瞬变电磁场的直接时域数值分析

为了深入了解瞬变电磁场的勘探原理,直接在时间域对负阶跃脉冲激发的二维瞬态场进行了数值分析.采用的方法是从反映电磁场基本规律的麦克斯韦方程组出发,导出时域电场的齐次扩散方程,对所研究的空间区域作差分离散,源作为初始条件加入,利用准静态近似处理空中边界,然后进行时间的逐步递推,由此展现瞬变电磁场在地下扩散随时间发展的全过程.通过模拟计算不同时刻瞬态电场在地下的分布形态及地面上感生电动势相应的变化,揭示了低阻异常体对感应涡流的聚集作用,低阻覆盖层对瞬变场扩散的减速作用,及瞬变场的延时效应.因此,瞬变电磁法对低阻体是敏感的,有上覆低阻层时探测同样的深度需要较长的时间,而延时效应瞬变场的晚期时段可反映埋藏较浅的异常体.     

Marine transient electromagnetic sounding of deep buried hydrocarbon reservoirs: principles,methodologies and limitations

The possibility of a time‐domain electromagnetic sounding method using excitation and measurement of vertical electric fields to search for and identify deeply buried reservoirs of hydrocarbons offshore is investigated. The method operates on source–receiver offsets, which are several times less than the depth of the reservoir. Geoelectric information is obtained from the transient responses recorded in the pauses between the pulses of electric current in the absence of the source field. The basics of the method, as well as its sensitivity, resolution, and the highest accessible depth of soundings for various geological conditions in a wide range of sea depths, are analyzed. For the analysis, 1D and 3D geoelectric models of hydrocarbon reservoirs are used. It is shown that under existing technologies of excitation and measurement of vertical electric fields, the highest accessible depth of soundings can be up to 4 km. Technology for the inversion and interpretation of transient responses is demonstrated on experimental data.     

Generalized Tikhonov's algorithm for accurate calculation of one-dimensional transient responses directly in time domain

In the last two decades, forward modelling for the time domain (transient) electromagnetic method has concentrated almost entirely on multi-dimensional models and algorithms. At the same time, the interpretation of real field data is still mainly one dimensional. This is caused by the lack of an efficient multi-dimensional acquisition procedure supported by sufficiently fast and reliable inversion software, on the one hand, and by the great efficiency of one-dimensional field set up and interpretation of the data on the other hand. The latter is particularly true for the short offset transient electromagnetic method, which is much less sensitive to multi-dimensional effects, compared to long offset methods. The most commonly used one-dimensional forward modelling algorithms are based on the spectral method, which requires calculating rapidly oscillating Fourier–Bessel (Hankel) integrals. Due to the very fast decay of short offset responses, the integrals become computationally unstable at late times of the transient process. Although this problem has been successfully solved for practically feasible measurement times of conventional short offset systems using transverse electric and mixed transverse electric and transverse magnetic fields, it turned out crucial for novel methods based on the use of unimodal transverse magnetic fields. These methods are much more sensitive to geoelectric parameters of the Earth in general and those of resistive targets, in particular, but they generate responses, which drop at late times significantly faster than those of conventional methods. Such behaviour of transverse magnetic fields represents severe computational problem for the spectral method, but is successfully solved by direct time domain algorithms. This article describes a generalization of the well-known Tikhonov's solution to a boundary value problem directly in time domain, which is applied to an arbitrary one-dimensional earth model excited by an arbitrary source. Contrary to existing spectral algorithms, the described method allows accurate calculations of both transverse electric and transverse magnetic transient responses at arbitrarily late times. On the other hand, it is more time efficient than finite-difference/finite element direct time domain algorithms and provides analytical late-stage asymptotic solutions.     

电性参数分块连续变化二维MT有限元数值模拟

为了易于模拟野外复杂地形和地下任意形状地电体模型,将有限元单元网格设计为三角单元;并考虑到野外实际勘探中,地球介质的电性参数均是连续变化的情况,单元内的场值和电性参数被设计为双线性变化;推导出二维起伏地形条件下大地电磁法有限元数值模拟算法;根据单元节点主场值和线性插值形函数间的关系,计算出单元节点的辅助场值;在二维起伏地形情况下,定义TE、TM模式视电阻率和阻抗相位.4个模型的计算的结果与解析法的均方根误差小于1%,地形模拟与前人的计算结果相符,模拟倾斜界面异常体,能有效的反映出其异常形态.     

基于自适应有限元的复电阻率法2.5维复杂构造电磁场模拟

复电阻率法在矿产、油气勘探调查中发挥着重要作用.为了认识复杂构造的复电阻率法电磁场的变化规律,本文基于自适应有限元方法,采用非结构化网格,引入Cole-Cole模型,实现了电偶源2.5D复电阻率法电磁场正演,可以模拟复杂地形和地电结构,正演结果更符合野外实际地质情况.通过将本文的计算结果与半空间模型解析解、层状介质和起伏模型结果进行对比,验证了本文算法的正确性.最后,基于复杂地电模型,通过正演模拟,系统分析了地形、激电参数、复杂构造对复电阻率法电磁场的影响特征.     

Joint 3D inversion of multiple electromagnetic datasets

Electromagnetic methods are routinely applied to image the subsurface from shallow to regional structures. Individual electromagnetic methods differ in their sensitivities towards resistive and conductive structures and in their exploration depths. If a good balance between different electromagnetic data can be be found, joint 3D inversion of multiple electromagnetic datasets can result in significantly better resolution of subsurface structures than the individual inversions. We present a weighting algorithm to combine magnetotelluric, controlled source electromagnetic, and geoelectric data. Magnetotelluric data are generally more sensitive to regional conductive structures, whereas controlled source electromagnetic and geoelectric data are better suited to recover more shallow and resistive structures. Our new scheme is based on weighting individual components of the total data gradient after each model update. Norms of individual data residuals are used to assess how much of the total data gradient must be assigned to each method to achieve a balanced contribution of all datasets for the joint inverse model. Synthetic inversion tests demonstrate advantages of joint inversion in general and also the influence of the weighting. In our tests, the controlled source electromagnetic data gradients are larger than those of the magnetotelluric and geoelectric datasets. Consequently, direct joint inversion of controlled source electromagnetic, magnetotelluric, and geoelectric data results in models that are mostly dominated by structures required by the controlled source electromagnetic data. Applying the new adaptive weighting scheme results in an inversion model that fits the data better and resembles more the original model. We used the modular system electromagnetic as a framework to implement the new joint inversion and briefly describe the new modules for forward modelling and their interfaces to the modular system electromagnetic package.     

电导率分块均匀的瞬变电磁25维有限元数值模拟

在吸收并修正部分前人工作的基础上，给出了电导率分块均匀的瞬变电磁25维有限单元法正演算法. 在该算法中，（1）采用在矩形网格中进一步三角细化的剖分方式，同时考虑到矩形单元中心节点的性质，求解线性方程组前用高斯消元法消除矩形网格中心节点上的待求未知量，这样一方面较准确地模拟出任意二维复杂地电断面，另一方面又大大地节省了计算量；（2） 采用计算二次场的算法，事先仅需获得电场和磁场沿地电构造走向方向两个分量的一次场，故而不但计算精度较高，而且不明显增加计算量. 最后，对几例典型模型进行正演，并与解析解对比，验证了本文方法的有效性.     

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。      

复杂地下异常体的可控源电磁法积分方程正演

可控源电磁法具有分辨率高及抗干扰能力强等特点,是一种重要的地电磁勘探方法.目前,可控源电磁法的高精度正演计算一直是其核心研究问题之一.传统积分方程法一般采用近似积分公式、简单矩形网格和近似的奇异性体积分计算技术,制约了体积分方程法处理复杂地下异常体的能力,降低了计算精度.针对上述问题,本文基于完全积分公式、四面体非结构化网格和奇异体积分的精确解析解来高精度求解复杂可控源电磁模型的正演响应.首先,从电场积分公式出发,推导了可控源电磁问题满足的积分方程;其次,借助于非结构化四面体网格离散技术,实现了地下复杂异常体的有效模拟.最后,利用散度定理把强奇异值体积分转换为一系列弱奇异性的面积分公式,并通过推导获得了这些弱奇异性的面积分公式的解析解,从而最终实现三维可控源电磁问题的高精度积分求解.以块状低阻体地电模型为测试模型,采用本文提出的积分方程方法获得的数值解与其他公开数值算法解进行对比分析,其对比结果具有高度的吻合性,验证了算法的正确性;同时,设计了球状及复杂地电模型进行算法收敛性测试,进一步验证算法的正确性以及能够处理地下复杂模型的能力.     

Numerical analysis of seismoelectric wave propagation in spatially confined geological units

Using numerical modelling, we investigate the evolution of seismoelectric effects induced by seismic excitation in spatially confined lithological units. Typical geometries represent clay lenses embedded in an aquifer or petroleum deposits in a host rock. In fluid‐saturated rocks, seismic waves can generate electromagnetic fields due to electrokinetic coupling mechanisms associated with such processes in the vicinity of the fluid‐mineral interface. Two seismoelectric phenomena are investigated: (1) the co‐seismic field associated with the seismic displacement at each point in a subsurface and (2) the interface response generated at layer boundaries. Our modelling uses a simplified time‐domain formulation of the coupled problem and an efficient 2D finite‐element implementation. To gain insight into the morphogenetic field behaviour of the seismoelectric effects, several numerical simulations for various target geometries were treated. Accordingly, we varied both the thickness of the confined units and the value of the electrical bulk conductivity in porous media. Analysis of these effects shows differences between interface responses for electrically conductive versus resistive units. So the pertinent contrast in electrical bulk conductivity controls the shape and structure of these seismoelectric conversion patterns. Moreover, the seismoelectric interface response captures both the petrophysical and geometrical characteristics of the geological unit. These models demonstrate the value of using seismoelectric interface response for reservoir characterization in either hydrogeological or hydrocarbon exploration studies.     

Transient electromagnetic surveys with unimodal transverse magnetic field: ideas and results

The theory behind transient electromagnetic surveys can be well described in terms of transverse magnetic and transverse electric modes. Soundings using transverse magnetic and transverse electric modes require different source configurations. In this study, we consider an alternating transverse magnetic field excitation by a circular electric dipole. The circular electric dipole transmitter is a horizontal analogue of the vertical electric dipole. Offshore surveys using circular electric dipole might represent an alternative to the conventional marine controlled‐source electromagnetic method at shallow sea and/or for exploring relatively small targets. Field acquisition is carried out by recording either electric or magnetic responses. Electric responses bear information on the 1D structure of a layered earth and successfully resolve high‐resistivity targets in marine surveys. Land‐based circular electric dipole soundings are affected by induced polarisation. On the contrary, magnetic responses are absent on the surface of a 1D earth, and as a result, they are very sensitive to any and even very small 3D conductivity perturbations. In addition, they are sensitive to induced polarisation or some other polarisation effects in the subsurface. At present, circular electric dipole transmitters and magnetic receivers are successfully used in on‐land mineral and petroleum exploration.     

三维CSAMT法非结构化网格有限元数值模拟

考虑到可控源音频大地电磁法(CSAMT)电偶极发射源与地下介质的三维结构特点,本文采用非结构化网格剖分技术,开展了三维CSAMT方法有限元数值模拟研究,将三维电磁场的背景场和异常场分别求解,避免了电偶极发射源的奇异性问题,并减小了计算区域.推导了三维异常电场遵循的有限元方程,加入散度条件进行约束以消除电场伪解;对非结构化网格单元采用高斯加权平均算法,得到了精度较高的异常磁场.针对层状介质模型,与积分方程法对比,验证了有限元算法的正确性;计算分析了典型三维地质模型的电磁响应,异常体反映明显.结果表明本文算法正确、可靠,适用于三维地质模型的CSAMT方法正反演研究.     

Cone-shaped source characteristics and inductance effect of transient electromagnetic method

Small multi-turn coil devices are used with the transient electromagnetic method (TEM) in areas with limited space, particularly in underground environments such as coal mines roadways and engineering tunnels, and for detecting shallow geological targets in environmental and engineering fields. However, the equipment involved has strong mutual inductance coupling, which causes a lengthy turn-offtime and a deep “blind zone”. This study proposes a new transmitter device with a conical-shape source and derives the radius formula of each coil and the mutual inductance coefficient of the cone. According to primary field characteristics, results of the two fields created, calculation of the conical-shaped source in a uniform medium using theoretical analysis, and a comparison of the inductance of the new device with that of the multi-turn coil, show that inductance of the multi-turn coil is nine times greater than that of the conical source with the same equivalent magnetic moment of 926.1 A·m². This indicates that the new source leads to a much shallower “blind zone.” Furthermore, increasing the bottom radius and turn of the cone creates a larger mutual inductance but increasing the cone height results in a lower mutual inductance. Using the superposition principle, the primary and secondary magnetic fields for a conical source in a homogeneous medium are calculated; results indicate that the magnetic behavior of the cone is the same as that of the multi-turn coils, but the transient responses of the secondary field and the total field are more stronger than those of the multi-turn coils. To study the transient response characteristics using a cone-shaped source in a layered earth, a numerical filtering algorithm is then developed using the fast Hankel transform and the improved cosine transform, again using the superposition principle. During development, an average apparent resistivity inverted from the induced electromotive force using each coil is defined to represent the comprehensive resistivity of the conical source. To verify the forward calculation method, the transient responses of H type models and KH type models are calculated, and data are inverted using a “smoke ring” inversion. The results of inversion have good agreement with original models and show that the forward calculation method is effective. The results of this study provide an option for solving the problem of a deep “blind zone” and also provide a theoretical indicator for further research.     

瞬变电磁2.5维反演中灵敏度矩阵计算方法(Ⅰ)

一种具体的反演方法要分三个重要的组成部分：1)反演算法;2)正演模拟;3)灵敏度矩阵计算．本文给出了快速计算瞬变电磁2．5维反演问题中灵敏度的简单推导．只需求解两个基本相同的边值问题(原始场和辅助场),然后通过在所针对的模型单元上,对上述两场的相应场量点乘,再进行面积积分,就可得到观测量对模型电导率参数的偏导数．模型上的计算结果和计算精度的分析将在本文的续篇(Ⅱ)中介绍。     

A study on the discrete image method for calculation of transient electromagnetic fields in geological media

We conducted a study on the numerical calculation and response analysis of a transient electromagnetic field generated by a ground source in geological media. One solution method, the traditional discrete image method, involves complex operation, and its digital filtering algorithm requires a large number of calculations. To solve these problems, we proposed an improved discrete image method, where the following are realized: the real number of the electromagnetic field solution based on the Gaver–Stehfest algorithm for approximate inversion, the exponential approximation of the objective kernel function using the Prony method, the transient electromagnetic field according to discrete image theory, and closed-form solution of the approximate coefficients. To verify the method, we tentatively calculated the transient electromagnetic field in a homogeneous model and compared it with the results obtained from the Hankel transform digital filtering method. The results show that the method has considerable accuracy and good applicability. We then used this method to calculate the transient electromagnetic field generated by a ground magnetic dipole source in a typical geoelectric model and analyzed the horizontal component response of the induced magnetic field obtained from the “ground excitation–stratum measurement” method. We reached the conclusion that the horizontal component response of a transient field is related to the geoelectric structure, observation time, spatial location, and others. The horizontal component response of the induced magnetic field reflects the eddy current field distribution and its vertical gradient variation. During the detection of abnormal objects, positions with a zero or comparatively large offset were selected for the drillhole measurements or a comparatively long observation delay was adopted to reduce the influence of the ambient field on the survey results. The discrete image method and forward calculation results in this paper can be used as references for relevant research.     

二维地电模型多参数反演方法及其在MT测深中的应用

二维地电模型电（电磁）测深法参数化反演,宜采用多参数反演方案.文中导出了多参数反演的基本数学模型,并进行了分解处理,使之变成与剖面上反演点数相等的多个相互独立的小数学模型的组合,用广义逆法逐个求解,即可得一次迭代中整个二维模型参数的修改量.大地电磁测深理论模型和实测数据反演结果表明所提出的二维多参数反演方法可行.它具有稳定的收敛性、较快的收敛速度、能适应较复杂构造的反演和计算量小等特点.     

基于二次场电导率分块连续变化的三维可控源电磁有限元数值模拟

从电偶源三维地电断面可控源电磁法的二次电场边值问题及其变分问题出发,采用任意六面体单元对研究区域进行剖分,并且在单元分析中同时对电导率及二次电场进行三线性插值,实现电导率分块连续变化情况下,基于二次场的可控源电磁三维有限元数值模拟.这个新的可控源电磁三维正演方法可以模拟实际勘探中地下任意形状及电性参数连续变化的复杂模型.理论模型的计算结果表明,均匀大地计算的视电阻率误差和相位误差分别为0.002%和0.0005°.分层连续变化模型的有限元计算结果表明,其与对应的分层均匀模型解析结果有明显差异.三维异常体组合模型以及倾斜异常体等复杂模型的有限元计算结果也有效地反映了异常形态.     

Interpretation of magnetic resonance soundings in rocks with high electrical conductivity

Magnetic resonance sounding (MRS) is an electromagnetic method designed for groundwater investigations. MRS can be applied not only for studying fresh-water aquifers, but also in areas where intrusion of saline water is rendering the subsurface electrically conductive. In the presence of rocks with a high electrical-conductivity attenuation and a phase shift of the MRS signal may influence the efficiency of the MRS method. We investigated the performance of MRS for allowing us to propose a procedure for interpreting MRS data under these conditions. For numerical modeling, we considered a subsurface with a resistivity between 0.5 and 10 Ω m. The results show that the depth of investigation with MRS depends upon the electrical conductivity of groundwater and surrounding rocks, on the depth of the saline water layer, and on the amount of fresh water above the saline water. For interpreting MRS measurements, the electrical conductivity of the subsurface is routinely measured with an electrical or electromagnetic method. However, due to the equivalence problem, the result obtained with these methods may be not unique. Hence, we investigated the influence of the uncertainty in conductivity distribution provided by transient electromagnetic measurements (TEM) on MRS results. It was found that the uncertainty in TEM results has an insignificant effect on MRS.     

海底油气藏及天然气水合物的时频电磁辨识

提出了伪随机多频海洋电磁法观测方案.采用伪随机多频信号作为激励场源,多偏移距同线偶极-偶极同时观测,相关辨识海底地电系统的频率特性和冲激响应,可以在时间域和频率域同时辨识海底高阻薄层.在时间域,瞬变冲激时刻可以直接指示海底地层电导率的变化;在频率域,利用多个频率的电场响应计算的频散率及其道闻变化量,相对相位道间变化量对高阻薄层有很好的反映.从而实现对海底油气及天然气水合物的多参数辨识.     

多通道瞬变电磁m序列全时正演模拟与反演

传统瞬变电磁方法主要用于金属矿勘查,无法满足油气资源高阻目标体的勘探需要.多通道瞬变电磁(MTEM)系统的出现解决了这一问题.该方法采用伪随机序列发射波形和拟地震观测方式,测量同线电场分量,记录全时发射电流及多道观测数据,实现对高阻薄层的高精度探测.鉴于国内对此方法的研究还处于理论探索阶段,尚未进行相应的仿真模拟和数据处理工作,本文针对m序列发射波形多通道瞬变电磁法的全时正演模拟和反演解释进行研究,为国内正在进行的MTEM仪器系统研发及数据解释提供理论指导.我们利用方波响应移位叠加和电流导数与阶跃响应褶积两种方法实现理论m序列和实际发射波形的全时正演模拟;再通过相关辨识技术,削弱噪声影响,计算脉冲响应;最后对积分得到的阶跃响应进行共中心点道集数据联合反演,获取地下电性分布信息.