【作者】 杨晓弘；

【导师】 何继善；

【作者基本信息】 中南大学 ， 地球探测与信息技术， 2009， 博士

【摘要】 频率域激电法以它特有的轻便、快捷、高效率等特点在资源勘查领域获得了广泛的应用,运用有限单元法推导过程简单、适合处理复杂几何形状的特点来对频率域激电法中激电参数进行正演数值模拟,分析和研究激电参数在不同测量装置、模型参数和起伏地形等情况下的特点和规律,可以为资料的解释提供科学依据和参考,为减少地球物理中的多解性做出有益的探索和尝试。由于频率域激电法所用的激励电流的频率通常介于10~2～10~2 Hz之间,所以可以假设矢量势A在不随时间变化或频率非常低的情况下忽略电磁效应,将大地模型中的参数用不同频率下得到的Cole-Cole模型响应来替换,用有限单元法对模型进行剖分、插值、单元分析、总体合成等处理,解大型稀疏线性方程组,求得模型上各个节点上的复电位值。根据激电参数的定义式就可以实现不考虑电磁效应的“频率域”激电参数的正演模拟。使用三棱柱剖分单元对大地模型进行剖分,在给出地表节点上的高程值后,可实现起伏地形条件下的激电参数的正演模拟。本文的研究取得了以下主要成果:1.基于前人的工作,在忽略电磁效应的情况下,从稳定电流场的基本方程出发,推导出三维区域点源场的边值问题,用广义变分原理推导出与其相对应的变分公式。通过用四面体单元和三棱柱单元对大地模型进行剖分、插值、总体集成,最后解方程,实现了在水平地形和起伏地形条件下频率域激电参数的正演模拟。2.推导了四面体剖分单元和三棱柱剖分单元的三线性插值形函数。将正六面体单元剖分为两个三棱柱单元后,可以通过给出地表节点的高程,快速实现对起伏地形模型的激电参数的数值模拟。将正六面体单元继续剖分为六个四面体单元,可以在不增加节点数目的情况下提高模拟的计算精度。3.用MATLAB计算机语言编制了一套基于有限单元法的频率域激电参数的正演模拟程序。通过对不同模型参数的正演模拟,表明该程序正确可靠,模拟精度满足数值模拟的基本要求。4.在水平地形条件下使用本程序模拟了中间梯度和偶极装置下常用的频域激电参数,分析了它们的变化规律和特点。模拟和分析了相频率参数的规律和特点,通过模拟表明该参数可以作为区分时间常数不同,极化率相同的极化异常体的有益参数,为区分金属硫化物和碳质页岩多提供了一种信息。5.模拟了三维起伏地形条件下,不同测深装置和不同形状极化体时的频域激电参数,分别探讨了山谷地形、山脊地形和复杂地形条件下激电异常的特点和变化规律。模拟结果表明地形本身不会产生激电异常,但地形的变化会对激电异常的形状和空间分布有较大影响。最后介绍和模拟了双频激电法与伪随机激电法中常用的激电参数,分析了它们的特点和变化规律。在本文的结论部分还指出了一些不足和今后工作的建议。更多还原

【Abstract】 Frequency-domain IP method establishes its position and function in exploration of mineral resources with its portable, rapid, and Efficient. The FEM （ finite element method ） is very simple to deal with complex boundary condition, and to simulate the frequency-domain IP. Studying the characters and laws of IP’s parameters under different measuring devices and undulate topography will provide scientific references and basis and reduce the multiplicities of interpretation. It is will be an attempt and exploration.Because of the frequency of the exciting current is usually between 10^-2～10² Hz, the vector A can be seen is not change with the time and the EM effect can be ignored in the low frequency. So the resistivity of the model can be replaced with the Cole-Cole model’s response under different frequency, and the model can be subdivide and interpolation, analysis, general synthesis. Solving the last received linear equations, we can get the complex voltages on each nodes. According to the definition of the IP’s parameter, we can get the frequency-domain parameters without considering the EM effect. Using the triangular prism element can finished the simulation of IP’s parameters under the undulate topography.The following is the main study results:1. On the base of other researcher, the paper from the basic equations of stable current field to derived the expressions of boundary problems under 3-D condition. without considering the EM effect and using the generalized variational structure principle, It can get the corresponding variational structure equation. For subdivide the 3-D model, interpolation, analysis, and general synthesis with the triangular prism element, we can carry out the simulation on frequency-domain IP’s parameters under level and undulate topography.2. Derived the tri-linear interpolation-shape function of hexahedron-tetrahedron and tri-prism element, and carry out frequency-domain IP forward simulation under 3-D level and undulate topography.3. Using the MATLAB computer language, complete a set of program of forward simulation based on FEM. Finally, using the simulation experiment, the result show that the program is stable, reliability and correct.4. In this chapter, the author simulate the frequency-domain IP parameters with the middle-gradient and the dipole-dipole array under level condition, and discuss the corresponding parameter-phase frequency, and show that the phase frequency can be regard as important parameter to distinguish different polarization body’s time constant, and it can be seen a choice to resolve the metal sulfides and the carbonaceous shale.5. In this chapter, the paper simulate the IP parameters with different depth-sounding equipment and polarization bodies under undulate topography, and plotted the model’s sectional drawing, discussed the abnormality’s character and the change law under the valley topography and ridge topography, and complex topography respectively. The results show that the terrain can not generate IP anomaly, but it can tensile, squeeze, and invert the anomaly greatly. It is even the basic changes.6. Finally, the paper simulate the parameters of the dual-frequency IP method and pseudo-random IP method, and discuss the character and law under different earth-electricity model, and show that the dual-frequency IP method has the frequency-domain IP’s character. And it has it’s special advantage. through simulate the pseudo-random IP method, the results show that this method can improve the efficiency and obtain multiple parameters at same time.In the last part of this paper, the author give some conclusions and proposals, which points out the deficiency in the paper and need to perfect place in the future.更多还原