【作者】 梁盛军；

【导师】 谭捍东；

【作者基本信息】 中国地质大学（北京） ， 地球探测与信息技术， 2011， 博士

【摘要】 电磁法勘探是一种有效的地球物理手段,随着高分辨率探测技术的发展,对电磁法正反演技术要求也越来越高。复电阻率法可以用多个参数从不同角度评价地质异常体,适合做精细反演解释。目前,复电阻率法正反演方法还不能满足实际工作的要求,三维数值模拟及反演解释仍处于探索阶段。本文研究复电阻率法三维正反演算法,推动复电阻率法正反演进入实用化阶段。复电阻率法三维正演问题采用交错采样有限差分算法。选取有限长度电偶源,将总场分解成一次场和二次场分别求解。在有限长度电偶源激发下,通过解层状介质的边值问题,采用快速汉克尔变换计算得到一次场的分布。基于Cole-Cole模型建立复电阻率模型,采用交错网格对研究区域剖分,将连续的积分方程离散化,设定边界处二次场值为零,形成线性方程组,解线性方程组可得到二次场。通过与已有算法计算结果对比来检验了三维交错采样有限差分算法的精度。复电阻率法三维反演的目的是获得Cole-Cole模型参数的分布,本文采用了三维共轭梯度—最小二乘顺序反演方案。为了获得每个网格单元随频率变化的复电阻率值,三维共轭梯度反演应用“拟正演”算法,每进行一次模型参数更新量计算只需要1次正演和2次“拟正演”,避免实际计算雅克比矩阵。计算雅可比矩阵的转置与一个向量的乘积可得到模型的更新方向,雅可比矩阵与另一个向量的乘积可得到模型更新步长。计算中仅需存储上一次反演模型更新方向,有效减小了存储空间的需求。对三维共轭梯度反演获得的复电阻率模型,利用最小二乘法反演获得每个网格单元Cole-Cole模型参数的分布。使用理论模型合成数据对反演算法的稳定性和有效性进行了检验。更多还原

【Abstract】 Electromagnetic method exploration is one of effective geophysical methods. High resolution exploring technology was developed in recent year, which asked for more efficient forward modeling and inversion method. Complex Resistivity(CR) method could be used for analyzing abnormally from different way with several parameters, and the method was suitable for small scale inversion. CR modeling and inversion technology could not meet the needs from application; Three Dimension(3D) modeling and inversion were still in the stage of researching. We carry out 3D CR modeling and inversion in the thesis, and made some progress in artificial data inversion.We choose 3D staggered grid finite difference method to solve modeling problem. Finite length electric dipole source was used to calculate electromagnetic field. Total field was divided into primary field and secondary field. Primary field was calculated by solving layer earth with finite length electric dipole source, Hankel transform was also used in the calculation. We set up CR with Cole-Cole model and mesh grid with staggered grid. After discretizing continual integral equation, linear equation was formed. Direchlet boundary was used as boundary condition. Secondary field could be obtained by solving linear equation. Cross check was made with integral equation code to testify accuracy of 3D staggered simulation method.The goal of CR 3D inversion is to get distribution of Cole-Cole model parameters, 3D Conjugate Gradient(CG) Least Square sequence inverse method was used as inversing method. In order to get the CR model parameter in each cell that changes with frequency, pseudo-modeling was used in 3D CG inversion to avoid computing Jacobin matrix. One time modeling and two time pseudo-modeling were computed in each time inversion. Updating direction was obtained by computing transformed Jacobin matrix multiply with a vector, updating step could be obtained by Jacobin matrix multiply with another vector. Updating vector was the only vector need be stored in each inversion, demands for storage space was decreased.CR model could be got by 3D CG inversion. Least square method was used to obtain Cole-Cole model parameter in each cell. Artificial data by theoretical model was used to check the stabilization and validation of the code.更多还原