井地电阻率成像2.5D正反演及其应用研究

发布时间：2018-07-31 08:42

【摘要】：相对于地表电阻率成像技术而言,井地电阻率成像技术将供电电极放入钻井,由于电极靠近探测目标体,故能激发出更强的异常,在地表接收电极中产生更大的电位差,其分辨率要明显优于地表装置形式。正是由于井地电阻率成像方法这些特点,因此,在城市工程勘查、深部隐伏矿床勘探以及在研究高含水期油田剩余油分布情况等方面具有很大的发展潜力和应用前景。本论文系统的总结了井地电阻率成像技术研究历史、应用现状及研究成果。在此基础上,以有限单元法对理论地电模型进行了2D正演数值模计算研究,同时利用正则化反演方法进行反演研究,取得了较好的效果。本文共分六章。第一章“绪论”部分,主要介绍了论文的研究背景、意义、井地电阻率成像正、反算法研究现状以及论文主要研究内容。第二章“井地电阻率成像的基本理论”部分,介绍了二维地电断面点源场电位满足的微分方程及边值条件,并列出了不同装置条件下计算视电阻率公式。第三章“井地电阻率成像2.5D有限单元法正演理论”部分是本章为论文的重点之一。井地电阻率法成像二维正演计算问题即是求解点源场二维电断面的边值问题,而二维地电断面电位满足的微分方程及边值条件可以等价为相应的变分问题。变分问题即泛函的极值问题,又可简化为多元函数的极值问题,而多元函数的极值问题是大家所熟知的。这就是有限单元法的基本思想。具体思路是:对点源二维地电断面,场(电位)实际上是三维的,但电位在二维目标体延伸方向具有对称性,因此可用余弦变换将电位满足的三维微分方程变成变换电位满足的二维微分方程。通过网格剖分,从而将边值方程简化为网格节点上多元函数线性方程,计算出傅氏电位,最后进行反余弦变换,即可计算出所求的电位。第四章“井地电阻率成像2.5D的正则化反演研究”部分为论文的另一个重点,主要介绍了正则化反演的基本原理,着重讨论了正则化因子和稳定因子的选取等内容。第五章“5井地电阻率成像技术的工程实例应用”部分介绍了几个应用实例及应用效果。第六章为“结论”部分,简述了工作成果以及工作中存在的欠缺之处。论文工作中,用C语言编制了井地电阻率成像2.5D正、反演程序。正演中反余弦变换采用了最优化法求解出的具有较高精度的滤波系数;反演中对正则化因子的计算方法以及稳定因子的选择对反演结果的影响进行了详细分析。通过对几种规则的地电模型试算、比较,验证了程序的准确性和有效性。在城市工程勘查的应用中,对工作区域内的溶洞、溶蚀裂隙破碎带及富水带等地质隐患亦取得了很好的勘查效果,能够精确地划分地电断面上的探测目标体的空间位置及其边界,为设计工作和后续施工提供了可靠的技术支持。
[Abstract]:Compared with the surface resistivity imaging technology, the well ground resistivity imaging technology puts the power supply electrode into the drilling. Because the electrode is close to the detecting object, it can excite stronger anomalies and produce greater potential difference in the surface receiving electrode. Its resolution is obviously superior to the surface device form. It is precisely because of these characteristics of well ground resistivity imaging that it has great development potential and application prospect in urban engineering exploration, deep hidden deposit exploration and the study of remaining oil distribution in high water-cut oil fields. This paper systematically summarizes the research history, application status and research results of well-ground resistivity imaging technology. On this basis, the 2D forward numerical model of the theoretical geoelectric model is studied by finite element method, and the regularization inversion method is used to carry out the inversion research, and good results are obtained. This paper is divided into six chapters. The first chapter, "introduction", mainly introduces the research background, significance, research status of resistivity imaging, inverse algorithm and the main research content of the paper. In the second chapter, "basic theory of borehole resistivity imaging", the differential equation and boundary condition of point source field potential in two-dimensional geoelectric section are introduced, and the formulas for calculating apparent resistivity under different conditions are listed. Chapter three, "forward theory of 2.5D finite element method for resistivity imaging of well ground", is one of the emphases of this paper. The two-dimensional forward modeling problem of borehole resistivity imaging is to solve the boundary value problem of two-dimensional electric section of point source field, and the differential equation and boundary condition of two-dimensional geoelectric section potential can be equivalent to the corresponding variational problem. The variational problem is the extreme value problem of functional, and it can be simplified as the extreme value problem of multivariate function, and the extreme value problem of multivariate function is well known. This is the basic idea of finite element method. The specific idea is that the field (potential) is actually three-dimensional for the two-dimensional geoelectric section of the point source, but the potential has symmetry in the extension direction of the two-dimensional object. Therefore, the three dimensional differential equation of potential can be transformed into two dimensional differential equation by cosine transform. The boundary value equation is simplified to the linear equation of multivariate function on the grid node by mesh division, and the Fourier potential is calculated. Finally, the potential can be calculated by inverse cosine transform. In chapter 4, "regularization inversion of well resistivity imaging 2.5D" is another important part of the paper. The basic principle of regularization inversion is introduced, and the selection of regularization factor and stability factor is discussed emphatically. In chapter 5, "Application of engineering example of 5 well resistivity imaging technology", several application examples and application results are introduced. The sixth chapter is the conclusion part, briefly describes the work results and the shortcomings in the work. In the work of this paper, a 2.5 D inversion program for well ground resistivity imaging is compiled with C language. In forward modeling, the inverse cosine transform uses the optimization method to solve the filtering coefficient with high accuracy, and the calculation method of regularization factor and the influence of the selection of stability factor on the inversion result are analyzed in detail. The accuracy and validity of the program are verified by the comparison of several regular geoelectric models. In the application of urban engineering exploration, good results have been obtained for geological hidden dangers such as caverns, fracture zones and water-rich zones in the working area. It can precisely divide the space position and the boundary of the detection object on the geoelectric section, which provides reliable technical support for the design and subsequent construction.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.322

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