起伏地形大地电磁二维有限元数值模拟

发布时间：2018-06-01 07:23

本文选题：大地电磁 + 二维数值模拟　；参考：《成都理工大学》2015年硕士论文

【摘要】：大地电磁测深法(MT)属于电磁法勘探中的频率域方法,利用天然交变场源对地球深部岩石的电性参数进行研究。大地电磁法已广泛应用于油气勘探、海洋及地球深部等探测,现已成为深部地球物理探测的一种重要方法和必不可少的手段。开展大地电磁测深工作时,往往并不是在平坦的地表处,而是在山区复杂地形条件下进行。复杂地形条件对野外实测数据影响非常大,给资料的处理和解释带来了很大困难。因此,对带地形的大地电磁数据进行数值模拟是非常必要的。在复杂的地形条件下提高资料处理精度和解释准确性仍是当今的难点问题之一,实现带地形的二维大地电磁正演是提高资料处理解释水平的重要途径,受到工作者们和研究者们的重视。因此,研究在起伏地形条件下的大地电磁数值模拟是一个很有意义的课题。目前,大地电磁法的二维正演问题已基本解决,在使用有限单元法,有限差分法和积分方程法等数值模拟方法解决二维大地电磁正演问题方面有广泛的研究结果;但在网格剖分方式、电性参数设定、辅助场定义和起伏地形模拟等方面,仍有改进之处。本文研究的就是起伏地形条件下大地电磁的数值模拟方法,并将有限单元法用于起伏地形条件下二维大地电磁场的正演计算。首先,由麦克斯韦方程组(Maxwell Equations)得出大地电磁场的基本方程亥姆霍兹方程(Helmholtz Equation)的有限元格式和大地电磁场所应该满足的边界条件。然后,以电磁场所满足的微分方程、边界条件和变分问题为出发点,推导出起伏地形下二维MT正演的有限元算法。在有限单元法网格剖分方式上,采用矩形网格内剖分三角形网格的方案,这种剖分方式便于对起伏地形的模拟,以适应各种水平或起伏地形情况。考虑到实际地层中的岩石,矿物体等在水平方向和垂直方向上电性参数是连续变化的,而在一些反演方法中,反演结果的电性参数也是连续变化,故将网格单元内的电性参数设定为线性变化。根据单元节点主场值和线性插值形函数间的关系,计算出单元节点辅助场值。在方程组的求解方面,采用变带宽存储解决含有大量零元素的大型稀疏矩阵的存储和方程组的求解问题,以节约内存使用量和提高计算速度。根据起伏地形情况下实测电磁场分量的特征,定义TE和TM两种模式下的视电阻率和阻抗相位计算公式。根据以上原理和结论编制一套实用的大地电磁正演程序,并设计了均匀层状模型、均匀半空间中含有电性异常体模型、有地表起伏的均匀半空间模型,以此验证程序的正确性。利用一维正演程序对当下比较热点的“低阻薄层效应”进行了简单的分析,正演结果基本正确,总结出的规律与前人吻合;对于二维正演,通过对多种模型的验证,得出不同地电断面的水平地形和起伏地形的正演模拟结果与前人模拟结果一致,模型参数基本吻合。结合两种极化模式的视电阻率和相位信息的横向和纵向分辨率特点,对地下异常体的深度定位、规模大小和方位判定表现出良好的效果。非水平地形情况下的正演响应结果也与正演模型基本符合,验证了本文方法的正确性和有效性。
[Abstract]:Magnetotelluric sounding (MT) is a frequency domain method in the exploration of electromagnetic method, using natural alternating field sources to study the electrical parameters of rock in the deep earth. Magnetotelluric method has been widely used in oil and gas exploration, ocean and earth deep exploration, and has now become an important method and indispensable means for deep earth physical exploration. When the magnetotelluric sounding work is carried out, it is often not at the flat surface, but in the complex terrain conditions of the mountain area. The complex terrain conditions have great influence on the field measured data, which brings great difficulties to the processing and interpretation of the data. Therefore, it is very necessary to simulate the magnetotelluric data with the terrain. It is still one of the difficult problems to improve the accuracy and interpretation accuracy of data processing under complex terrain conditions. The realization of two-dimensional magnetotelluric forward modeling with terrain is an important way to improve the level of data processing and interpretation, which is paid attention to by workers and researchers. Therefore, the magnetotelluric numerical simulation under the undulating terrain conditions is studied. At present, the two dimensional forward problem of magnetotelluric method has been basically solved. There are extensive research results in the use of finite element method, finite difference method and integral equation method to solve the two-dimensional magnetotelluric forward problems. However, the method of grid division, the setting of electrical parameters, the definition of auxiliary field and the definition of auxiliary field The numerical simulation method of magnetotelluric in undulating terrain is studied in this paper, and the finite element method is applied to the forward calculation of the two-dimensional magnetotelluric field under the undulating terrain conditions. First, the basic equation of the magnetotelluric field is obtained by the Maxwell equation group (Maxwell Equations). The finite element format of the Helmholtz Equation equation and the boundary condition that the magnetotelluric place should satisfy. Then, based on the differential equations, boundary conditions and variational problems which are satisfied by the electromagnetic field, the finite element algorithm for the two-dimensional MT forward modeling under the undulating terrain is derived. A scheme of triangulating triangular meshes, which facilitates the simulation of undulating terrain to adapt to a variety of horizontally or undulating topographic conditions. Considering the continuous variation of the electrical parameters in the horizontal and vertical directions, the rock in the actual stratum and the mineral body are continuously changed, and the electrical parameters of the inversion results are also in some inversion methods. It is a continuous change, so the electrical parameters in the grid unit are set as linear changes. According to the relationship between the home value of the node and the linear interpolation function, the auxiliary field values of the unit nodes are calculated. In the solution of the equations, the storage of large sparse matrices with a large number of zero elements and the solution of the equations are solved by the variable bandwidth storage. In order to save the amount of memory use and improve the speed of calculation, according to the characteristics of the measured electromagnetic field components in the fluctuating terrain, the formulas of the apparent resistivity and impedance phase in the two modes of TE and TM are defined. A set of practical magnetotelluric forward sequence is developed based on the above principles and conclusions, and a homogeneous layered model is designed, and the uniform half space is designed. There is an electrical anomaly body model and a uniform half space model with surface undulation to verify the correctness of the program. By using one dimensional forward program, the "low resistance thin layer effect" is simply analyzed. The forward results are basically correct and the rules are in agreement with the predecessors. The simulation results of horizontal and undulating terrain of different geoelectric sections are consistent with the previous simulation results, and the model parameters are basically consistent. Combining the transverse and longitudinal resolution characteristics of the apparent resistivity and phase information of the two polarization modes, the depth location, size and azimuth of the underground anomaly body are determined. Good results. The forward response results of non horizontal terrain are also consistent with the forward modeling, which verifies the correctness and effectiveness of the method.
【学位授予单位】：成都理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.325

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