【作者】 龚强；

【导师】 胡祥云；

【作者基本信息】 中国地质大学 ， 地球探测与信息技术， 2007， 硕士

【摘要】 目前国内大多数CSAMT资料处理都用一维反演方法，即假定地球介质是水平层状地电结构，这对于横向变化较大的介质结构的反演则是不真实的。为了合理的模拟可控信号源的三维特征应该使用三维有限元方法。受计算机内存和计算速度的限制，三维方法的实用化受到限制。在许多情况下，地电结构沿走向变化很小，只沿倾向发生变化。这种地电结构是二维的，而人工源是三维的，因此CSAMT资料的观测可用2.5维有限元方法进行数值模拟。本文从麦克斯韦方程组出发，建立了2.5维有限元CSAMT数值模拟方法，其核心是把地电参数变化小的走向方向通过傅立叶变换转化成波数域，用一系列波数模拟二维波数域电磁场的特征。用横向均匀的三层地电结构模型展示了2.5维数值模拟的特征，并和一维模拟结果进行了比较，证实了有限元方法2.5维CSAMT数值模拟的可靠性。在此基础上对地电结构已知的实际模型进行了2.5维数值模拟，计算其电磁场值，视电阻率和视阻抗相位，从而判断此2.5维数值模拟的正确性。为2.5维反演打下基础。本文首先调研了CSAMT国内外的研究现状，确定研究的突破点和创新点在于通过反傅立叶变换，求出侧面剖面十公里范围内电磁场的变化特征，并与一维模型的解析解进行对比，了解二维模拟的精度。在第二章中，研究一维地电模型条件水平电偶源的理论公式和解析解，利用快速汉克变换滤波系数法，做了一维正演计算，并与前人相同地电模型下的解析解进行对比，确定了一维正演程序的可靠性和正确性，进而为验证二维有限单元算法做基础。第三章，具体讨论了沿构造方向地电结构不变或变化较小的条件下，在该方向做傅立叶变换，变换到波数域，通过麦克斯韦方程组及电磁场边界条件，建立电偶源情况下电磁场满足的偏微分方程组，然后通过泛函建立与偏微分方程组等价的变分问题。第四章，详细介绍变分问题下有限单元数值计算方法，包括三角单元剖分，线性方程组的建立，下三角的存储和线性方程组的简化，电磁场其它分量的求取。由于在有限单元算法中采用了二次场算法，线性方程组的求解需要波数域一次场的电磁场值，所以第五章详细推导了波数域电磁场一次场的求解公式。求解到波数域电磁场场值后，需要做反傅立叶变换才能得到常用空间域的电磁场值，第六章则详细介绍了反傅立叶变换的理论和方法。为了检验有限单元算法的正确性，需要做一维地电条件下有限单元数值解和解析解的对比，在第七章，本文详细列出了H型、K型、KH型地电结构下有限单元数值解和解析解的对比图及误差图，对比的场值包括Ex、Hy和Hz，对比剖面包括1公里处、2公里处、4公里处、6公里处、8公里处、10公里处、12公里处；频率范围为10^-2～10⁴Hz。为进一步验证有限单元二维正演的有效性，在第八章做了中间低阻体和中间高阻体两种二维模型的二维正演计算，绘出了这两种模型条件下的视电阻率图和视相位图。由于可控音频大地电磁采用的是人工源，所以比起天然源有很高的信躁比，即使在有工业干扰的地区，也可以获得较好的信躁比。近年来，CSAMT方法在国内外打开了应用局面，并取得了显著的效果。该方法广泛应用在地下水资源勘察、地热勘察、工程物探、金属矿勘查、煤田地质灾害预测等领域。本文利用有限单元算法，实现了电偶源二维正演程序。其创新点在于，在二维地电结构下，x方向布源，通过逆傅立叶变换算出侧面剖面12公里以内的电磁场特征值，并做了一维地电结构条件下有限单元算法结果和解析解的比较，从而验证该有限单元算法的准确性。另外，本文还做了两种异常体条件下的电磁场正演结果。通过有限单元数值模拟的结果和解析解的对比，认为该正演结果在10公里以内可以达到较满意的精度。通过对异常体的正演模拟，得到了反映异常的效果，因此认为该正演程序有效，在低频情况下做适当改进方可用来做静校正，近场校正和二维反演。不足之处在于，低频（频率小于10Hz）时，有限单元算法和解析解结果相差较大，需要做理论上及算法的探讨和研究。随着侧面剖面y值的增大，有限单元算法和解析解结果的误差随之增大，这是由于逆傅立叶变换波数选取的范围不够，以及在波数域中电磁场的变化曲线拟合程度不够。在靠近有限单元网格的边缘，数值模拟结果和解析解结果误差也较大，这就要求网格的剖分要合适，边界网格要够大。靠近源的测点电磁场值也算不准确，因为在有源的地方，电磁场趋近无穷大，电磁场边界条件不满足。更多还原

【Abstract】 Now most of CSAMT data processing methods are developed in one dimension. that is thatsupposing the earthmedia is horizontal layers, this will cause some wrong results for an earthwhose conductivity varies in two or three dimensions. For some case’s, the survey lines areparallel to the geologic structure’s dip direction. In such situation, to consider three dimensionssource and two dimensions earth is enough. In order to reasonably Simulate the three dimensionsource and two dimensions earth, this paper introduces a 2. 5D finite element forward modelmethod for CSAMT data, which bases on the Maxwell’s equation. The main principle of thisforward modeling method is to synthesize data for three dimensional signal source with a seriesof different wave numbers in geologic structure’s strike direction (direction x in Cartesioncoordinate system). One typical three layers model is used for 2.5D forward modeling, Becausefor such typical model the EM caused with a 3D source has an analytical integralsolution,through numerical method, The EM field values is easy to determined.Thoughcomparison with these two methods, the reliability of 2. 5D modeling method and software isverified. Then we introduce another model outlined from known geological structure andcaculated it’s electro-magnetic field. The results show that the 2.5D forward modeling methodand correspond software in this paper provides a good tool for CSAMT data modeling becausethe finite element method can be used for the models with lateral variation of earth electricproperties, it will be useful to model 3D source and 2D earth media.Firstly, this paper investigated the researchment of CSAMT in the world, and then consider-ed that the new work should be work out the electro-magnetic field ten kilometers away from themain section and then make compareration of 1-D forward solutions, to kown the method isvalidity. In chapter two, this paper worked out the formulas of electic dipole on a layeredmedium, and made 1-D farward by the Hankel Transformation Method. The compareration withthe other work showed that the 1-D farward is correct, so the I-D farward solution can be usedto vadidate the 2-D forward solution. In chapter three, using the Maxwetl’s equentions and theboundary conditions, this paper worked out the actual differential equations, and then workedout the finite element method equations. In chapter four, this paper paticularly introduced thefinite element method, including triangle element analysis, linear equations foundation, triangleelement storage and linear equations predigestion, others variables calculation. Because of thefinite element method using second field, the first field is needed to solve the linear equations,and in chapter five, the first field formulas are worked out and can be calculated by chavemethod. When the elecromagnetic field is worked out from the linear equention, the athwartfourier transformation is needed to give the actual elecromagnetic field, and in chapter six, thetheory and method of athwart fourier transformation is particularly gaven out. In order to checkup the correctness of the finite element method solution, the comparation of 1-D solutionbetween the finite element method solution shoud be show out, and in chapter seven, this papershow out three kinds of different earth model structure comparation between the finite elementmethod solution and 1-D solution, the comparation including Ex, Hy and Hz field, and theprofile is from 1 kilometer, 2 kilometer, 4 kilometer, 6 kilometer, 8 kilometer, 10 kilometer and 12 kilometer. For more validation, in chapter eight, this paper show out the solution of twodifferent model structure which one is low resistivity in the center and the other one is highresistivity in the center, which including resistivity and phasic pictures both.Because of the CSAMT method using manpower, the signal is much better to incept, eventhough in the industrial interferential area. In these years, the CSAMT method having been usedin many areas, such as, groundwater reconnaissance, terrestrial heat reconnaissance,engineering exploration, metal mine exploration, coalfield disaster forecast and so on.Using the finite element method, this paper carded out the electic dipole source 2-D modelstructure forward program. The innovation point is that the source is in x direction, the earthmodel structure is 2-D, and the solution is 12 kilometers away form the source. Through thecomparation between 1-D solution and 2-D solution, we believe that the finite element method iscorrect. What is more, this paper show out the solution of two different model structure whichone is low resistivity in the center and the other one is high resistivity in the center, whichvalidates the correctness also.The comparation between 1-D solution and 2-D solution shows that the solution in 10kilometers is acceptable, and the 2-D model structure forward shows the finite element methodis availability. So, the program can be used to near field emendation and 2-D reverse.This program has shortages also, when the frequency is low(lower than 1 Hz), thecomparation between 1-D solution and 2-D solution is unacceptable, it needs theory and methodimprovement, when the distance of the profile y becoming larger the error is larger, this issimply because of the athwart fourier transformation is not enough, at the edge of the finiteelement gridding the electromagnetic field forward is also unacceptable, so it need proper finiteelement gridding, what is more, the electromagnetic field near the source can not be calculatedcorrectly, because the electromagnetic field near the source is tend to infinite.更多还原