地震的感应磁效应（二）

本文是“地震的感应磁效应（一）--三维电磁感应的数值理论”一文的继续。首先从理论和实际计算两个方面证明了三维电磁感应数值方程解的唯一性、收敛性和稳定性,从而充实了作为研究地壳、上地幔电性结构横向不均匀性理论基础的“三维数值方法”。作为这一理论方法的实际应用,文中对不同源场周期和具有不同埋藏深度的三维电导率异常体进行了模拟计算,以研究地震感应磁效应的大小、空间分布特征和频率特性。模拟计算结果表明,对于周期从数秒到数分钟的地磁短周期变化,若电导率异常体的线度与5至7级地震的震源体积大体相当,其电导率较原背景电导率高近一个量级,其感应磁效应主要特征为:在异常体正上方,地面磁场的水平分量变化最大,相对变化量约30％;在异常体于源场方向一致的两侧,垂直分量变化最大,相对变化量约40-50％。因此,观测短周期地磁场的异常变化,有可能是监测地震孕育过程地下电性变化的一种试验途径。但由于上述异常强度在空间上衰减迅速,所以观测必须接近震源区,这对测点的选择是个不利的因素。     

关于非均匀介质中电导率按深度变化时的势及其视电阻率函数

本文共分六部分内容。在前言中,简述了电测深方面有关研究的情况,尤其叙述了E.S.Sampaio（1976）的结果。 因本文采用的方法不同,从而求解了适合要求的微分方程定解问题,获得了电导率以 （其中α、σ₀、σ₁均为正实数,β为实数）按深度变化时势的分布。 其次,当β=0时,对电导率σ=（σ₀+σ₁z）^α按深度变化时势的分布,应用Bessel函数的积分表达时,明显地改进和推广了E.S.Sampaio（1976）结果中的重要部分。 最后,结合实际作出了第一类、第二类标准化视电阻率函数。这种视电阻率函数,推广了Wenner和Schlumberger分别作出的视电阻率函数的有关部分,对电阻率法和激发极化法,都有其理论价值和实际意义。     

一点修正

由于本人不慎,在《二维与三维位场在频率域的等价定理》一文（见《地球物理学报》1979年第1期）的（34）式中出现错误。熊光楚同志指出了这个问题（见《地球物理学报》1979年第3期第312-314页）。现修正如下: 设等价的二度体模型的密度分布函数σ^*（ξ,ζ）是三维模型密度分布σ（ξ,η,ζ）沿η     

局部地区地磁日变分析方法及中国地区S_q场的经度效应

本文首先介绍了舒斯特（Schuster）以及别科娃（Benkova）日变分析的方法,并提出了利用“逐次近似法”分析日变经度效应的新方法;然后介绍了利用“逐次近似法”对中国地区1959年s_q场分析的初步结果。结果表明,“逐次近似法”对于局部地区日变分析是适宜的。     

用大地测量资料反演的1976年唐山地震的位错模式

运用反演理论探讨了由“零频”资料反演大地震震源模式的基本原理和方法,并用大地测量资料反演了1976年唐山7.8级地震的位错模式。得到的结果表明唐山地震的发震构造是一个总体走向为北东49°的右旋-正断层,断层面倾向南东,倾角76°。这个地震的断层长84公里,宽34公里,走向滑动错距459厘米,倾向滑动错距50厘米,地震矩4.3×10²⁷达因-厘米,应力降29巴,应变降4.3×10^-5,释放的能量3.7×10²³尔格。由形变资料反演的平均错距和地震矩远大于由地震波资料定出的平均错距（270厘米）和地震矩(1.8×10²⁷达因-厘米),它表明在地震区的地壳内震前可能已经发生了无震滑动--断层蠕动。无震滑动的规模比主震还要大一些,它的矩估计约为2.5×10²⁷达因-厘米。唐山地震前虽然没有前震,但是却有规模这么大的“震前蠕动”,这可能是唐山地震与其他许多有前震的地震（如海城地震）的根本区别,它的许多与别的地震不同的前兆可能与此有关。     

地震的感应磁效应（一）——三维电磁感应的数值理论

地震的感应磁效应包括两部分:（一）三维电磁感应的数值理论;（二）地震感应磁效应的模拟计算。本文是其中的第一部分,从Maxwell方程推得的扩散方程出发,给出了一般三维电磁感应的基本方程、边界条件和求解方法,建立了完整的三维电磁感应的数值理论。计算结果将另文讨论。     

山东泰安地区断层的最新活动与“泰山震

在卫星图像解译的基础上,对泰安地区５条主要断裂进行了野外地质地貌考察和年代学研究,发现泰山山前断裂为晚更新世晚期活动断裂,最新活动时代为距今（１．４２±０．１２）×１０４ａ。然后,讨论了发生在公元前１８３１年的“泰山震”的发震构造,认为“泰山震”可能与泰山山前断裂活动有关,可能是一次没有地表破裂、震级小于６．５级的中等强度地震     

电性任意各向异性且分块连续变化CSAMT三维有限元数值模拟

考虑地球介质电导率任意各向异性且随空间位置连续变化的情况,本文实现了直接求解电磁场的可控源音频大地电磁测深（CSAMT）三维有限元数值模拟.首先给出了电导率任意各向异性介质中CSAMT二次电场满足的控制方程及其相应变分问题,然后采用任意六面体单元对研究区域进行剖分,在网格单元中对任意各向异性电导率进行线性插值,解决了实际工作中岩矿石电导率各向异性且连续变化的情况,将变分问题转化为线性代数方程组的求解.电导率各向异性且连续变化一维模型三维有限元数值模拟结果与电导率各向异性且分层均匀渐进模型解析解结果对比验证了方法的有效性;三维地电模型电导率随位置线性变化且各向同性、主轴各向异性、方位各向异性和倾斜各向异性的数值模拟结果表明,电导率各向异性且连续变化对CSAMT视电阻率和相位数据均有明显的影响.     

三度剩余磁力异常源全方位成像的理论和方法

首先在球坐标系中导出了三度磁性体的“拟引力位”V（p）、“拟引力场”F（p）、磁位U（p）、总磁场T（p）和任意方向磁场分量（p户）等球谐级数正演通式．然后,采用（p）,F（p）和V（p）等3个球谐级数正演通式,建立了复杂条件下三度剩余磁力异常源全方位成像方法．最后,给出了“成像”理论方法体系的应用实例．     

声波测井时裸眼井中弹性波的传播

本文分析了简化模型下声波测井时裸眼井（内充流体一般是泥浆）中弹性波的传播,此波场可看成是轴向传播有不同波矢的分波的叠加。分析表明,对于井外只有单一均匀岩层且无限深的井,仅对如（18）式所示的特征频率成分才存在具有轴向传播最大相速度v_zm=c₂的所谓“首波”;而v_x > c₂及c₂ > v_z>b₂的分波却不存在,此处c₂和b₂分别是井外岩层的纵波和横波速度。这正解释了文献[3]中所报道的裸眼井的“过滤效应”。分析还表明,对于井外具有多层岩层的井,只在一定条件下才存在与上述特性相近的“首波”。本文结果对声速测井显然是重要的。     

Integral equation of relationship on the apparent conductivity and true conductivity in induction logging

This paper investigates the relation between the induced electromotive force measured by induction logging tool and the apparent conductivity, and the relation between the apparent conductivity and the formation true conductivity. Assuming the conductivity in Green’s function to be the function of the field point coordinate, the apparent conductivity expression of electric-field intensity is derived using Green’s formula, and the integral equation has been established representing the relationship of the apparent conductivity with the true conductivity under this condition. The integral equation is analyzed and then leads to the conclusion that the equivalent conductivity is the apparent conductivity and the values of the apparent conductivity function contain the true conductivity, and the method derived the true conductivity from the apparent conductivity around the well axis is put forward. The validity of the approach given in this paper is verified through numerical calculation. On the basis of above means, the transmitter coil produces an electric-field distribution in formation at every point where the induction logging tool moves along a wellbore, and a number of the receiving coils obtain an apparent conductivity distribution; this is what induction electric-field logging is.     

利用阵列感应测井仪信号反演非均匀分布地层电导率

基于非线性积分方程,利用井轴上阵列感应成像测井仪（AIT）的单频测量信号,将变形玻恩（Bom）迭代方法用于地球物理测井反演,用正则化方法求出地层电导率分布。文中首先给出对于未知电导率分布的非线性积分方程,然后用玻恩近似使非线性积分方程线性化,求出电导率分布。在迭代过程中,数值模式匹配法用于求解阵列感应的正演问题。数值计算表明,用井轴上 AIT 的单频测量信号得到的成像结果与真电导率剖面分布吻合较好。     

A fast integral equation solver for 3D induction well logging in formations with large conductivity contrasts

Simulation of induction logging responses in formations with large conductivity contrasts is an important but challenging problem due to the singularity of a linear system caused by large contrasts. Also, three‐dimensional (3D) analysis of complex geophysical structures usually encounters high computational demands. In this paper, a pre‐corrected fast Fourier transform (pFFT)‐accelerated integral equation method is applied to overcome these difficulties. In the approach, the entire formation is included in the solution domain. The volume integral equation is set up in the region based on the fact that the total field is the summation of the excitation field and the secondary field. The emitted field by the transmitter coil (treated as a magnetic dipole) is regarded as the excitation of the system. Then the method of moments (MoM) is used to solve the integral equation. To reduce the high computational requirements of the MoM, the pFFT method is used to speed up the solution of the matrix equation and reduce the memory requirement as well. The resultant method is capable of computing induction logging problems involving large and complex formations. For problems with high conductivity contrasts, the solution of the matrix equation usually converges very slow or even fails to converge due to the large condition number of the coefficient matrix. To overcome this difficulty, an incomplete LU pre‐conditioner is used to significantly speed up the convergence of the matrix equation, thus further reducing the computation time. Numerical results show that the present method is efficient and flexible for 3D simulation of induction logging and is specifically superior for problems with high conductivity contrasts.     

Potential field of a stationary electric current in a stratified medium with a three-dimensional perturbing body

Summary The potential of the electric field of a stationary current in a two-layered Earth is calculated by applying Green's formula in the case where a three-dimensional inhomogeneity of different conductivity is located in the basement of the layer. It is proved that the potential outside and inside the perturbing body can be calculated from the potential of an electric double-layer distributed on the surface of this body. An integral equation of the Fredholm type is derived for the surface density of the double-layer, together with some of its integral properties. A similar procedure can be applied to computing the magnetic anomalies of three-dimensional magnetized bodies, geothermal anomalies due to three-dimensional inhomogeneities of different heat conductivity, as well as to potential problems of theoretical electrical engineering.     

3-D Global Induction in the Oceans and Solid Earth: Recent Progress in Modeling Magnetic and Electric Fields from Sources of Magnetospheric,Ionospheric and Oceanic Origin

Electromagnetic induction in the Earth’s interior is an important contributor to the near-Earth magnetic and electric fields. The oceans play a special role in this induction due to their relatively high conductivity which leads to large lateral variability in surface conductance. Electric currents that generate secondary fields are induced in the oceans by two different processes: (a) by time varying external magnetic fields, and (b) by the motion of the conducting ocean water through the Earth’s main magnetic field. Significant progress in accurate and detailed predictions of the electric and magnetic fields induced by these sources has been achieved during the last few years, via realistic three-dimensional (3-D) conductivity models of the oceans, crust and mantle along with realistic source models. In this review a summary is given of the results of recent 3-D modeling studies in which estimates are obtained for the magnetic and electric signals at both the ground and satellite altitudes induced by a variety of natural current sources. 3-D induction effects due to magnetospheric currents (magnetic storms), ionospheric currents (Sq, polar and equatorial electrojets), ocean tides, global ocean circulation and tsunami are considered. These modeling studies demonstrate that the 3-D induction (ocean) effect and motionally-induced signals from the oceans contribute significantly (in the range from a few to tens nanotesla) to the near-Earth magnetic field. A 3-D numerical solution based on an integral equation approach is shown to predict these induction effects with the accuracy and spatial detail required to explain observations both on the ground and at satellite altitudes. On leave from Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Russian Academy of Sciences, 142190 Troitsk, Moscow region, Russia.     

电导率各向异性的海洋电磁三维有限单元法正演

本文提出了一种基于非结构化网格的海洋电磁有限单元正演算法.为了回避场源奇异性,文中选用二次场算法,将背景电阻率设置为水平层状且各向异性,场源在水平层状各向异性介质中所激发的一次场通过汉克尔积分得到.基于Coulomb规范得到二次矢量位和标量位所满足的Maxwell方程组,通过Galerkin加权余量法形成大型稀疏有限元方程,采用不完全LU分解(ILU)预条件因子的quasi-minimum residual(QMR)迭代解法对有限元方程进行求解得到二次矢量位和标量位;进而,利用滑动平均方法得到二次矢量位和标量位在空间的导数,由此得到二次电磁场;通过一维模型对算法的可靠性进行验证,与此同时,针对实际复杂海洋电磁模型,比较有限元模拟结果与积分方程模拟结果,进一步验证算法精度.若干计算结果均表明,文中算法具有良好的通用性,适用于井中电磁、航空电磁,环境地球物理等非均匀且各向异性介质中的电磁感应基础研究.     

Incorporating known petrophysical model in the seismic full-waveform inversion using the Gramian constraint

In this paper, we develop a general approach to integrating petrophysical models in three-dimensional seismic full-waveform inversion based on the Gramian constraints. In the framework of this approach, we present an example of the frequency-domain P-wave velocity inversion guided by an electrical conductivity model. In order to introduce a coupling between the two models, we minimize the corresponding Gramian functional, which is included in the Tikhonov parametric functional. We demonstrate that in the case of a single-physics inversion guided by a model of different physical type, the general expressions of the Gramian functional and its gradients become simple and easy to program. We also prove that the Gramian functional has a non-negative quadratic form, so it can be easily incorporated in a standard gradient-based minimization scheme. The developed new approach of seismic inversion guided by the known petrophysical model has been validated by three-dimensional inversion of synthetic seismic data generated for a realistic three-dimensional model of the subsurface.     

Torsional response of pile embedded in a poroelastic medium

The response of a cylindrical elastic pile embedded in a homogeneous poroelastic medium and subjected to torsional loading is studied for the first time. Based on the Muki's model, the pile-porous medium system is decomposed into a fictitious pile system and an extended porous medium system. The one-dimensional, vertical, elastic pile and the three-dimensional poroelastic medium are solved, respectively. Considering the mixed boundary-value conditions at the interface of pile and soil, a Fredholm's integral equation of the second kind for the bar-force is established. The force and the displacement of the pile are calculated by applying numerical quadrature.