有限长接地线源频谱激电2.5维复电阻率反演

Frequency spectral induced polarization is one of geophysical methods is mainly used to explore metal mineral deposit. It is significant advantage that there are multiple parameters to be recorded about an abnormal. The traditional SIP processing has some problems, because EM coupling, the dilution factor and the DC-based inversion were applied. A novel processing will be study, taking into account the distance of electrode array and EM coupling to numerical simulation. Then, SIP data were inversed to complex resistivity of the two dimensional model. At last, complex resistivities changed with frequency of the model were decomposed using the Cole-Cole model. There are two advantages for the new processing, one is the EM coupling was considered by forward problem, other is the direct inversion of complex resistivity improve stability of inversion because avoided to inaccuracy of mathematical model about complex resistivity.The finite element method was applied,there are three methods to behalf the finite length grounded wire source, the secondary field algorithm, numerical integration of the dipole field and pseudo-delta function method.For the inversion, a special processing base on the minimum filled elements was applied to process sparse matrix created by forward problem. The linear sparse system was solved using direct method based on graph theory. The inversion objective function was designed by considered the different of complex resistivity by frequency is smooth and complex resistivity spatial Information, then it is solved by the Gauss-Newton method and nonlinear conjugate gradient method.

频谱激电是当前金属矿产勘探的主要地球物理学方法之一，其最大优点是具有多参数反应异常的能力。本项目针对频谱激电数据解释中电磁耦合、稀释系数与基于直流反演存在的问题，结合频谱激电法野外实际采用的观测装置形式，提出开展有限长接地线源同时考虑激电与电磁感应的正演、直接反演复电阻率的反演，并通过对反演单元复电阻率进行真谱分解的数据解释思路。正演考虑电磁感应、直接反演复电阻率可回避去耦处理和由于复电阻率数学模型不精确引起的反演不稳定问题，研究工作将为该方法的数据解释提供新途径。拟采用有限单元进行正演，通过异常场算法、偶极场数值积分及伪狄拉克函数表示场源解决有限长线源的引入问题，采用基于最小填入元思想的矩阵重排算法处理正演矩阵，应用基于图论思想的稀疏矩阵直接分解方法提高正演求解效率；反演方面，引入复电阻率频变平滑及复电阻率空间信息设计正则化反演目标函数，采用牛顿与非线性共轭梯度法求解反问题。

研究工作根据频谱激电数据解释的实际需求，完成了考虑电磁感应的2.5维复电阻率正演、反演。开发了基于有限单元正演与正则化反演的地球物理正反演统一程序框架，奠定了研究工作的基础。从电磁场基本理论出发推导了复电阻率2.5维问题正演计算的总场与二次场算法理论公式；采用有限单元进行了数值计算，通过基于二叉树结构的收缩网格进行剖分，利用直接求解法求解稀疏线性方程组，实现了复电阻率2.5维问题数值计算；研发了基于模型分辨率的自适反演算法，通过复电阻率频变约束等实现了复电阻率2.5维反演。