瑞雷波斜入射下层状半空间中沉积谷地周围的三维散射研究

针对层状半空间中沉积谷地对斜入射瑞雷波的三维散射问题, 采用直接刚度法计算自由场波场, 以层状半空间中移动斜线均布荷载动力格林影响函数求解三维散射波场, 建立了求解该问题的间接边界元方法. 通过与已有结果的比较, 验证了该方法的正确性, 并以均匀半空间以及弹性基岩上单一土层场地中沉积谷地为例进行了计算分析. 研究结果表明: 层状半空间与均匀半空间中沉积谷地对瑞雷波的散射存在显著差别; 层状半空间中瑞雷波的振动模态对沉积附近位移幅值有着重要影响; 土层刚度和厚度等参数也对沉积附近位移幅值大小及空间分布有着显著的影响.      

层状半空间中周期分布凸起地形对平面SH波的散射

提出了一种新的以层状半空间中周期分布斜线荷载动力格林函数为基本解的间接边界元方法,研究了周期分布凸起地形对平面SH波的散射问题.方法将散射波场分解为凸起内部散射波场和凸起外部散射波场.凸起内部散射波场通过在凸起闭合边界上施加虚拟斜线荷载产生的动力响应来模拟,而凸起外部散射波场则通过在凸起与半空间交界面上施加虚拟周期分布斜线荷载产生的动力响应来模拟.周期分布斜线荷载动力格林函数的引入,使得本文方法仅需针对一个凸起进行边界单元的离散和求解,便可完成问题的求解,避免了通过截断无限边界求解而引入的误差,方法具有较高精度的同时显著降低了求解自由度.文中通过与已有结果的比较,验证了方法的正确性,并以均匀半空间和基岩上单一土层中周期分布凸起为例进行了数值计算分析.研究表明,凸起间距对凸起地形间的动力相互作用有着显著的影响,同时层状半空间中周期分布凸起地形对SH波的散射与均匀半空间情况也有着显著的差别.     

Self-potential global tomography including topographic effects

This paper is an extension of a previous study, in which the principles of self-potential ground surface tomography were outlined. The new arguments which are here set forth are the proper accounting for the topographic effects and a robust approach to global 3D tomography. The 2D case is initially considered in order to facilitate a full understanding of the new method. In order to gauge the topographic distortions, the concepts of slope effect and surface regularization are introduced, as suitable means to compute point by point correction factors of the measured self-potential data, prior to the recognition of the tomographic images of the primary and induced electric sources underground. The tomographic approach is then developed by introducing again the concepts of the scanning function and of the charge occurrence probability function, which were amply dealt with in the previous paper. The new approach to 3D global tomography means here the composition of charge occurrence probability functions related to any two orthogonal surface components of the natural electric field, in order to account fully for the total surface component of the self-potential field and hence to elicit the greatest amount of information. Two field examples are presented to show the full effectiveness of the proposed method. They refer, respectively, to a near-surface investigation for archaeological purposes and to a very deep investigation in an active volcanic area.     

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.     

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.     

三维时间域航空电磁有理Krylov正演研究

常规的三维时间域航空电磁模拟通常采用隐式步长方法进行时间离散,需要几次矩阵分解和上百次右端源项回带,计算效率较低.为了提高正演计算效率,本文提出使用有理Krylov方法求解时间域电场扩散方程.首先使用非结构四面体网格进行空间离散,采用Nédélec矢量基函数近似四面体单元内的电场;然后基于有限元离散给出矩阵指数和矢量乘积表示的电场显式解;最后采用有理Arnoldi算法构造Krylov子空间内的正交基函数并进一步求解矩阵指数与矢量的乘积,直接得到任意时刻的电场解向量,避免步长离散过程.此外,本文还提出一种指数加权偏移参数优化方法,使得有理Arnoldi近似在瞬变衰减晚期具备更高的精度,从而降低Krylov子空间阶数并提高计算效率.通过和层状模型解析解的对比验证了有理Krylov方法的精度.针对三维异常体模型使用全局网格和局部网格剖分并和其他数值方法比较,进一步说明了有理Krylov方法的有效性.     

1D and 2D Cole-Cole-inversion of time-domain induced-polarization data

A new method for the 2D inversion of induced polarization (IP) data in the time domain has been developed. The entire IP transients were observed and inverted into 2D Cole-Cole earth models, including resistivity, chargeability, relaxation time and the frequency constant. Firstly, a modified 1D time-domain electromagnetic algorithm was used to calculate the response of a layered polarizable ground. The transient signals were then inverted using the Marquardt method to derive the Cole-Cole parameters of each layer. However, model calculations showed that the EM effects could be neglected for the time range (>1 ms) and for the transmitter–receiver distances (<50 m) used in this study. Therefore, the induction effects were not considered for the solution of the 2D inverse problem and a DC solution was applied. An approximative forward algorithm was introduced in order to calculate the IP transients directly in the time domain and in order to speed up the inverse procedure. The approximation is highly accurate, and this is demonstrated by comparing the approximations with their exact solutions up to 3D. The inverse algorithm presented consists of two steps. The transient voltages of an array data set were inverted separately into a two-dimensional resistivity model for each time channel. The time-dependent resistivity of each cell was then interpreted as the response of a homogeneous half-space. In the 2D inversion algorithm, a 3D DC algorithm was used as a forward operator. The method only requires a standard 2D DC inversion and a homogenous half-space Cole-Cole inversion. The developed algorithm has been successfully applied to synthetic data sets and to a field data set obtained from a waste site situated close to Düren in Germany.     

Frequency-domain modelling of airborne electromagnetic responses using staggered finite differences1

A 3D frequency-domain EM modelling code has been implemented for helicopter electromagnetic (HEM) simulations. A vector Helmholtz equation for the electric fields is employed to avoid convergence problems associated with the first-order Maxwell's equations when air is present. Additional stability is introduced by formulating the problem in terms of the scattered electric fields. With this formulation the impressed dipole source is replaced with an equivalent source, which for the airborne configuration possesses a smoother spatial dependence and is easier to model. In order to compute this equivalent source, a primary field arising from dipole sources of either a whole space or a layered half-space must be calculated at locations where the conductivity is different from that of the background. The Helmholtz equation is approximated using finite differences on a staggered grid. After finite-differencing, a complex-symmetric matrix system of equations is assembled and preconditioned using Jacobi scaling before it is solved using the quasi-minimum residual (QMR) method. The modelling code has been compared with other 1D and 3D numerical models and is found to produce results in good agreement. We have used the solution to simulate novel HEM responses that are computationally intractable using integral equation (IE) solutions. These simulations include a 2D conductor residing at a fault contact with and without topography. Our simulations show that the quadrature response is a very good indicator of the faulted background, while the in-phase response indicates the presence of the conductor. However when interpreting the in-phase response, it is possible erroneously to infer a dipping conductor due to the contribution of the faulted background.     

DIRECT CURRENT ELECTRIC POTENTIAL FIELD ASSOCIATED WITH TWO SPHERICAL CONDUCTORS IN A WHOLE-SPACE1

Bispherical coordinates are used to derive an exact mathematical solution for the potential field generated by direct current electric conduction in an earth model consisting of two spherical inclusions in a uniform whole-space. The solution takes the form of a spherical harmonic expansion in bispherical coordinates; coefficients in the expansion are obtained by solving sets of linear equations. Rapid forward modelling of numerous interesting situations in d.c. resistivity prospecting is facilitated by the generality and computational efficiency inherent to this new solution. For example, the accuracy of image (or superposition) methods for calculating potential solutions can be quantified. Similarly, the ability of d.c. conduction methods to resolve two distinct bounded bodies in three-dimensional space can be examined by repeatedly calculating the secondary potential or apparent resistivity response of an earth model as a selected parameter is varied. Synthetic mise à la masse, crosshole, or areal potential data sets can be generated for subsequent use in inversion studies. Improvements in solution technique derived here also apply to a simpler model consisting of a single sphere buried in a half-space.     

ASH-source in an elastic half-space with a non-homogeneous surface layer

Summary The response of an elastic half-space with a non-homogeneous surface layer due to aSH-source operating in the non-homogeneous layer of an elastic half-space have been studied. The elastic and physical constants vary exponentially in the surface layer. The surface displacement consists of several integrals. On approximate evaluation of these integrals, they are identified as direct or reflected pulses.     

面向目标自适应有限元法的带地形三维大地电磁各向异性正演模拟

传统三维大地电磁各向异性模拟均是基于规则六面体网格,计算精度有限且较难拟合复杂地质条件.本文采用面向目标自适应非结构矢量有限元法,对三维大地电磁各向异性介质进行模拟.首先从电场双旋度方程出发,利用伽辽金方法建立变分方程;然后利用电流密度连续性条件构建适合大地电磁各向异性问题的加权后验误差估计方法,实现面向目标的网格自适应正演;最后通过典型算例分析各向异性对网格自适应和大地电磁响应的影响特征以及各向异性的识别方法.本文算法能够高精度地拟合起伏地表和任意各向异性介质,适用于分析复杂地电条件大地电磁响应特征,为提高大地电磁资料解释水平提供了理论基础.     

Numerical modeling of the 2D time-domain transient electromagnetic secondary field of the line source of the current excitation

To effectively minimize the electromagnetic field response in the total field solution, we propose a numerical modeling method for the two-dimensional (2D) timedomain transient electromagnetic secondary field of the line source based on the DuFort-Frankel finite-difference method. In the proposed method, we included the treatment of the earth-air boundary conductivity, calculated the normalized partial derivative of the induced electromotive force (Emf), and determined the forward time step. By extending upward the earth-air interface to the air grid nodes and the zero-value boundary conditions, not only we have a method that is more efficient but also simpler than the total field solution. We computed and analyzed the homogeneous half-space model and the flat layered model with high precision—the maximum relative error is less than 0.01% between our method and the analytical method—and the solution speed is roughly three times faster than the total-field solution. Lastly, we used the model of a thin body embedded in a homogeneous half-space at different delay times to depict the downward and upward spreading characteristics of the induced eddy current, and the physical interaction processes between the electromagnetic field and the underground low-resistivity body.     

陆地可控源电磁法探测效果的频率响应

陆地可控源电磁法的观测资料可依据频段范围近似地划分为近区场、中间区场及远区场,但采用测量相互正交电、磁分量,并计算视电阻率的资料处理方式只适用于远区场数据.为更有效地利用陆地可控源电磁法不同区间场的观测资料,本文结合三维数值模拟技术并采用电场分量直接进行反演的策略,对不同区间电场的响应特征与探测效果进行了分析.数值模拟结果表明:近区电场的异常响应最明显,异常响应不随频率发生显著变化,但纵向分辨能力差;远区电场异常响应随频率发生显著变化,其探测深度取决于频率的高低;中间区场较为复杂,地表电场异常响应的等值线中心并不是位于异常体中心正上方,而是在沿场传播方向上向异常体与围岩的分界面处偏移,并且发现中间区场资料的加入会影响反演结果的准确性.综合合成数据和野外实测资料的反演结果,发现结合近区场和远区场资料而舍弃中间区场资料的反演效果更佳,这为陆地可控源电磁法资料的反演解释提供了一种有效途径.     

An approximate analytical approach to compute geoelectric dipole–dipole responses due to a small buried cube

A simple analytical solution is presented for computing direct current (DC) electric field distortion due to a small cube in a homogeneous half-space, measured with a dipole–dipole array on the surface. Both the transmitter and the receiver may have any orientation; furthermore their position on the horizontal surface and the depth of the cube can be freely selected. It is shown that a simple approximate analytical method may replace more complicated 3D numerical modelling algorithms.
The approximation lies in the linearization of the problem: the secondary source (i.e. the cube) is considered as a system of three perpendicular electric dipoles. In spite of this first-order approximation, in the case of realistic depths z ( z R ≈0.1–0.5, where R is the transmitter–receiver distance), this approximate solution fits very well with true 3D numerical modelling results, and with analogue modelling results if a R ≤0.1, where a is the length of the side of the cube. Due to its simplicity, this method could be used for computing DC field distortion effects, estimating parameter-sensitivities, or even determining some initial models for further inversions.     

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。      

Two- and three-dimensional modelling of half-space and train-track embankment under dynamic loading

Two modelling approaches for the analyses of half-space and train-track embankment on half-space subjected to dynamic loads are presented and compared. A three-dimensional (3D) modelling approach is performed by a coupled Boundary Element–Boundary Element method (BE–BE) and a two-dimensional (2D) one by a coupled Boundary Element–Finite Element method (BE–FE). Both approaches employ time domain algorithms. The comparison between the results of the presented approaches points out whether a problem can be treated as a 2D or as a 3D case. As an application, a parametric study of the wave propagation problem in a train-track embankment with an underlying half-space is presented.     

用扩散电场法估算CHTEM-I系统的探测深度

时间域航空电磁系统的探测深度是一项关键技术参数,在系统研制设计和资料解释中都有重要作用.当目标层与围岩电性差异不大或目标层引起的异常响应不明显时,常规的估算探测深度方法不再适用,为克服这种缺陷,本文提出了一种系统探测深度的估算方法,该方法通过模拟电场在均匀半空间模型和层状模型中的扩散过程,记录电场最大幅值在地下的瞬时位置,将系统的探测深度定义为观测到的响应值等于给定的噪声水平时,对应时刻的地下介质中感应电场幅度的最大值对应的深度.论文以我国自主研制的直升机时间域航空电磁系统CHTEM-I为例,根据对不同条件下的计算结果的分析,给出了探测深度与模型电导率、飞行高度和噪声水平之间的关系曲线,并总结出一些能够提高系统探测深度的建议.结果表明半空间模型电导率在0.000295~0.0422 S/m范围内,CHTEM-I系统可以在噪声水平与t^－0.5成正比条件下达到300 m的探测深度.本文方法的估算结果不受模型层厚薄,或目标层与围岩电性差异小等因素影响,因而具有较高的实用性.文中的结论对时间域航空电磁系统设计有理论指导意义,也可用于其它时间域电磁勘探系统探测深度的估算.     

三维复杂山谷地形SV波垂直输入地震反应分析

本文基于显式有限元法研究了地震波垂直入射时三维复杂山谷地形对地震地面运动的影响,在数值分析中应用了三维化二维的解法和黏弹性人工边界的处理方法,实现了地震波垂直输入下三维复杂场地地震动数值模拟,并验证了该方法的合理性.以四川桃坪地区一山谷地形作为研究对象,基于地表高程数据分别建立了二维和三维场地模型,对比研究表明:在复杂地形情况下考虑二、三维模型时具有明显差异,三维模型能更真实地反映地形变化对地震动的影响,复杂地形条件下有必要考虑三维实际场地模型.本文对边界自由场的处理方法也可用于处理三维复杂场地地震动斜入射问题,为三维复杂地形场地地震效应研究提供参考.     

Scattering and diffraction of plane SH-waves by periodically distributed canyons

A new method is presented to study the scattering and diffraction of plane SH-waves by periodically distributed canyons in a layered half-space. This method uses the indirect boundary element method combined with Green’s functions of uniformly distributed loads acting on periodically distributed inclined lines. The periodicity feature of the canyons is exploited to limit the discretization effort to a single canyon, which avoids errors induced by the truncation of the infinite boundary, and the computational complexity and the demand on memory can be significantly reduced. Furthermore, the total wave fields are decomposed into the free field and scattered field in the process of calculation, which means that the method has definite physical meaning. The implementation of the method is described in detail and its accuracy is verified. Parametric studies are performed in the frequency domain by taking periodically distributed canyons of semi-circular and semi-elliptic cross-sections as examples. Numerical results show that the dynamic responses of periodically distributed canyons can be quite different from those for a single canyon and significant dynamic interactions exist between the canyons.     

Wavelet analysis of lightning return stroke

In this investigation, time series consisting of electric field waveforms of 15 positive return strokes and 10 negative return strokes were analyzed. The data came from a summer thunderstorm in March in a range of about 200 km around São José dos Campos, São Paulo. The electric field recording system consisted of a flat plate antenna with a decay time constant of 260 μs and a sample rate of 800,000 samples per second. The bandwidth observed was up to 100 kHz and the recording system was synchronized with GPS time and located at São José dos Campos. Wavelet analysis of the electric field waveforms was done in order to investigate the behavior of the return stroke spectrum in time. The return stroke was suggested to be divided into two portions: initial stage and overshoot (for far return stroke) and initial stage and ramp (for close return stroke). The return stroke power spectrum was observed to be distributed in a frequency range with the peak value also distributed in a fraction of this range. Power peaks for ramps are stronger than power peaks for initial stage and overshoot. Finally, it was observed how powerful the wavelet is in the analysis of lightning.