节点文献
频率域可控源二维有限元正演数值模拟
【作者】 李杰；
【导师】 柳建新；
【作者基本信息】 中南大学 ， 地球探测与信息技术， 2010， 硕士
【摘要】 频率域可控源大地电磁法由于人工源的加入使其克服了大地电磁法中天然场源信号微弱的缺点,因此在矿产普查、油气勘探等方面得到了广泛的应用。本文主要对频率域可控源电磁法二维正演问题进行研究,并通过全区视电阻率对过渡区以及近区数据进行校正。本文采用有限单元法进行数值模拟。用Matlab为程序编译工具,采用双线性插值和双二次插值的有限单元法,推导出了相对应的边值问题和变分问题满足的微分方程。为了模拟无穷远边界并满足计算机的内存需求,在保证计算精度的情况下设计了非均匀网格剖分。在程序编制过程中,只存储有限元系数矩阵的非零元素,大大节省了存储空间。通过计算几个典型模型的卡尼亚视电阻率拟断面图和相位拟断面图,得出了不同模型下电磁场响应特征的分布规律,验证了算法的正确性。针对频率域可控源电磁法中卡尼亚电阻率在过渡区和近区畸变的问题,给出了全区视电阻率的迭代公式,并对典型的一维层状模型以及简单二维模型进行了计算。过渡区和近区数据经过校正后,可以正确反映出模型的地电特征,证明了线源下近区勘探的可能性。
【Abstract】 Because of the artificial source, fCSEM has overcome the weakness of natural source, which is the shortcoming of MT, so it has been widely used in the mineral, oil and gas exploration and so on. This paper has done some studies on the 2D forward problem of fCSEM, and uses the whole range apparent resistivity to rectify the date which are collected near the source.The finite element method was used for numerical simulation. Based on Matlab as programming tool, we adopted the finite element method of linear interpolation and second interpolation in a rectangular element for solving the fCSEM forward problem and derived the corresponding formulas for calculating. In order to simulate the infinity border and meet the demand of computer memory, the non-uniform gird is designed to ensuring the accuracy. In programming, we only stored the non-zero elements of the finite element matrix for saving the calculation memory. By numerical simulation of several typical models, we verified the correctness of the forward modeling algorithm.The iterative formula of the whole range apparent resistivity was develpped to solving the problem of distortion of Cagniard apparent resistivity when the date are collected near the source. Typical 1D layered model and simple 2D model are calculated. After rectify the date, it can accurately reflect the characteristics of the model which verified the fact that the exploration near the source is possible.