基于矢量有限元和瀑布式多重网格法的大地电磁带地形三维并行正演研究

Magnetotelluric (MT) method is widely used in the mineral, oil and gas exploration, groundwater monitoring, geological hazard prediction, engineering geological survey and the study of the deep structure of the earth. However, currently MT data interpretation mainly relies on the 1D and 2D inversions. This cannot satisfy the requirements of high-precision of geological interpretation. For solving this problem, we propose a 3D MT forward modeling algorithm based on vector finite element method with unstructured mesh and cascadic multigrid method, which can quickly and accurately calculate MT responses under undulating surface conditions. In order to ensure the accuracy of 3D MT modeling under complex terrain conditions, we adopt vector finite element method with unstructured mesh to solve double curl electric field equation. With the help of the octree algorithm, we realize the fast mapping between nested tetrahedral meshes. We will design reasonably multigrid interpolation operator and smoothing operator based on tetrahedral edge element, and propose a GPU parallel 3D MT forward modeling method with vector finite element method based on cascade multigrid method. High-precision numerical simulation of MT data with hundreds of millions of degrees of freedom can be implemented rapidly on the computing server. Through numerical simulations on well-known benchmark MT models, we can analyze and improve the algorithm, which lays the foundation for the further application of the method. The project has an important theoretical and practical value for promoting the rapid development of forward modeling and inversion and enhancing the MT data processing and interpretation.

大地电磁法被广泛用于矿产及油气勘探、地下水监测、地质灾害预报、工程地质勘察及深部地球结构研究。然而，目前其解释手段仍局限于一维和二维反演，远不能满足我国高精度地质解释的需求。本项目针对这一现状拟提出一种基于非结构网格矢量有限元与瀑布式多重网格法的三维大地电磁正演算法，快速、高精度计算起伏地表条件下的大地电磁响应。对电场满足的双旋度方程，采用基于非结构网格的矢量有限元法，可保证复杂地形条件下三维大地电磁正演的精度。利用八叉树算法，实现粗密嵌套四面体网格之间的快速映射。合理构造基于四面体棱单元的多网格插值算子与磨光算子，提出基于瀑布式多网格法的三维大地电磁矢量有限元GPU并行正演方案，进而在计算服务器上实现上亿自由度的三维带地形大地电磁快速、高精度正演。通过国际标准模型测试并改进算法，为方法进一步应用奠定基础。本项目对促进勘探电磁法正反演的快速发展，提升资料解释水平，具有重要的理论和实际意义。

大地电磁法被广泛用于矿产及油气勘探、地下水监测、地质灾害预报、工程地质勘察及深部地球结构研究。一维二维大地电磁反演已不能满足目前我国对于地质解释的高精度需求，快速精细化的三维反演成了研究热点。而三维正演是反演的基础，反演的速度和精度很大程度依赖于正演。..本项目主要开展基于非结构网格矢量有限元与瀑布式多重网格法的三维大地电磁正演算法研究。本项目成功对EXCMG进行推广与改进，应用到具有起伏地表、各向异性电导率的大地电磁正演问题中。EXCMG算法与经典迭代求解器相比，效率大幅领先，和较为成熟的代数多网格求解器相比，也具有相当大优势。个人台式机上可快速求解上亿未知数的三维大地电磁正演问题。随着问题规模增加，EXCMG效率优势更明显。EXCMG是三维大地电磁正演的有效方法。通过大量典型模型的计算与分析，测试并改进算法，为后续三维反演的研究奠定基础。本项目的研究成果可在电磁法勘探等地球物理领域得到广泛的应用，具有重要的理论意义和工程实用价值。

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