基于高阶叠层矢量有限元法的回线源瞬变电磁法带地形三维正演

Due to the larger exploration depth and better resistance to cultural disturbances, surficial controlled-source electromagnetic (CSEM) methods have already been the indispensable techniques for prospecting the deposits located in the second deep space of lithosphere (500-1000m). However, the CSEM methods are susceptible to the interference caused by rugged topography, and the precision of existing numerical methods is relatively low at the observation points near the transmitting source due to its singularity. In this study, the higher-order vector finite element method based on unstructured tetrahedral grids will be employed in order to obtain high-accuracy electromagnetic response, and the loop source is taken as example because it is affected seriously by the source singularity. In our scheme, the loop source will be viewed as the combination of finitely many horizontal electric dipoles, which could be denoted in the form of Delta function. Then, the mesh near the dipoles will be refined locally by the unstructured meshing technique. Finally, the accurate electromagnetic response will be obtained by the higher-order vector finite element method based on hierarchical basis functions. Additionally, we will study the distortion effect to electromagnetic response caused by rugged topography, and take porphyry deposit as a example. In conclusion, the research from this project will not only enhance the accuracy of three dimensional forward with topography for loop-source transient electromagnetic method, but also lay a solid foundation for improving data interpretation level.

地面可控源电磁法由于勘探深度大、抗干扰能力强是第二深度空间（500-2000m）找矿的主要技术，但是由于其发射源敷设于地表，资料解释受地形起伏影响较大。鉴于现有数值方法用于可控源电磁法带地形三维正演的近区数值解精度不理想，本课题拟采用基于非结构化四面体网格的高阶矢量有限元法实现可控源电磁法带地形的精确三维正演。本课题以受场源奇异性影响较大的回线源瞬变电磁法为例，首先将回线源分解为有限多个电偶源并以Delta函数逐个处理，然后采用非结构化网格对电偶源周边区域进行局部加密，最后采用高阶叠层矢量有限元法获取精确的瞬变电磁响应。在此基础上，本课题拟进一步研究起伏地形引起的瞬变电磁场畸变效应，并以典型斑岩型矿床为例开展实例研究。本课题研究成果不仅可提高回线源瞬变电磁法带地形三维正演的精度，而且还为进一步改善瞬变电磁法资料解释水平奠定基础。

我国金属矿产资源多分布于地形起伏、交通不便的偏远山区，起伏地形给电磁法野外数据采集带来巨大不便。航空电磁法虽然可以克服这种不利影响，但其勘探深度较浅。因此，勘探深度大、抗干扰能力强的地面可控源电磁法仍将占据深部金属矿产勘探的主导地位。然而，地面可控源电磁法却面临一个亟待解决的难题：起伏地形使得发射源铺设形态复杂、激发的电磁场发生畸变。.回线源瞬变电磁法是地面可控源电磁法的重要分支。本项目以复杂形态回线源瞬变电磁法三维正演为研究对象，主要取得了如下成果：.⑴ 基于电磁场正演计算的总场算法，实现了复杂形态回线源的瞬变电磁法三维正演。该算法中，采用基于非结构化四面体网格的矢量有限单元法在空间域离散电场总场Helmholtz方程，如果基于时步法还需采用后退欧拉法在时间域离散控制方程。复杂形态场源加载技术是该算法实现的关键：首先将其分解为一系列首尾相接、方向不尽相同的电偶源，再将这些电偶源进一步分解为与坐标轴平行的三个子电偶源，进而实现复杂形态场源以电偶源形式的逐个、逐向加载。通过与矩形回线和圆形回线在层状介质表面激发电磁场的解析解，与块状高导体、垂直接触带等模型的多种数值解对比，验证了本算法的正确性。.⑵ 首次将Euler和Talbot算法应用于瞬变电磁法勘探的一维正演领域，并发现这两种算法在双精度计算环境下获取的瞬变电磁响应精度远高于Gaver-Stehfest算法，其中Euler算法更适用于垂直磁偶源和回线源瞬变电磁法，而Talbot算法更适用于基于水平电偶源的海洋可控源电磁法。.⑶ 系统总结了瞬变电磁法诸多成功案例背后蕴含的地球物理模型，并将其划分为四类：矿床学模型、水文地质模型、地质构造模型和人文模型，并认为特定地电模型分析和地下流体动态监测为瞬变电磁法应用的两个重点发展方向。.本项目复杂形态回线源瞬变电磁法三维正演算法的顺利实现，为研究地形起伏、复杂形态激发源引起的电磁场畸变提供了强有力的手段，也为三维反演奠定了坚实基础。