversions of the electrode array datasets for the synthetic data inversion. The model resolution matrix of the suggested arrays was used to analyse the inversion results. This model resolution analysis also showed the advantage of the joint inversion of bipole–bipole, pole–bipole, bipole–pole, and pole–tripole arrays. We also used sensitivity sections from each of the arrays and their superpositions to explain why joint inversion gives better resolution than the any individual inversion result.     

Assessment of the reliability of 2D inversion of apparent resistivity data

The reliability of inversion of apparent resistivity pseudosection data to determine accurately the true resistivity distribution over 2D structures has been investigated, using a common inversion scheme based on a smoothness‐constrained non‐linear least‐squares optimization, for the Wenner array. This involved calculation of synthetic apparent resistivity pseudosection data, which were then inverted and the model estimated from the inversion was compared with the original 2D model. The models examined include (i) horizontal layering, (ii) a vertical fault, (iii) a low‐resistivity fill within a high‐resistivity basement, and (iv) an upfaulted basement block beneath a conductive overburden. Over vertical structures, the resistivity models obtained from inversion are usually much sharper than the measured data. However, the inverted resistivities can be smaller than the lowest, or greater than the highest, true model resistivity. The substantial reduction generally recorded in the data misfit during the least‐squares inversion of 2D apparent resistivity data is not always accompanied by any noticeable reduction in the model misfit. Conversely, the model misfit may, for all practical purposes, remain invariant for successive iterations. It can also increase with the iteration number, especially where the resistivity contrast at the bedrock interface exceeds a factor of about 10; in such instances, the optimum model estimated from inversion is attained at a very low iteration number. The largest model misfit is encountered in the zone adjacent to a contact where there is a large change in the resistivity contrast. It is concluded that smooth inversion can provide only an approximate guide to the true geometry and true formation resistivity.