【作者】 胡博；

【导师】 岳建华；

【作者基本信息】 中国矿业大学 ， 地球探测与信息技术， 2010， 博士

【摘要】 矿井瞬变电磁法是井下找水探水的有力工具,以其方便灵活的施工技术得到广泛的应用,在生产实践中取得很好的应用效果。本文针对矿井瞬变电磁法中固有的全空间场理论问题进行了深入研究。根据煤系地层的特点,建立地电模型,研究了全空间瞬变电磁场的1D和3D正演数值模拟算法,重点用边界元数值算法研究井下3D巷道空间对全空间瞬变电磁场的影响。从电磁场满足的麦克斯韦方程组和边界条件出发,定义了洛伦兹规范和库伦规范下的两组位函数对,推导了其满足的控制方程和边界条件,作为正演数值模拟的理论基础。1D水平层状介质模型的瞬变电磁场,用分离变量法推导了垂直和水平磁偶极子源的矢量位求解方法。矿井瞬变电磁法中常用圆形或方形的多匝小回线装置进行发射和接收,都可以根据磁偶极子源的场做线积分得到。不管是分离装置还是重叠装置,除去早期个别点外,均匀全空间的场值均大于地下半空间的场值,且二者的衰减规律一致。半空间场的理论不能很好的适用于全空间场。用小回线源半空间的解析解验证了滤波算法的正确性。当线圈架设倾斜一定角度时,将偶极子源分解为垂直和水平偶极子共同作用的结果,z方向磁通量的变化率主要受分解后垂直偶极子部分作用的影响,而x方向磁通量的变化率主要受分解后水平偶极子部分作用的影响。为了更加形象直观的描述层状介质模型系统,引入等效电路的描述方式。本着根据模型选择基本解使其满足控制方程的同时满足一定边界条件的思想,推导了含3D巷道的全空间水平层状介质模型的边界元算法。选择库伦规范下水平层状介质中电磁场位函数作为基本解,目的是利用该位函数对满足的边界条件消除无穷大表面上的面积分。对巷道边界进行三角网格剖分,采用分区均匀的规则三角网格剖分算法,可以很容易地实现区域的边界拟合,网格生成的速度快、质量好且数据结构简单。并采用混合元离散算法,避免了角点处法向导数不唯一的问题。仿照矿井直流电法勘探对巷道影响因数的定义,定义一个新的巷道影响因数,用于研究不同时刻巷道对视电阻率的影响。均匀介质中的巷道影响特征可归纳为先减小后增大,再减小再增大的趋势。收发装置分别位于巷道底板中心和巷道顶板中心时,巷道影响是相同的;收发距越大,较早观测时间内巷道影响越大,巷道影响迅速变小,随时间增加,各种收发距下巷道对瞬变响应的影响趋于一致;围岩导电性越差,巷道影响越小;巷道的几何尺寸越大,巷道影响越大,巷道长度对较晚观测时间内的场影响较大,而巷道宽度和高度对较早观测时间内的场影响较大。分别模拟了两层、三层和四层模型中的巷道影响特征。结果表明,巷道空间的存在,使得视电阻率发生显著变化,且层状介质中的巷道影响规律不同于均匀介质。模拟了各层地电参数变化对巷道的影响特征,综合分析可知,改变巷道所在层参数对巷道影响因数的影响最大,整个观测时间内都有影响;其次是改变直接底板和间接底板岩层的电阻率对巷道影响因数的影响较大,且直接底板和间接底板岩层的电阻率越小,对巷道影响因数的影响越大;最后是改变含源层顶板岩层电阻率对巷道影响因数的影响最小,只对观测曲线的尾支有影响,且含源层顶板岩层电阻率增大到一定程度后,巷道影响因数几乎不再变化。自主设计了水平层状介质1D和3DBEM正演软件,COM组件成功地将Matlab和VB接口,从而使Matlab强大的计算功能和图形显示功能与可视化的开发界面充分结合起来,取长补短。程序发布后,可在没有安装Matlab客户端机器上运行,完全脱离了Matlab工作环境,可移植性大大增强。VB调用COM组件,编程代码大大简化,缩短了开发时间,同时实现了算法的保密。可视化的操作界面,使用起来更加灵活方便,可任意改变模型参数,便于人机交互。更多还原

【Abstract】 Mine transient electromagnetic method (MTEM) is a powerful tool for detecting underground water. It is widely used in production and practice, achieving satisfactory results for its convenient and flexible field works. In the dissertation, the whole space field theory inherent in of MTEM was studied in detail. According to the characteristics of coal bearing strata, 1D and 3D geo-electric models were designed to study the numerical simulation of transient electromagnetic field in whole space, focusing on the boundary element method (BEM) simulating the influence of 3D roadway on transient electromagnetic fields in whole space.Based on Maxwell’s equations of electromagnetic fields and boundary conditions, two pairs of potential functions were introduced in terms of Coulomb and Lorentz gauges, whose control equations and boundary conditions were deduced as the theory basis of numerical simulation. The transient electromagnetic field in 1D layered medium model was calculated. The solving method of vector potential of vertical and horizontal magnetic dipole source were deduced by method of separation of variables. Circular or quadrate multi-coils are common used as transmitter-receiver in MTEM. Their electromagnetic fields can be got by calculation of line integral of the electromagnetic fields of magnetic dipole. No matter separated loops or coincident loops, the magnetic field in whole space is greater than the field in half space, besides several points in early times. And they have the same attenuation. The theory of half space cannot be well suited to whole space.When the transmitter coils are arbitrarily oriented; the transient electromagnetic field can be seen as the interaction of a VMD and a HMD. Z component of changing rate of magnetic flux is mainly decided by the decomposed VMD, as well as x component of changing rate of magnetic flux by the decomposed HMD. Equivalent circuit method is introduced to visually describe layered medium model system.BEM is used to study 3D roadway model in layered medium. The fundamental solution not only needs to satisfy the control equation, but also needs to satisfy certain boundary conditions at the same time. For 3D roadway model in layered medium, fundamental solutions are the potential functions in terms of Coulomb of layered medium model. The purpose is to use the boundary conditions of the potential functions to eliminate surface integral of infinite interface. It is easy to fit the roadway surface by rule triangular mesh generation algorithm. The algorithm is practical. And the structure of data is simple. Boundary integral equation is discrete by hybrid element method to resolve sketches of corner and edge. A new roadway influence factor was defined to study the influence of roadway on apparent resistivity the same as the definition of roadway influence factor in mine DC prospecting. The roadway influence factor decreases first then increases, and decreases and then increases again in homogeneous medium. When the transmitter-receiver located on floor and roof, the influence is the same. The greater the transmitter-receiver distance is, the greater the roadway influence factor is in earlier times. The roadway influence factor decreases rapidly with time, then keeps steady. The worse the conductivity of surrounding rock is, the smaller the roadway influence factor is. The bigger the physical dimension of the roadway is, the greater the roadway influence factor is. The length of roadway influences more in later times, while the width and height of roadway influences more in earlier times.The influences of roadway in two, three and four layered models were simulated. It is resulted that the apparent resistivity changes greatly because of the roadway. The influence of roadway in layered medium is different from the one in homogeneous medium. The influence of roadway was studied for different geo-electric parameters. Through the integrative analysis of the results, it is known that the apparent resistivity is influenced most by changing geo-electric parameters of the layer contained roadway in all times. Secondly, the apparent resistivity is influenced more by changing the resistivity of direct floor and indirect floor. And the smaller the resistivity of direct floor and indirect floor is, the greater the apparent resistivity changes. At last, the apparent resistivity is influenced smallest by changing the resistivity of roof. Roadway influence factor just changes at the end of the curve. And if the resistivity increases to some degree, the influence changes little.Forward software was explored to modeling 1D and 3D transient electromagnetic fields. COM module was designed to connect Matlab and VB used COM builder contained in Matlab. So the powerful calculated function and graphical display function of Matlab and visual exploited interface were combined fully. The program can work without Matlab environment. The portability was improved greatly. Because the COM module was called by VB, the codes was simplified, the exploited time was reduced and the arithmetic was kept secret. It is man-machine interactive and more convenient to change the parameters of models by visual operated interface.更多还原