中文摘要：

三维反演解释是电磁法勘探发展的重要趋势,而如何提高三维反演的可靠性、稳定性和计算效率是算法开发者们目前的研究重点.本文实现了一种频率域可控源电磁（CSEM）三维反演算法.其中正演基于拟态有限体积法离散化,利用直接矩阵分解技术来求解大型线性系统方程,不仅准确、稳定,而且特别有利于含有大量发射场源位置的CSEM勘探情况;对目标函数的最优化采用高斯牛顿法（GN）,具有近似二次的收敛性;使用预条件共轭梯度法（PCG）求解每次GN迭代所得到的法方程,避免了显式求解和存储灵敏度矩阵,减小了计算量.以上这些方法的结合应用,使得本文的三维反演算法准确、稳定且高效.通过陆地和海洋CSEM勘探场景中的典型理论模型的反演测试,验证了本文算法的有效性.

英文摘要：

The Controlled-source electromagnetic（CSEM）method in the frequency domain has evolved into an established technique for mineral resources prospecting and hydrocarbon exploration.An increasing trend is to carry out three-dimensional（3D）CSEM surveys as EM explorations now are increasingly conducted in complex geological environments in order to improve the spatial resolution of subsurface conductivity structure.Quantitative interpretation of large-scale CSEM data in the frequency domain requires efficient and stable 3Dforward modeling and inversion codes.Considerable efforts have been contributed to developing numerical algorithms concerning 3Dinversion of CSEM data that can accurately and efficiently recover subsurface electrical structure over last decade.Most existing3 Dinversion algorithms employ Krylov subspace iterative methods as their forward solvers.Iterative techniques usually need little memory due to only matrix-vector products storagerequired,and they are fast for computation of single field solution.However,there are two main issues when using iterative solvers for 3D CSEM problems：（1）The ill-conditioning of linear systems arising from discretization of Helmholtz equation can lead to poor behavior of iterative solvers and even divergence in some cases.（2）Iterative solvers are very time-consuming for multi-source problems.These difficulties become major impediments when solving large-scale multi-source CSEM problems using iterative solvers.Given the availability of more powerful workstations or computer clusters,direct methods have been increasingly used for solving 3D CSEM problems.Compared to iterative methods,direct solvers have several distinct advantages：（1）They provide more accurate solutions.（2）They are less prone to ill-conditioning of matrix, making them more robust for highly heterogeneous models or non-uniform grids.And（3）they separate the solving of linear system into an expensive matrix factorization and comparably inexpensive forward-backward substitution s