均匀半空间瞬变电磁场直接时域响应数值分析

近源时域电磁场具有信号强、探测深度大和精度高等优点,但传统瞬变电磁场理论中偶极子近似在近源区会引起较大误差,推导瞬变电磁场直接时域解析式是解决这一问题的关键.本文在点电荷微元假设下通过时域格林函数,采用分离变量等方法推导出了上半空间一次有源波动场和反射波的时域解析式和下半空间二次无源波动场的时域解析式,结合均匀半空间瞬变电磁场的边界条件给出了均匀半空间瞬变电磁场的直接时域解析式,进而利用第一型曲线积分,通过沿回线源叠加推导出圆回线源在瞬变电磁场中的直接时域解析式.然后在半空间表面上,与传统的电偶极源假设下的表达式作了比较.数值结果表明两者在远源区的计算结果相差甚微,而近源区则存在很大误差.本文利用真正点元（点电荷）严密推导给出的均匀半空间表面上瞬变电磁场的直接时域解析式适用于全场区探测,克服了偶极子假设下只适用远场区的不足,为瞬变电磁法的进一步发展和实际勘探提供了新的理论基础.     

偶极子假设引起的大回线源瞬变电磁响应偏差分析

偶极子假设下的场点近似解与场点的瞬变电磁精确解存在一定的误差,文中对偶极子假设引起的误差进行了探索性研究.首先分析了由恒定电流偶极子公式“比拟”出的谐变偶极子位函数解.分别计算了静态场中磁偶极子和电偶极子的近似解与各自对应的未做偶极子假设的电流环和载流导线的精确解之间的误差值,然后分析了谐变偶极子微元与点电荷微元的误差...     

Electromagnetic fields generated by finite‐length wire sources: comparison with point dipole solutions

In present‐day land and marine controlled‐source electromagnetic (CSEM) surveys, electromagnetic fields are commonly generated using wires that are hundreds of metres long. Nevertheless, simulations of CSEM data often approximate these sources as point dipoles. Although this is justified for sufficiently large source‐receiver distances, many real surveys include frequencies and distances at which the dipole approximation is inaccurate. For 1D layered media, electromagnetic (EM) fields for point dipole sources can be computed using well‐known quasi‐analytical solutions and fields for sources of finite length can be synthesized by superposing point dipole fields. However, the calculation of numerous point dipole fields is computationally expensive, requiring a large number of numerical integral evaluations. We combine a more efficient representation of finite‐length sources in terms of components related to the wire and its end points with very general expressions for EM fields in 1D layered media. We thus obtain a formulation that requires fewer numerical integrations than the superposition of dipole fields, permits source and receiver placement at any depth within the layer stack and can also easily be integrated into 3D modelling algorithms. Complex source geometries, such as wires bent due to surface obstructions, can be simulated by segmenting the wire and computing the responses for each segment separately. We first describe our finite‐length wire expressions and then present 1D and 3D examples of EM fields due to finite‐length sources for typical land and marine survey geometries and discuss differences to point dipole fields.     

短偏移距电磁探测技术概述

由于人工源电磁探测效果与收发距离有一定关系,本文首先分析了收发距离为零的中心回线源瞬变电磁法（Transient Electromagnetic Method,TEM）视电阻率定义和算法特点,回溯了从圆形回线到矩形的修正式中心回线装置的发展过程;概述了从中心回线发展到接地导线源短偏移瞬变电磁（Short-Offset TEM,SOTEM）理论上的可行性;列举了将LOTEM（Long-Offset TEM）从数倍于探测深度的观测区推进到近源区后的探测实例.对于频率域人工源电磁法,介绍了起源于MT（Magneto-Telluric）的CSAMT（Controlled Source Audio-frequency Magneto-Telluric）与电磁频率测深法不同发展道路.电磁频率测深将观测区从远区推进到了中区;广域电磁法通过全区视电阻率新定义不仅提高了解释精度,而且将传统CSAMT远场观测模式推进到中区探测模式;最后指出,如能采用新的点微元假设计算方法,可有望分离自有场和辐射场,实现频域电磁近源探测.     

瞬变电磁场时域格林函数解

近源时间域电磁场具有信号强、探测深度大、精度高等优点,但传统勘探电磁场理论中偶极子近似在近源会引起较大误差,导致这一优势的发挥受到了制约.开展直接时间域电磁场解析式研究,是解决这一问题的途径之一.本文提出在点电荷微元假设下,引入时域格林函数,求取瞬变电磁场时间域解析解.采用积分运算法,把电磁场阻尼波动方程的求解问题转化为求其格林函数积分形式解的问题;建立辅助路径解决奇点问题,利用复分析中的约当引理、留数定理和广义函数等理论和方法,推导计算出时间域格林函数的时空四重广义积分.得到达朗贝尔方程的直接时域格林函数精确解析式,与传统方法“比拟”出的公式具有相同的形式,验证了本文推导的时域格林函数解析公式的正确性;推导出扩散方程的直接时间域解析解.通过与时变点电荷源时间域的电磁响应近似表达式进行对比,得出本文所推导的公式计算精度较高的结论;建立了全空间回线源瞬变电磁场问题的直接时间域求解公式.为解决全场区瞬变电磁场精细探测直接时域解析问题提供了基础理论.     

复杂场源形态的海洋可控源电磁三维正演

在使用电偶极发射源的可控源电磁法(CSEM)勘探中,发射源的方位、长度、形状等对观测数据有重要的影响,然而现有的大部分三维数值模拟方法没有全面地将这些因素考虑进来,很多都只能应对非常简单的场源形态,例如单一方位的点电偶极子,这有可能显著降低模拟结果的准确性.本文实现了基于交错网格有限体积(FV)离散的海洋CSEM三维正演算法,能够模拟形态相对复杂的场源,包括任意方位的有限长直导线和弯曲导线发射源.该算法使用一次场/二次场方法,只需对二次场使用FV法求解,避免了场源的奇异性问题;一次场的计算为一维正演问题,使用准解析法求解,并且只要在计算一次场时考虑复杂的场源形态便可以实现同样场源的三维正演.通过与一维理论模型的解析解对比验证了三维程序的准确性,并针对三维理论模型进行了一系列正演测试,初步考察了场源形态对三维正演结果的影响.     

海底电性源频率域CSEM勘探建模及水深影响分析

为了探索我国海域油气和水合物等高阻目标体CSEM勘探的可行性和方法技术,本文研究了在海水中水平电性源激励下有限水深海洋地电模型的频率域电磁响应,为进一步的1D和3D仿真计算奠定了理论基础.在推导电磁响应公式时,首先给出了各层介质的Lorentz势,然后根据Coulomb势与Lorentz势的关系,得到了各层介质的Coulomb势.各层介质中的电磁场均可以由Lorentz势或者Coulomb势计算得到,但在有限元计算时Coulomb势具有优势.长导线源的电磁场和势函数可以由电偶源的电磁场和势函数沿导线长度积分得到.文中具体给出了海水中水平电偶源和长导线源在海水层的电磁场公式,并根据该公式计算了不同水深环境下海底表面的电磁场分布,分析了海水深度对海底油气储层电磁异常的影响.结果表明,随着水深减小,异常幅度和形态特征发生明显变化.当水深很浅时(如50 m),只有同线方向的E_x和E_z两个电场分量存在明显异常.最后,以两个已知海底油田为例,计算了不同水深环境下可观测到的电场异常,展示了电性源频率域CSEM在海底勘探中(包括浅海环境)的良好应用前景.对于该方法实用化过程中还需进一步解决的问题,文中结尾部分也进行了初步探讨.     

井间电磁测量的2．5维层析成像方法

利用正则化最小二乘反演方法实现了井间电磁测量数据的层析成像,对井间地层电阻率进行了重建。在成像算法中,我们假设了井间电磁的激发与接收采用电磁偶极子源,井间介质仅在二维（xoz）平面内变化。在数值模拟中,通过对构造走向（y方向）的Fourier变换,将三维电磁场问题转化为一系列二维问题,用等参有限元方法在波数域求解,使实际地层模型的处理得以实现。对于波数域中每个波数对应的电磁场方程采用等参有限元求解,并用高斯积分将波数域解变换为空间域电磁场。利用源与接收器电磁场的互易原理,实现了电磁场响应对电导率分布灵敏度的快速计算。针对正演模拟中源点的奇异性,我们采用具有一定面积的伪艿函数表达源电流分布,使数值解精度得到提高。用层状介质的解析解与数值计算结果的对比,验证了模拟算法的精度。用介质扰动产生的电磁场变化检验互易性定理计算灵敏度的有效性。对简单块状模型、斜向裂缝带模型及“大”字模型的模拟数据成像结果表明,本文介绍的层析成像方法是正确有效的。     

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.     

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.     

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.     

基于电场矢量波动方程的三维可控源电磁法有限单元法数值模拟

从可控源电磁法的基本原理出发,推导了基于电场矢量波动方程的三维边值问题,利用广义变分原理,把边值问题转换为变分问题,并引入散度条件,避免了伪解的出现,使有限元计算在理论上更加完备.在准静态近似条件下,把水平电偶极子在空中和大地的远区电场闭合表达式作为有限元计算中的区域外边界条件,解决了边界条件加载的困难;把应用于地震模拟中的伪delta函数引入到可控源电磁法中的三维有限元模拟中,消除了源点的奇异性,提高了方程组的稳定性.通过对均匀大地和层状介质模型的模拟,检验了程序的正确性,并对典型的地质体模型进行了数值模拟,分析了其变化规律.     

THE ELECTRICAL CURRENT PATTERN INDUCED BY AN OSCILLATING MAGNETIC DIPOLE IN A SEMI-INFINITE THIN PLATE OF INFINITESIMAL RESISTIVITY*

Several papers have been published in which the electromagnetic anomalies are described that are produced by conductive ore bodies of different shapes. No publications are available, however, in which the electrical current pattern is described that is induced in these ore bodies. Yet an insight in this electrical current pattern would be valuable in order to assess the possibilities of different electromagnetic techniques, for instance with regard to the determination of the dip and of the depth extent of plate shaped ore bodies. In the present paper computations are given of the electrical current pattern induced by an oscillating magnetic dipole in a semi infinite plate shaped orebody of infinitesimal thickness, in which the penetration depth of the current is infinitesimal to a higher order than the thickness of the plate. The computations are based upon an equation derived by Wesley for the magnetic field produced in these conditions, combined with the relation between the electrical current density in a laminar sheet and the magnetic field produced by this current at the surface of the sheet. The results of the computations show that, if the horizontal distance between the dipole source and the sheet is sufficiently small, the maximum current density of the return current may occur at a depth below the upper edge of the sheet which is appreciably smaller than the depth of the upper edge of the sheet below the surface. The depth of the return current becomes large when the horizontal distance between the source and the sheet is large.     

CSAMT勘探中场区、记录规则、阴影及场源复印效应的解析研究

由矢量位导出均匀大地表面上水平接地谐变电偶极子地下电磁场的闭合表达式, 将地层波和地面波显式地区分开来, 据此定义了与远区场和近区场对应的地面波区和地层波区. 对长期困扰CSAMT勘探工作者的记录点问题、阴影和场源复印效应问题给出了物理解释. 由地层波与地面波之比给出了定量划分场区的方法, 每一场分量最佳记录规则下的条件和判断是产生阴影和场源复印效应的前提. 山西沁水盆地CSAMT勘探覆盖点的推断结果表明, 阴影和场源复印效应是由地层波所携带的源与观测点之间、源下方真实地质情况的信息决定, 是可以利用的.     

基于局部加密非结构网格的海洋可控源电磁法三维有限元正演

本文基于非结构网格实现了海洋可控源电磁法三维有限元正演模拟.该算法采用完全非结构网格剖分,可以模拟任意起伏地形和复杂地电模型.为了避免场源的奇异性,采用一次场/二次场分解算法,一次场由基于Schelkunoff势函数的一维解析公式得到.为了提高算法的精度和效率,采用对测点附近单元和异常体区域进行体积约束加密的方法,实现了非结构网格的局部加密.一、二维模型计算和分析表明,本文采用的局部加密方法能够明显地改善算法的精度,最大相对误差基本在1%以内.对三维模型计算及对比分析,说明了该算法对三维可控源电磁正演的实用性.复杂海底地形模型的正演模拟表明,海底地形对电磁场的影响很大,在进行海洋可控源电磁资料解释时,地形的影响有必要考虑在内.     

The electromagnetic response of a horizontal electric dipole buried in a multi‐layered earth

The electromagnetic response of a horizontal electric dipole transmitter in the presence of a conductive, layered earth is important in a number of geophysical applications, ranging from controlled‐source audio‐frequency magnetotellurics to borehole geophysics to marine electromagnetics. The problem has been thoroughly studied for more than a century, starting from a dipole resting on the surface of a half‐space and subsequently advancing all the way to a transmitter buried within a stack of anisotropic layers. The solution is still relevant today. For example, it is useful for one‐dimensional modelling and interpretation, as well as to provide background fields for two‐ and three‐dimensional modelling methods such as integral equation or primary–secondary field formulations. This tutorial borrows elements from the many texts and papers on the topic and combines them into what we believe is a helpful guide to performing layered earth electromagnetic field calculations. It is not intended to replace any of the existing work on the subject. However, we have found that this combination of elements is particularly effective in teaching electromagnetic theory and providing a basis for algorithmic development. Readers will be able to calculate electric and magnetic fields at any point in or above the earth, produced by a transmitter at any location. As an illustrative example, we calculate the fields of a dipole buried in a multi‐layered anisotropic earth to demonstrate how the theory that developed in this tutorial can be implemented in practice; we then use the example to examine the diffusion of volume charge density within anisotropic media—a rarely visualised process. The algorithm is internally validated by comparing the response of many thin layers with alternating high and low conductivity values to the theoretically equivalent (yet algorithmically simpler) anisotropic solution, as well as externally validated against an independent algorithm.     

长偶极大功率可控源电磁波响应特征研究

地球物理学中关于电磁波勘探研究通常采用的是地球半空间模型.然而,对于几十公里的有限长电缆源（长偶极源）,远距离电磁波场探测必须要考虑电离层的影响,它是一个全空间问题.关于包含电离层、空气层和地球介质（我们称“地-电离层”模式）的电磁波场特征的研究在国外较少,国内几乎是空白.本文采用全空间积分方程法首先对小尺度的可控源电磁波场特征进行了研究,由于此时电离层的影响可忽略,它应该和半空间成熟的CSAMT模拟结果一致,对比结果表明,二者是一致的,验证了全空间模拟方法的可靠性和有效性.随后进行了50 km长电缆电离层和空气层高度都为100 km的“地-电离层”模式大尺度电磁波场模拟,以探讨大尺度可控源电磁波场的特征.给定频率的“地-电离层”模式电磁场的衰减曲线表明长电缆远距离电磁波场由于受电离层的作用存在衰减逐渐变小的过渡场和衰减变小的波导场.为了探讨复杂介质“地-电离层”模式电磁波特征,对“地-电离层”模式的典型地盾和地台多层介质模型进行了数值模拟,得到了偶极源长度50 km、电流200A、收发距离远达1600 km和2500 km的合理的电磁场结果.最后,对一简单含油储层结构模型进行了长偶极、大功率、远距离电磁波场响应计算.储层横向不均匀复杂结构模拟的结果表明,考虑电离层和大气层的“地-电离层”模式大尺度深层复杂介质模拟时,电磁场对深部目标体仍有很好的异常响应.     

Induction in a layered plane earth by uniform and non-uniform source fields

A review of electromagnetic induction in a multi-layered earth is built around a development of the general theory from first principles. Induction by transient and periodic fields and by dipole and electrojet sources are discussed and the method of complex images is briefly described. The review concludes with a discussion of induction by elementary harmonic sources whose non-uniformity is characterised by Price's ν-parameter and which include the uniform source field (ν=0) as a special case. The conditions under which the source may be assumed uniform for computing the surface impedance and other ratios of field components are examined.     

水平分层孔隙介质中点源激发的震电波场数值模拟及分析

为认识地震波诱导的电磁场的特性,本文研究地震波在孔隙介质中由于动电效应引起的电磁场.基于Pride弹性-电磁耦合方程组推导了双力偶震源对应的位移-应力-电磁场间断向量的表达式,模拟了双力偶源激发的震电波场.作为比较,还模拟了爆炸点源激发的震电波场.结果表明：存在伴随纵波的电场,其各分量的波形与固相位移对应分量的波形相似,但相位相反;存在伴随横波的磁场,其波形与固相位移波形相似;双力偶震源还激发出了独立传播的辐射电磁场,其速度比纵波至少高一个数量级,几乎是“瞬间同时”到达了每个接收器,但是其强度比伴随电磁场小得多,且随着源距增大而迅速减小.本文研究还表明：伴随纵波的电场强度不仅与地震纵波幅度和动电耦合系数有关,还与由介质孔隙结构决定的流-固两相动力协调性有关,存在一种动力协调介质,纵波在这种介质中不引起电场.