基于数据空间的大地电磁二维共轭梯度反演研究

发布时间：2018-02-04 01:52

本文关键词： 数据空间共轭梯度(CG) 二维反演大地电磁法　出处：《东华理工大学》2015年硕士论文　论文类型：学位论文

【摘要】：大地电磁测深法(MT)是以天然电磁场为场源,通过观测相互正交的电场和磁场分量并计算卡尼亚视电阻率和相位来研究和解决地质问题的一种频率域电磁法。国内外地球物理工作者已提出了多种反演方法,并在实际应用中取得良好效果,但对已有方法的改进优化和新方法的探索研究从未停止。本文首先利用有限差分法实现TE和TM模式下的二维大地电磁正演,并通过典型地电模型验证了算法的准确性和适用性。然后开展了基于数据空间的共轭梯度反演算法实现大地电磁二维反演研究。该算法是在OCCAM反演算法基础上利用共轭梯度算法求解模型更新算子,由于从模型空间M转换到数据空间N内计算,极大减小了计算内存和运行量,另外只需计算JACOBI矩阵或矩阵转置与向量的乘积,避免JACOBI矩阵直接存储和计算。利用开发的基于数据空间的共轭梯度反演算法,试算了几个典型地电模型,通过与非线性共轭梯度反演算法(NLCG)对比表明:DCG反演算法具有NLCG算法相同准确性,且具有收敛速度更快和纵向分辨率更高的优势。论文还开展噪声水平、初始模型、正则化因子等反演参数研究,结果表明正则化因子采用“L”曲线法选取较好,该反演方法具有较强抗噪能力、对初始模型依赖性较小、适应性强等特点。因此本文开发的基于数据空间的MT二维共轭梯度反演算法是一种稳定、可靠的反演算法,为大地电磁实际数据资料解释和三维反演研究提供新途径。
[Abstract]:Magnetotelluric sounding (MT) is a natural electromagnetic field source. A frequency-domain electromagnetic method for studying and solving geological problems by observing the components of electric and magnetic fields which are orthogonal to each other and calculating Kania apparent resistivity and phase. Many inversion methods have been proposed by geophysicians at home and abroad. Good results have been obtained in practical application, but the improvement and optimization of existing methods and the exploration of new methods have never stopped. Firstly, the finite difference method is used to realize two-dimensional magnetotelluric forward modeling in te and TM modes. The accuracy and applicability of the algorithm are verified by typical geoelectric model. Then, the conjugate gradient inversion algorithm based on data space is developed to realize two-dimensional inversion of magnetotelluric. The algorithm is based on OCCAM inversion algorithm. The conjugate gradient algorithm is used to solve the model update operator. Because of the transformation from the model space M to the data space N calculation, the computational memory and the running amount are greatly reduced, and the JACOBI matrix or matrix transpose and vector product are only calculated. To avoid the direct storage and calculation of JACOBI matrix, several typical geoelectric models are calculated by using the developed conjugate gradient inversion algorithm based on data space. The comparison with the nonlinear conjugate gradient inversion algorithm shows that the NLCG algorithm has the same accuracy. And it has the advantage of faster convergence speed and higher vertical resolution. The paper also studies the inversion parameters such as noise level, initial model, regularization factor and so on. The results show that the regularization factor is better selected by "L" curve method, the inversion method has strong anti-noise ability and has less dependence on the initial model. Therefore the MT 2D conjugate gradient inversion algorithm based on data space developed in this paper is a stable and reliable inversion algorithm. It provides a new way for the interpretation of magnetotelluric data and the study of 3D inversion.
【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】：P631.325

【参考文献】