Magnetotelluric response of a two-dimensional sloping contact by the finite element method

Summary The finite element method, with triangular elements, is used to study the effect of a two-dimensional sloping contact on the surface electromagnetic fields. It is found in the case ofH-polarization and small slopes that the electric field and the apparent resistivity near the contact, on the conductive side, are higher than their asymptotic values. In the case ofE-polarization the apparent resistivity and phase values on the conductive side fall off less rapidly to their asymptotic values with decreasing slope resulting in higher apparent resistivity and phase values on the conductive side, than those expected for a vertical contact. The peak in the amplitude and phase of the normalized vertical magnetic field shifts from the resistive side for a vertical contact to the conductive side for a sloping contact. Far from the sloping contact, on the conductive side, higher values are observed for the normalized vertical magnetic field than in the case of a vertical contact.     

Electromagnetic profiling interpretation across vertical faults and dikes

When a vertical fault or dike scatters a normally incident TE-mode plane wave, the horizontal components of the electric and the magnetic fields vary along the direction perpendicular to the strike. This scattering is also responsible for the formation of a vertical component of the magnetic field, which also varies along the direction perpendicular to the strike. Analysis of the lateral variations of the field components permits the identification of the type of geological structure, either fault or dike, as well as an estimate of the position of the geological contacts and the electrical conductivity of each medium. Previous exact analytical solutions have shown that two Fourier cosine integrals can express each field component. A series of functions specified for each model represent the kernel of each integral. From the field components obtained from the first non-zero term of each series, we calculated the following functions: the dip angle and the ellipticity of the vertical polarization ellipse in a plane perpendicular to the strike of the structure, and the azimuth and the ellipticity of the horizontal ellipse. We established master-curves of these functions for the interpretation of vertical faults and dikes for the polarization ellipsoid, for instance VLF or audio-frequency methods. This representation has as variable the induction number     , and as parameters σ ₂/ σ ₁ and     , where a denotes the half-thickness of the dike. The interpretation procedure using curve fitting is possible because the induction number is represented on a logarithmic scale. This procedure represents an important step before automatic interpretation is carried out. Two case histories using field data illustrate the effectiveness of the procedure and the type of quantitative interpretation obtained from it.     

Processing of magnetotelluric data

The processing of magnetotelluric data involves concepts from electromagnetic theory, time series analysis and linear systems theory for reducing natural electric and magnetic field variations recorded at the earth's surface to forms suitable for studying the electrical properties of the earth's interior.The electromagnetic field relations lead to either a scalar transfer impedance which couples an electric component to an orthogonal magnetic component at the surface of a plane-layered earth, or a tensor transfer impedance which couples each electric component to both magnetic components in the vicinity of a lateral inhomogeneity.A number of time series spectral analysis methods can be used for estimating the complex spectral coefficients of the various field quantities. These in turn are used for estimating the nature of the transfer function or tensor impedance. For two dimensional situations, the tensor impedance can be rotated to determine the principal directions of the electrical structure.In general for real data, estimates of the apparent resistivity are more stable when calculated from the tensor elements rather than from simple orthogonal field ratios (Cagniard estimates), even when the fields are measured in the principal coordinates.     

A study of transient variations in the Earth’s electromagnetic field at equatorial electrojet latitudes in western Africa (Mali and the Ivory Coast)

In the framework of the French-Ivorian participation to the IEEY, a network of 10 electromagnetic stations were installed at African longitudes. The aim of this experiment was twofold: firstly, to study the magnetic signature of the equatorial electrojet on the one hand, and secondly, to characterize the induced electric field variations on the other hand. The first results of the magnetic field investigations were presented by Doumouya and coworkers. Those of the electric field experiment will be discussed in this study. The electromagnetic experiment will be described. The analysis of the electromagnetic transient variations was conducted in accordance with the classical distinction between quiet and disturbed magnetic situations. A morphological analysis of the recordings is given, taking into consideration successively quiet and disturbed magnetic situations, with the results interpreted in terms of the characterization of external and internal sources. Particular attention was paid to the effects of the source characteristics on the induced field of internal origin, and to the bias they may consequently cause to the results of electromagnetic probing of the Earth; the source effect in electromagnetic induction studies. During quiet magnetic situations, our results demonstrated the existence of two different sources. One of these, the S_R^E source, was responsible for most of the magnetic diurnal variation and corresponded to the well-known magnetic signature of the equatorial electrojet. The other source (the S_R*^E source) was responsible for most of the electric diurnal variation, and was also likely to be an ionospheric source. Electric and magnetic diurnal variations are therefore related to different ionospheric sources, and interpreting the electric diurnal variation as induced by the magnetic field diurnal variation is not relevant. Furthermore, the magnetotelluric probing of the upper mantle at dip equator latitudes with the electromagnetic diurnal variation is consequently impossible to perform. In the case of irregular variations, the source effect related to the equatorial electrojet is also discussed. A Gaussian model of equatorial electrojet was considered, and apparent resistivities were computed for two models of stratified Earth corresponding to the average resistive structure of the two tectonic provinces crossed by the profile: a sedimentary basin and a cratonic shield. The apparent resistivity curves were found to depend significantly on both the model used and the distance to the center of the electrojet. These numerical results confirm the existence of a daytime source effect related to the equatorial electrojet. Furthermore, we show that the results account for the observed differences between daytime and night-time apparent resistivity curves. In particular, it was shown that electromagnetic probing of the Earth using the classical Cagniard-Tikhonov magnetotelluric method is impossible with daytime recordings made at dip latitude stations.     

多辐射场源地空瞬变电磁法多分量全域视电阻率定义

本文针对多辐射场源地空瞬变电磁法理论,建立了相应的多分量全域视电阻率定义方法.分析了利用磁场强度进行多辐射场源地空系统全域视电阻率定义的优点,针对磁场强度的各个分量,提出了各自的全域视电阻率算法,实现了多分量、全时域、全空域视电阻率计算,并分析了偏移距对全域视电阻率的影响.通过调整源的相对位置及电流方向等参数,多辐射源瞬变电磁地空系统不仅可以加强不同分量信号强度,削弱随机干扰,还可更好地分辨地下异常体的位置.通过对所设计模型的处理,证实了多辐射场源地空系统多分量全域视电阻率算法的有效性,也验证了多辐射场源地空系统的优势.     

电性源瞬变电磁地空逆合成孔径成像

电性源地空瞬变电磁法具有工作效率高、勘探深度大、采集信号信噪比高、适用于地形地质条件复杂地区等优点.但是,到目前为止,由于尚未建立起该方法的解释系统,大大制约了该方法的发展.本文旨在建立起完整的地空电磁探测系统,丰富整个探测系统的理论.本文围绕地空瞬变电磁法全域视电阻率定义、瞬变电磁虚拟波场的克希霍夫偏移成像、逆合成孔径成像方法三个科学问题进行了系统研究.提出了用磁场强度定义全域视电阻率的迭代算法,理论模型试验结果表明计算出的视电阻率曲线首支趋于第一层电阻率,尾支趋于最后一层电阻率,实现了全空域、全时域视电阻率的计算;在先前研究的基础上,实现了适合电性源地空装置的瞬变电磁虚拟波场的克希霍夫偏移成像;采用相关迭加技术,实现孔径内多测点数据合成,将传统的单点处理方式发展成为逐点推移多次覆盖的逆合成孔径处理方法.层状模型试验表明:(1)全域视电阻率能够光滑、完整、渐变地反映出模型的电性信息变化;(2)当改变三层模型中间层电阻率时,全域视电阻率曲线随着参数的改变分异明显,对电性层的识别容易且直观;(3)由于在电阻率计算中同时考虑了接收机高度、偏移距、时间等各参数的影响,全域视电阻率可实现全空域、全时域的视电阻率计算.含水采空区的复杂模型算例表明:(1)根据不同测线的全域视电阻率结果可以看出,在靠近采空区的位置,全域视电阻率断面可以清晰地反映出采空区的空间位置,随着测线离采空区越来越远,采空区异常越来越弱直至消失;(2)波场变换和偏移成像的结果显示存在两个电性差异较大的界面,上界面指示地表,由于空气和大地之间的电性差异较大,故该界面波场信号反映强烈,遍布整个区域,下界面异常信号则主要集中在中部,向外逐渐减弱,指示采空区;(3)逆合成孔径成像结果表明地表界面在合成前后没有变化,而采空区异常合成后范围明显变小,且异常边界清晰,指示的采空区位置与模型吻合很好.本文借助于逆合成孔径雷达成像的基本思想,建立了一套电性源瞬变电磁地空逆合成孔径成像方法.基于反函数思想结合迭代算法提出的电性源地空瞬变电磁法的全域视电阻率定义方法,实现了全空域、全时域的视电阻率计算;借鉴瞬变电磁拟地震偏移成像算法,实现了瞬变场的三维成像;借鉴逆合成孔径雷达的思想,提出电性源瞬变电磁地空逆合成孔径算法,进一步提高了成像的分辨率.采空区模型算例表明相关叠加合成确实具有增强有用信号、提高信噪比、提高分辨率的诸多优点,证实了瞬变电磁地空逆合成孔径成像方法的有效性.     

正交水平磁偶源的电磁场分布规律

正交水平磁偶源是模拟天然场源的较好人工源,可以方便地实现可控源高频大地电磁张量测量.正交水平磁偶源的电磁场分布规律是野外工作布置的理论基础,为此计算了均匀大地模型正交水平磁偶源的电磁场.计算结果表明:电磁场水平分量在各个象限都有一相对低值带,对应的标量视电阻率形成了畸变带,但张量视电阻率畸变带消失;张量视电阻率曲线形态显示出近区的低阻、过渡区的高阻隆起和远区趋于真值的规律.通过野外试验验证理论计算结果,在无法准确确定地下介质电阻率参数的情况下,以天然电磁场计算的电阻率为参照对比研究了正交水平磁偶源电磁场的分布规律.试验结果表明:正交水平磁偶源与电偶源的电磁场同样的存在近区、过渡区和远区;在远区,正交水平磁偶源与测点的相对位置对张量测量结果几乎没有影响,即在远区可以在任何方位测量;正交水平磁偶源的布置要考虑收发距的影响,保证测量在远区进行.     

湖相沉积盆地内隐伏断裂的电阻率层析成像探测——以通海盆地为例

本文利用电阻率层析成像方法对湖相沉积盆地——通海盆地内的小江断裂的西支断裂进行了探测。发现在电阻率图像的较深区域才能识别出断裂的位置和产状,它在通海盆地内的走向约为N47°E,倾角约为57°～66°,视倾向为NW或N,与以往的研究结果基本一致。     

STUDY ON THE ELECTRICAL STRUCTURE OF THE ANQIU AND JUXIAN ELECTROMAGNETIC STATIONS IN THE TANLU FAULT ZONE

The Yishu fault zone is one of the branch faults of the Tanlu fault zone in its central part. Moderate and strong earthquakes occurred in the Yishu fault zone repeatedly. Due to its complex structure, the Yishu fault zone attracts much attention from earthquake researches. The Anqiu and Juxian electromagnetic stations in Shandong Province locate near the Anqiu-Juxian Fault and Changyi-Dadian Fault, which are branches of the Yishu fault zone, respectively. Geoelectric field and geomagnetic field observation were carried out in these two stations. The Wudi electromagnetic station is in the west of Tanlu fault zone in the Jidong-Bohai block and 230km from Anqiu electromagnetic station. This paper firstly describes the crustal structure near the electromagnetic stations by using magnetotelluric(MT)method. By processing the data carefully, we obtain the MT data in good quality near the stations. The MT data of each electromagnetic station and its nearby area suggests that the electrical structure and geological structure of the station are comparable. This paper applied 1-D and 2-D inversion for MT data and obtained the crustal electrical structure model beneath the Anqiu and Juxian seismic station. The shallow electrical structure from the MT method was compared with the results of symmetrical quadrupole electrical sounding. The model suggests that the electrical structure beneath the Anqiu and Juxian electromagnetic stations is complex and shows the feature of block boundary. The Wudi electromagnetic station is located inside a basin, the crustal structure shows layered feature typical for the stable blocks. Beneath the Anqiu electromagnetic station, there is a 1km-thick relative low resistivity layer in the shallow crust and a high resistivity body beneath it with a depth of 13km. There is a high resistivity structure in the crust beneath the Juxian electromagnetic station. The crustal structures are divided into two different parts by Anqiu-Juxian Fault and Changyi-Dadian Fault, respectively. More conductive layers appear to the west of the two faults. Plenty of fluid possibly exists within the conductive body to the west of Changyi-Dadian Fault, which plays important role in the earthquake generation. There is a relative low resistivity layer in the crust within 1~2km beneath the Wudi electromagnetic station. Beneath the relatively low resistivity layer, a relatively high resistivity layer extends to a depth of around 15km, and the resistivity value decreases with the increase of depth. The electrical resistivity model suggests the seismic activity of the Yishu fault zone around the Anqiu and Juxian electromagnetic stations should be taken into account seriously, and monitoring and research on it need to be strengthened. The results of this paper provide a certain reference value for the crustal structure research to similar stations.     

The boundary integral calculations of the forward problem for D.C. sounding and MMR methods for a 3-D body near a vertical contact

Summary The paper presents comprehensive theory based on the boundary integral method for calculations of the electric potential, electric field and corresponding magnetic field due to a pair of D.C. source electrodes near a vertical resistivity contact in the halfspace, indlucing a 3-D disturbing body in the vicinity of the contact. Special attention is paid to the case when the disturbing body touches the vertical contact. Results of numerical calculations are presented in the form of sounding curves and a set of isoline graphs for potential, components of the electric and magnetic field (total and anomalous) on the surface of the Earth. It is shown that the presence of the disturbing body at the contact is most pronounced in the electrical characteristics. Anomalies in the magnetic field are small in comparison to the field due to the electric current in the electrode cable and primary currents flowing from the electrodes.     

3D LBFGS inversion of controlled source extremely low frequency electromagnetic data

The controlled source extremely low frequency (CSELF) electromagnetic method is characterized by extremely long and powerful sources and a huge measurement range. Its electromagnetic field can therefore be affected by the ionosphere and displacement current. Research on 3D forward modeling and inversion of CSELF electromagnetic data is currently in its infancy. This paper makes exploratory attempts to firstly calculate the 1D extremely low frequency electromagnetic field under ionosphere-air-earth coupling circumstances, and secondly analyze the propagation characteristics of the background electromagnetic field. The 3D staggered-grid finite difference scheme for solving for the secondary electric field is adopted and incorporated with the 1D modeling algorithm to complete 3D forward modeling. Considering that surveys can be carried out in the near field and transition zone for lower frequencies, the 3D Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) inversion of CSELF electromagnetic data is presented (in which the sources, or primary fields, are included), with the aim of directly inverting the impedance data, regardless of where it is acquired. Derivation of the objective functional gradient is the core component in the inversion. Synthetic tests indicate that the well-chosen approximation to the Hessian can significantly speed up the inversion. The model responses corresponding to the coexistence of conductive and resistive blocks show that the off-diagonal components of tensor impedance are much more sensitive to the resistivity variation than the diagonal components. In comparison with conventional scalar inversion, tensor inversion is superior in the recoveries of electric anomalies and background resistivity.     

ATTEM系统中电流关断期间瞬变电磁场响应求解的研究

在瞬变电磁法中,由于发射电流关断时间不为零、接收线圈的谐振频率有限,早期瞬变电磁信号发生畸变,只能舍弃,因此存在着探测盲区. 针对这一问题,研究了瞬变电磁方法中发射电流关断期间总磁场的形成过程,论证了一次场、二次场和总瞬变场的关系,分析了接收线圈的频率特性和关断时间对瞬变电磁场的影响,提出从总磁场中剔除一次磁场影响的方法,从而获得电流关断期间和电流关断后的早期瞬变电磁场. 采用吉林大学自主研制的瞬变电磁测量系统(ATTEM)在长春市伊通河活断层进行勘探,进一步验证了算法的有效性,缩短了瞬变电磁法的勘探盲区,实现了近地表4 m以下的勘探,可以清晰地分辨近地表的低阻异常,提高了浅层探测精度和分辨率.     

Geoelectromagnetic variations over a sloping ocean floor up to and including the coastline

Summary The electric and magnetic field variations over an arbitrarily sloping ocean floor are represented in series of Bessel functions forH-polarized uniform plane wave excitation. Calculation of the spatial variations of electric eurrents and apparent resistivity near a coastline will determine the usefulness of the magnetotelluric method in this application.The work presented herein was conducted at the Institute for Applied Mathematics of the University of Oslo, Oslo, Norway.     

多源频率域地空系统三维电磁响应分析

地空电磁法已经成为深部资源勘探的重要地球物理方法,但对频率域地空系统的三维多源电磁响应特征研究较少.本文设计了多种激励源组合方式,采用非结构化有限元数值模拟方法,对三维地电模型的空中垂直磁场的响应特征进行了研究.首先推导了基于电场的双旋度公式及其变分形式,加入罚项以减少伪解的影响.接着把有限元稀疏矩阵方程转换为频率的函数,采用Krylov子空间投影方法,通过模型降阶算法降低稀疏矩阵的阶数,实现多频点的快速计算.建立了三维低阻体模型、高阻体模型以及两个相邻低阻体模型,分别采用单源、双源、三源和四源激励模式,从垂直磁场的总场、二次场响应和全域视电阻率等方面进行分析比较.结果表明:多源地空电磁法不仅可以增加总场的强度,而且可以改变异常体的二次电磁响应分布规律.各电偶源延长线呈正三角形分布的三源和矩形分布的四源激励模式在增强信号强度以及削弱异常体的边界效应方面具有一定的优势,是一种优化的多源激励方式.     

Delineation of Shallow Subsurface Structure by Azimuthal Resistivity Sounding and Joint Inversion of VES-TEM Data: Case Study near Lake Qaroun, El Fayoum, Egypt

An azimuthal resistivity survey was conducted at the transition zone between the desert area and the cultivated land near Lake Qaroun, Egypt. This area has been affected by an east-west trending fault system as indicated from the surface geology. Apparent resistivity values were plotted along azimuth on a polar diagram. Resistivity anomalies, for most of the AB/2 values with long axes strike in a direction parallel to the contact between the desert and cultivated lands, indicate the presence of electrical macro-anisotropy, mainly due to the faulting effect, at this area. Vertical electrical soundings (VES) and transient electromagnetic (TEM) measurements were conducted at eight stations along a line that crosses the boundary between the desert and cultivated land. Joint inversion of VES-TEM data was successfully used for identification of the subsurface lithostratigraphic succession and demonstrated the effect of the fault zone on the investigated subsurface medium. Apparent anisotropy coefficients at all current electrode spacings were calculated, plotted against AB/2 values and compared with the geoelectrical cross section. The effect of the fault zone was detected at AB/2 spacings equal to 100 m and extended downward and is largely related to the depth of the fault, as indicated in the constructed cross section.     

水平多层大地上垂直磁偶极频率测深的全波视电阻率

本文根据视电阻率定义的原则,以及用不同的场量定义的视电阻率效果不同这一事实,提出一种新的全波视电阻率定义.在全区同时用均匀大地上电磁场的三个分量来分区定义祝电阻率.在远区视电阻率由磁场的水平分量求出,在近区由磁场的垂直分量或其实分量定义,而在过渡区则由电场的水平分量确定.用这种方法定义的视电阻率为电磁响应的单值函数,它随频率变化的曲线显著改善,能直观地反映地层电阻率随深度的变化,数值比较接近地层的真电阻率值,假极值效应明显压低.在计算中用切比雪夫多项式分段拟合均匀大地电磁响应的反函数,并给出一套系数,由此算出的视电阻率误差小于1％.     

安徽霍山地震区深部电性结构和发震构造特征

霍山地震区位于大别造山带北缘华北板块与扬子板块接触带上,是大别造山带及周边地震活动最频繁、最集中的地区.83个大地电磁测点组成的大地电磁三维阵列覆盖了整个霍山地震区.用多重网格法、印模迭代重构法和非线性共轭梯度法对阵列数据进行三维带地形反演,获得了地震区深部三维电性结构.电性结构显示,北大别、北淮阳区的中上地壳为电阻率1000Ωm以上的高阻区,中下地壳为电阻率数十欧姆米的相对低阻区;六安盆地电阻率整体较低,中地壳存在显著的电阻率为几欧姆米的壳内高导层.北西向的晓天—磨子潭断裂分隔了北大别高阻层和北淮阳高阻层,在浅部向NE倾,深部向SW倾;北东向的落儿岭—土地岭断裂切穿北大别上地壳高阻层.小震双差定位结果表明,地震主要发生在NE向延伸的落儿岭—土地岭断裂附近的北大别、北淮阳中上地壳的高阻区,并集中于NW向的晓天—磨子潭断裂运动所造成的构造薄弱带中;2014年M S4.3霍山地震震源深度较深,位于北大别高阻区内部的电性梯度较大的区域.综合上述结果我们认为,霍山地震区的主要发震断裂为落儿岭—土地岭断裂,断裂的运动变形充分利用了晓天—磨子潭断裂早先活动所形成的构造薄弱带,断裂下方壳源高导体中的流体沿断层传播使断层强度弱化,使得这些薄弱带区易于发生小地震.由于北大别、北淮阳构造区显著高阻层的存在,我们认为霍山地震区存在发生6级以上中强震的深部孕震环境.     

非均匀电磁波在导电媒质界面反射的横向偏移

由电磁场边值关系给出了非均匀电磁波在导电媒质界面反射时反射系数所产生的附加相角. 利用这一附加相角导出了非均匀电磁波在导电介质界面的横向偏移,并进行了横向偏移的相关计算,绘出了横向偏移随入射角的变化曲线. 结果表明：在导电媒质界面反射电磁波的横向偏移随入射角的增大而增大,当入射角接近90°时,电磁波在界面要传播较长时间后才返回第一种媒质. 在同一入射角电场偏振化方向在入射面的电磁波要比电场偏振化方向垂直于入射面的电磁波的横向偏移大,随着电磁波频率的增加横向偏移变小.     

全空间条件下矿井瞬变电磁法粒子群优化反演研究

煤矿井下矿井瞬变电磁法(MTEM)探测中,电磁场呈全空间分布,全空间瞬变电磁反演是复杂的非线性问题,目前反演计算中全空间响应主要由半空间响应乘以全空间响应系数来得到,导致反演结果中顶板和底板异常(或前方和后方异常)叠加在一起难以分离,造成分辨率下降.论文提出采用粒子群优化算法(PSO)进行全空间MTEM反演,通过理论分析,在常规的粒子群算法基础上提出了一种新的进化公式改进策略,提高了粒子群算法的寻优能力.基于全空间瞬变电磁场理论,编写了粒子群算法反演程序,进行全空间条件下五层含巷道的复杂模型的反演计算.结合某矿井巷道顶板、底板岩层及断层含水性的探测实例,对实测数据进行反演计算和解释,探测结果得到钻探证实.研究表明,改进的粒子群优化算法对理论模型和实际资料的反演拟合程度较高,实现了矿井顶板、底板视电阻率异常的分离,提高了全空间瞬变电磁勘探资料的解释精度和分辨率.     

Improved imaging of a karst aquifer using focused source electromagnetic and differentially normalized method: a qualitative analysis

Geophysical investigations using conventional techniques applied to groundwater exploration can often present strong limitations involving high financial costs, complex acquisition logistics and high ambiguity in results. Dispersion of the electric current flow, induced polarization) effects, cultural noises and shallow lateral heterogeneities represent the main problems faced by geoelectric methods in these types of surveys. Moreover, elements such as intrusions and mineralization at different depths may be responsible for signal attenuation as well as high resistivity in unsaturated zones and complex three-dimensional formations or clayey zones cause variations in the electric current. The focused source electromagnetic and differentially normalized method approaches can help to solve some these issues. Aiming at a higher signal-to-noise ratio, the focused source electromagnetic method and approaches of the differentially normalized method, first applied to petroleum exploration, are tested on a groundwater target, in a karst environment sectioned by a diabase dyke. We performed the processing and analysis on real IP resistivity profiling data acquired with two-way dipole-dipole array, guided by magnetic data acquired on the same profile, mapping a diabase dyke. The inversion of focused source electromagnetic method/differentially normalized method was not performed, instead that we converted the induced polarization–resistivity data to a differential signal to qualitatively prove the presence of aquifer. Joint interpretation of focused source electromagnetic method curves and inverted two-dimensional induced polarization–resistivity sections allowed for precise delineation of a conductive zone associated with the karst aquifer, le magnetics allowed for the definition of a neighbour dyke. The techniques have great potential in the aid of groundwater exploration, contributing substantially to the reduction of interpretation ambiguity. Focused source electromagnetic method/differentially normalized method/ approaches show that a simple linear combination of the conventional geoelectric data is able to remove the geological noise and provide the vertical focusing of the electric current.