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...     

Turning off low and high currents in a transmitter loop used in the transient electromagnetic method

In near-surface transient electromagnetic studies, it is desirable to measure the transient response starting from the earliest possible time. This requires the current in the transmitter loop to be switched off quickly, which necessitates working with a low transmitter current. As for deep-target transient electromagnetic studies, the transmitter current is as high as possible. The transmitter current's turn-off waveform and total duration affect the transient voltage response, especially at early times, which is to be accounted for when interpreting transient electromagnetic data. This article discusses the difference in switching off low and high current in a horizontal loop used as the source of the primary magnetic field in the transient electromagnetic method. Low and high currents are turned off in fundamentally different ways. When the current to be switched off is low, the loop can be represented as a symmetric combination of two transmission lines grounded at the middle of the loop perimeter. Such a representation of a loop allows calculating the current turn-off waveform at any point of the loop. The waveform and total duration of switching off a low current does not depend on its magnitude, but is determined by the period of natural oscillations of the current in the loop and the resistance of a shunting resistor. Switching off a low current in a loop can be represented as the sum of stepped current waves travelling along the loop wire. As a consequence, the current at different points of the loop perimeter is turned off at different times. In contrast to a low current, a high current is switched off linearly in time and synchronously at all points of the loop perimeter. The wave phenomena appear only at the very beginning of the current shutdown for a time interval that is much less than the total current turn-off duration. Presentation of the loop using a simple lumped-circuit model predicts the waveform and duration of the high current turn-off that coincide with the measured ones. There are two reasons why the article may be of interest to those engaged in the theory and/or practice of electromagnetic geophysical methods. First, it contributes to a general understanding of how the current in the transmitter loop is turned off. Second, the article shows how the parameters of a transmitter loop determine the current turn-off duration and thus the minimum depth of the transient electromagnetic sounding method.     

考虑关断时间的回线源激发TEM三维时域有限差分正演

从麦克斯韦旋度方程出发可以直接导出瞬变电磁场扩散方程,然而扩散方程不含电场对时间的一阶导数,不能构成显式的时域有限差分方程,借鉴du Fort-Frankel有限差分离散方法引入虚拟位移电流项构建显式时域有限差分方程.对Wang和Hohmann的经典时域算法进行了两点改进:第一,通过将矩形回线源电流密度加入麦克斯韦方程组的安培环路定理方程,实现回线源瞬变电磁激发源加入;第二,在计算中考虑关断时间.第一点改进使时域有限差分方程考虑了一次场的计算,并且源的计算不再依赖均匀半空间模型响应作为初始条件,使算法能够适应表层电阻率不均匀时的三维复杂模型.由于实际观测中不可能出现阶跃电流的关断形式,第二点改进可以方便设置发射电流下降沿.采用改进的三维时域有限差分正演算法对均匀半空间模型、四类三层模型、均匀半空间中含有低阻块体模型进行了计算并分别与解析解、线性数字滤波解、积分方程解和Wang的三维时域有限差分解进行了对比验证.以H模型为例,采用建立的三维时域有限差分正演算法计算了不同关断时间的斜阶跃脉冲回线源瞬变电磁中心点感应电动势衰减曲线.以实际地质资料为基础,构建包含两层采空区的三维复杂模型,以1 μs的极短关断时间进行了复杂模型定回线源瞬变电磁响应计算,并计算了该复杂模型的视电阻率曲线.     

频率域2维电磁测深资料的RRI反演

本文将大地电磁反演中的RRI方法应用于线源频率测深模型资料的反演中.当背景电导率变化很小时,可用变化前的电场来近似代替变化后的电场,从而在反演方程的推导过程中将有源电磁场中的源项消掉,得到和大地电磁场相同的反演方程,使有源电磁波的反演也可以应用RRI方法.反演过程中所需要的模型资料通过有限元方法得到,该资料不需做近场校正,直接用适合于有源电磁场的RRI方法反演,避免了近场校正带来的误差.数值模型结果证明该方法是可行的.最后,用RRI方法讨论了当源和目标区间存在低阻异常体时只对目标区反演的可行性,对实际工作的解释有一定的指导意义.     

Insight into the marine controlled‐source electromagnetic signal propagation

In marine controlled‐source electromagnetic (CSEM) surveys the subsurface is explored by emitting low‐frequency signals from an electric dipole source close to the sea‐bed. The main goal is often to detect and describe possible thin resistive layers beneath the sea‐bed. To gain insight into how CSEM signals propagate, it is informative to study a stratified model. The electromagnetic field is then given in terms of integrals over TE‐ and TM‐polarized plane‐wave constituents. An asymptotic evaluation of the field integrals for large propagation distances results in explicit spatial expressions for the field components and the derived expressions can be used to analyse how the CSEM signals propagate. There are two major signal pathways in a standard CSEM model. One of these pathways is via the thin resistive layer and the resulting response is accounted for by a pole in the reflection response for the TM mode. The signal is propagating nearly vertically down to the resistor from the source, then guided while attenuated along the reservoir, before propagating nearly vertically up to the receiver. The response is slightly altered by the sea‐bed interface and further modified in shallow water due to multiple reflections between the sea‐surface and sea‐bed at both the source and receiver sides. The other major signal pathway is via the resistive air half‐space, the so‐called airwave. The airwave is generated by the TE mode and interacts with the subsurface via vertically propagating signals reflected between the sea‐surface and subsurface at both the source and receiver sides.     

Coil response inversion for very early time modelling of helicopter‐borne time‐domain electromagnetic data and mapping of near‐surface geological layers

Very early times in the order of 2–3 μs from the end of the turn‐off ramp for time‐domain electromagnetic systems are crucial for obtaining a detailed resolution of the near‐surface geology in the depth interval 0–20 m. For transient electromagnetic systems working in the off time, an electric current is abruptly turned off in a large transmitter loop causing a secondary electromagnetic field to be generated by the eddy currents induced in the ground. Often, however, there is still a residual primary field generated by remaining slowly decaying currents in the transmitter loop. The decay disturbs or biases the earth response data at the very early times. These biased data must be culled, or some specific processing must be applied in order to compensate or remove the residual primary field. As the bias response can be attributed to decaying currents with its time constantly controlled by the geometry of the transmitter loop, we denote it the ‘Coil Response’. The modelling of a helicopter‐borne time‐domain system by an equivalent electronic circuit shows that the time decay of the coil response remains identical whatever the position of the receiver loop, which is confirmed by field measurements. The modelling also shows that the coil response has a theoretical zero location and positioning the receiver coil at the zero location eliminates the coil response completely. However, spatial variations of the coil response around the zero location are not insignificant and even a few cm deformation of the carrier frame will introduce a small coil response. Here we present an approach for subtracting the coil response from the data by measuring it at high altitudes and then including an extra shift factor into the inversion scheme. The scheme is successfully applied to data from the SkyTEM system and enables the use of very early time gates, as early as 2–3 μs from the end of the ramp, or 5–6 μs from the beginning of the ramp. Applied to a large‐scale airborne electromagnetic survey, the coil response compensation provides airborne electromagnetic methods with a hitherto unseen good resolution of shallow geological layers in the depth interval 0–20 m. This is proved by comparing results from the airborne electromagnetic survey to more than 100 km of Electrical Resistivity Tomography measured with 5 m electrode spacing.     

Three‐dimensional controlled‐source electromagnetic modelling with a well casing as a grounded source: a hybrid method of moments and finite element scheme

Steel well casings in or near a hydrocarbon reservoir can be used as source electrodes in time‐lapse monitoring using grounded line electromagnetic methods. A requisite component of carrying out such monitoring is the capability to numerically model the electromagnetic response of a set of source electrodes of finite length. We present a modelling algorithm using the finite‐element method for calculating the electromagnetic response of a three‐dimensional conductivity model excited using a vertical steel‐cased borehole as a source. The method is based on a combination of the method of moments and the Coulomb‐gauged primary–secondary potential formulation. Using the method of moments, we obtain the primary field in a half‐space due to an energized vertical steel casing by dividing the casing into a set of segments, each assumed to carry a piecewise constant alternating current density. The primary field is then substituted into the primary–secondary potential finite‐element formulation of the three‐dimensional problem to obtain the secondary field. To validate the algorithm, we compare our numerical results with: (i) the analytical solution for an infinite length casing in a whole space, excited by a line source, and (ii) a three‐layered Earth model without a casing. The agreement between the numerical and analytical solutions demonstrates the effectiveness of our algorithm. As an illustration, we also present the time‐lapse electromagnetic response of a synthetic model representing a gas reservoir undergoing water flooding.     

Signal detectability of marine electromagnetic methods in the exploration of resistive targets

We compare selected marine electromagnetic methods for sensitivity to the presence of relatively thin resistive targets (e.g., hydrocarbons, gas hydrates, fresh groundwater, etc.). The study includes the conventional controlled‐source electromagnetic method, the recently introduced transient electromagnetic prospecting with vertical electric lines method, and the novel marine circular electric dipole method, which is still in the stage of theoretical development. The comparison is based on general physical considerations, analytical (mainly asymptotic) analysis, and rigorous one‐dimensional and multidimensional forward modelling. It is shown that transient electromagnetic prospecting with vertical electric lines and marine circular electric dipole methods represent an alternative to the conventional controlled‐source electromagnetic method at shallow sea, where the latter becomes less efficient due to the air‐wave phenomenon. Since both former methods are essentially short‐offset time‐domain techniques, they exhibit a much better lateral resolution than the controlled‐source electromagnetic method in both shallow sea and deep sea. The greatest shortcoming of the transient electromagnetic prospecting with vertical electric lines and marine circular electric dipole methods comes from the difficulties in accurately assembling the transmitter antenna within the marine environment. This makes these methods significantly less practical than the controlled‐source electromagnetic method. Consequently, the controlled‐source electromagnetic method remains the leading marine electromagnetic technique in the exploration of large resistive targets in deep sea. However, exploring laterally small targets in deep sea and both small and large targets in shallow sea might require the use of the less practical transient electromagnetic prospecting with vertical electric lines and/or marine circular electric dipole method as a desirable alternative to the controlled‐source electromagnetic method.     

瞬变电磁法中心回线装置资料解释方法的改进

中心回线装置是瞬变电磁勘探中最常用的装置之一.中心回线装置的视电阻率一般从回线中心点场的公式出发导出.在现场实际施工中,为提高工作效率,把发射回线中部三分之一的区域作为观测范围.通过对场分布特征的分析研究表明,与中心点相比,观测区边缘处的感应电动势数值偏离达15%~25%,这与广泛存在于华北型煤系中赋存深度为400~1000 m的陷落柱、导水小断层等引起的异常相比,已经不可忽略.大定源回线公式可以准确地表示任意场点的感应电动势,由此导出视电阻率无边缘效应影响;观测按照中心回线方式并保持在近区进行,可使感应电动势和视电阻率之间的转换简单而直接.理论和实际应用结果表明,这些措施进一步提高了瞬变电磁探测中心回线方法的探测精度.在有上覆低阻屏蔽层的情况下,对埋深500~700 m的陷落柱给出了明显的异常反映,并被井下掘进所验证.     

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.     

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。     

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.     

时变海面与其上方导体平板的复合电磁散射研究

应用当前的数值方法求解动态海面与目标的复合电磁散射,由于海面的变化,在不同时刻需要对阻抗矩阵各元素及海面表面电流重新求解,因而要耗费大量内存和运算量.为了克服这一问题,本文应用物理光学(PO)近似求解了导体海面表面电流及导体平板的一阶散射场,应用基尔霍夫近似给出了海面的后向散射场,同时借助互易性定理降低了求解平板和海面之间二次耦合散射场的难度,讨论了平板尺寸、风速等对后向复合散射场的影响.另外,本文还推导出了耦合散射场多普勒谱频移的理论公式,详细分析了复合后向散射场的Doppler 频谱特性.     

ELECTROMAGNETIC SOUNDING NEAR A LARGE SQUARE LOOP SOURCE OF CURRENT*

An electromagnetic sounding experiment with a large square loop as source was carried out on the dried-up bed of a water reservoir near the town of Dharmavaram in Andhra Pradesh. The sounding was performed in both geometric and parametric modes, and involved measurements of phase as well as amplitude of the vertical magnetic field inside and outside the loop. The six-frequency EM system used for the experiment was found to be a workable system for electromagnetic sounding. The results of the experiment more or less confirm the conclusions from theoretical modeling. They also show that even though the earth is not always electrically horizontally layered over a sufficiently large lateral extent for the one-dimensional model to be strictly valid, it is still possible to apply such modeling to sounding curves taken one part at a time and obtain layer parameters which check qualitatively with the layer parameters obtained from direct current resistivity sounding.     

基于各向异性分析的微地震震源矢量场重建和裂缝解释

针对微地震裂缝解释的复杂性,从震源矢量场的重建开始研究,在研究VTI介质速度模型各向异性条件下的走时和透射系数的变化特征基础上,形成了各向异性条件下的群、相速度及透射系数的计算方法.针对多级检波器水平分量朝向的多向性特点,提出了多级检波器水平分量的偏振分析方法,得到了完整的水平特征矢量,克服了单级检波器水平分量偏振分析构建特征矢量信息不全的问题,形成了高精度微地震事件定位方法,实现各向异性VTI介质速度模型的高斯束微地震格林函数正演模拟.利用格林函数模拟场、观测记录场,从构建完整场研究入手,重建震源矢量场.根据重建的震源矢量场,提出了裂缝解释的全新的系列方法,包括单条裂缝、裂缝网络的解释方法.通过实际资料的测试分析,验证了研究技术的实用性.     

瞬变电磁法深度探测正演模拟研究

针对当前瞬变电磁法探测能力有限的问题,利用一次磁场理论公式,分析相同磁矩下、不同发射线圈一次磁场分布及衰减规律,从而确定其信号深度影响范围;对水平层状介质相同磁矩下、不同发射线圈的二次场进行数值模拟,采用Guptasarma和Singh滤波算法及余弦变换法,利用均匀半空间解析公式进行验证,并对不同正演模型结果进行分析,总结发射磁矩决定探测深度大小。对磁矩相同条件下产生的结果数据进行拟合,得出有效探测深度与线圈边长2倍相当的结论,可为野外矿井生产与工程勘探提供施工布置与定量解释的指导依据,从而提高野外工作效率。     

Fast and accurate three‐dimensional controlled source electromagnetic modelling†

We present a fast approximate method for three‐dimensional low frequency controlled source electro‐magnetic modeling. We apply the method to a synthetic model in a typical marine controlled source electromagnetic scenario, where conductivity and permittivity are different from the known background medium. For 3D configurations, fast computational methods are relevant for both forward and inverse modelling studies. Since this problem involves a large number of unknowns, it has to be solved efficiently to obtain results in a timely manner, without compromising accuracy. For this reason, the Born approximation, extended Born approximation and iterative extended Born approximation are implemented and compared with the full solution of the conjugate gradient fast Fourier transformation method. These methods are based on an electric field domain integral equation formulation. It is shown here how well the iterative extended Born approximation method performs in terms of both accuracy and speed with different configurations and different source positions. The improved accuracy comes at virtually no additional computational cost. With the help of this method, it is now possible to perform sensitivity analysis using 3D modelling in a timely manner, which is vital for controlled source electromagnetic applications. For forward modeling the solution at the sea‐bottom is of interest, because that is where the receivers are usually located. For inverse modeling, the accuracy of the solution in the target zone is important to obtain reasonably accurate conductivity values from the inversion using this approximate solution method. Our modelling studies show that the iterative extended Born approximation method is fast and accurate for both forward and inverse modelling. Sensitivity analysis as a function of the source position and different reservoir sizes validate the accuracy of the iterative extended Born approximation.     

A RECTANGULAR LOOP SOURCE OF CURRENT ON A TWO-LAYERED EARTH*

Using the concept of reciprocity and the known solution for the electric field of a vertical oscillating magnetic dipole source placed over a two-layered halfspace, an integral expression for the vertical magnetic field produced by a horizontal rectangular loop, carrying an oscillating current and placed on the surface of the same halfspace, is deduced. This expression is such that it can be evaluated by a combination of straightforward numerical integration and digital linear filter techniques. Displacement currents everywhere in space are neglected. Fields both inside and outside the loop are presented as sounding curves. A little over a decade of frequencies (100–3000 Hz) appears to be the minimum requirement and two decades (100–10000 Hz) are sufficient for most situations. Parametric and geometric sounding curves both show good resolution of subsurface layering. Phase shows better resolution than amplitude. Similarly, resolution is higher when conductivity increases with depth than when it decreases. Besides being useful for the electromagnetic depth sounding for layered earth structures, such computations can be applied to determine normal corrections to Turam observations, whenever a rectangular loop of finite size is used as a transmitter.     

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.     

Trans‐dimensional Bayesian inversion of controlled‐source electromagnetic data in the German North Sea

This paper presents the first controlled‐source electromagnetic survey carried out in the German North Sea with a recently developed seafloor‐towed electrical dipole–dipole system, i.e., HYDRA II. Controlled‐source electromagnetic data are measured, processed, and inverted in the time domain to estimate an electrical resistivity model of the sub‐seafloor. The controlled‐source electromagnetic survey targeted a shallow, phase‐reversed, seismic reflector, which potentially indicates free gas. To compare the resistivity model to reflection seismic data and draw a combined interpretation, we apply a trans‐dimensional Bayesian inversion that estimates model parameters and uncertainties, and samples probabilistically over the number of layers of the resistivity model. The controlled‐source electromagnetic data errors show time‐varying correlations, and we therefore apply a non‐Toeplitz data covariance matrix in the inversion that is estimated from residual analysis. The geological interpretation drawn from controlled‐source electromagnetic inversion results and borehole and reflection seismic data yield resistivities of ～1 Ωm at the seafloor, which are typical for fine‐grained marine deposits, whereas resistivities below ～20 mbsf increase to 2–4 Ωm and can be related to a transition from fine‐grained (Holocene age) to unsorted, coarse‐grained, and compacted glacial sediments (Pleistocene age). Interface depths from controlled‐source electromagnetic inversion generally match the seismic reflector related to the contrast between the different depositional environments. Resistivities decrease again at greater depths to ～1 Ωm with a minimum resistivity at ～300 mbsf where a seismic reflector (that marks a major flooding surface of late Miocene age) correlates with an increased gamma‐ray count, indicating an increased amount of fine‐grained sediments. We suggest that the grain size may have a major impact on the electrical resistivity of the sediment with lower resistivities for fine‐grained sediments. Concerning the phase‐reversed seismic reflector that was targeted by the survey, controlled‐source electromagnetic inversion results yield no indication for free gas below it as resistivities are generally elevated above the reflector. We suggest that the elevated resistivities are caused by an overall decrease in porosity in the glacial sediments and that the seismic reflector could be caused by an impedance contrast at a thin low‐velocity layer. Controlled‐source electromagnetic interface depths near the reflector are quite uncertain and variable. We conclude that the seismic interface cannot be resolved with the controlled‐source electromagnetic data, but the thickness of the corresponding resistive layer follows the trend of the reflector that is inclined towards the west.