各向异性介质大地电磁二维反演和三维自适应有限元正演

It is widely known that the electric conductivity in the Earth’s subsurface shows anisotropic effects. The electric structures with different anisotropy directions can cause distortions of the magnetotelluric responses, such as impedance phase rolling out of quadrant for many MT sites, or real induction vectors at long periods point systematically a particular direction in a very large scale. These phenomena can only be explained by using an anisotropic conductivity model. Numerical methods and codes for modeling MT responses in 2D or 3D arbitrary anisotropy structures are very few, and the inversion method and code are not available to our best knowledge. We have already developed an adaptive finite element algorithm for MT modeling in 2D conductivity structures with arbitrary anisotropy, which has laid a solid foundation for developing 2D anisotropy inversion method. The solution of the inverse problem is obtained by minimizing a global objective functional consisting of data misfit, a structural constraint and an anisotropy constraint. The total variation functional and gradient support functional are employed for the structure penalty. The vector finite element modeling algorithm for MT fields in 3D arbitrary anisotropic structures can avoid extraneous solution and obtain stable and reliable electric and magnetic fields.

众所周知，地下介质的电导率常常表现为各向异性。具有不同各向异性方向的电性结构会导致大地电磁响应出现异常，如连续测点阻抗相位超象限现象、大范围内长周期实感应矢量统一指向某一特定方向。这些异常现象往往只能通过电导率各向异性模型来解释。由于其复杂性，国际上电导率任意各向异性介质二、三维MT数值模拟方法少见，反演研究进展缓慢，国内的相关研究不多。申请者已研发成功电导率任意各向异性介质二维MT自适应有限元正演算法，为二维反演研究奠定了基础。从反演目标函数构建方式出发，将总变异泛函和梯度支撑类型泛函作为模型目标函数，并增加了一个各向异性惩罚函数，提出各向异性介质MT二维反演方法。基于矢量有限元法的任意各向异性介质MT三维数值模拟算法能够有效地避免出现伪解并获得稳定、可靠的电磁场分布。本课题是一项急待开展的前沿研究，有望取得一些重要成果。

本报告是国家自然科学基金面上项目“各向异性介质大地电磁二维反演和三维自适应有限元正演”结题报告。根据项目任务书要求，我们开展了各向异性介质大地电磁场二维反演和正演方法研究工作，取得了一些创新性结果：推导出了电阻率各向异性介质大地电磁二维反演灵敏度矩阵计算公式；实现了二维各向异性大地电磁反演，并应用于青藏高原实测大地电磁数据反演解释中，提出了青藏高原北部测区内各向异性电性结构模型；实现了任意各向异性介质大地电磁三维自适应矢量有限元正演，分析了不同网格细化比例对数值模拟结果的影响，详细地讨论了倾斜界面和倾斜电阻率各向异性海底对大地电磁响应的影响；基于各向异性介质大地电磁三维正演程序模拟了大地电磁阻抗相位超象限现象，分析了电阻率各向异性体的规模和参数变化对阻抗相位的影响；实现了三维任意各向异性大地电磁拟态有限体积正演算法，并通过一维理论模型验证了算法的有效性，进一步模拟了三维各向异性模型大地电磁响应，较详细地讨论了电阻率各向异性对三维大地电磁响应的影响。. 发表带项目资助标注的论文10篇，均为SCI论文；培养博士后1名，博士生5名、硕士生2名，在站博士后2名，在读博士生2名、硕士生4名