基于非结构化网格的复杂形态回线源瞬变电磁法三维正反演研究

Surface loop-source transient electromagnetic methods are widely applied to exploring for mineral deposits, hydrogeological investigation and other fields. However, a transmitting loop always presents a three-dimensional (3D) complex shape due to topography and other factors in these methods. How to make fine data-processing and interpretation is a difficulty that must be faced. This suggests a 3D inversion should be used to fully extract and make use of the geoelectric information carried by the electromagnetic field for a complex-shaped loop. 3D forward modeling is the most important method of studying transient electromagnetics excited by a complex-shaped loop, is also the foundation for 3D inversion. A complex-shaped transmitting loop is viewed as a combination of many electric dipoles, each of which may have its own direction. An unstructured tetrahedral mesh combined with a local refinement technique can be able to accurately delineate and impose these dipoles in a numerical method. A time-domain vector finite element method based on an unstructured tetrahedral mesh will be employed as the forward modeling solver to study the transient electromagnetics excited by a complex-shaped loop in this project. The effects of the realistic waveform for a transmitting current, induced polarization, and electric anisotropy will be incorporated in this forward modeling solver. Based on the above forward solver, Gauss-Newton method will be applied to 3D constrained inversion in this project. Within this inversion, Krylov subspace iterative solvers will be employed for solving the normal system of equations at each Gauss–Newton step, and the scheme of decoupling meshes used for forward modeling and inversion will also be used to improve the inversion efficiency. This study will accelerate 3D inversion applying to field cases.

地面回线源瞬变电磁法已广泛应用于资源勘探、水文地质调查等领域。然而，起伏地形等因素引起的发射回线形态畸变是地面回线源瞬变电磁法资料精细处理解释直面的难题。为了充分提取和利用复杂形态回线源激发电磁场携带的地电信息，建议采用三维反演开展资料处理解释。三维正演是研究复杂形态回线源激励瞬变电磁场与复杂地形和地质体耦合的最重要手段，也是三维反演的基础。复杂形态回线源可视为多个首尾相接、方向不尽相同的电偶源，采用非结构化四面体网格和局部加密技术能够精确描述和有效加载这些电偶源。本项目拟采用基于非结构化四面体网格的时域矢量有限单元法开展考虑发射电流实际波形、激发极化效应和电各向异性的复杂形态回线源瞬变电磁法三维正演；在此基础上，开展基于高斯牛顿法的三维约束反演研究，并通过采用Krylov子空间迭代法求解高斯牛顿法法方程、解耦正演和反演网格等措施提高计算效率，加速回线源瞬变电磁法三维反演的实用化。