多种线圈模式地面核磁共振三维正反演研究

The conductive structure of the underground and loop configuration have significant impacts on SNMR data and its interpretation. Actually, groundwater aquifers are usually complex 3-D structures, hence, the corresponding forward response and inverse interpretation will be inaccurate if aquifers are treated as 1-D layered or 2-D models, and reducing the reliability of SNMR technique finally. Besides, using combinations of coincident and multi-offset loops can take full advantage of the range of sensitivities offered by different loop configurations to variations in subsurface free-water concentration. In this proposal, we are aiming to develop efficient and robust 3D forward modeling and inversion algorithms for SNMR data based on multi-offset measurements and incorporating complex electrical structure. The key of SNMR forward modeling is the calculation of excitation magnetic field. We view the circular loop source as the combination of a certain number of horizontal electric dipoles (HEDs). And the unstructured tetrahedral mesh and local refinement technology will be combined to effectively reduce the adverse effects of field source singularity. Then, the vector FE solver based on the total electric field and an open-source package of direct solvers named MUMPS are used to calculate the magnetic field distribution. As for the inverse problem, the Gauss-Newton (GN) algorithm will be applied considering its quasi-quadratic convergence rate to limit the number of expensive matrix factorization. In addition, coincident and multi-offset loop data sets will be combined to yield higher resolution tomograms for groundwater. In summary, the goal of this project is to implement a robust SNMR 3D modelling algorithm incorporating complex electrical structure and an efficient 3D inversion code for SNMR data based on multi-offset measurements, thus improving the interpretation capacity of SNMR data in the complex hydrogeological environment, and expand its potential in hydrogeological investigations, water quality assessment and other fields.

地下介质电性结构与线圈工作模式对地面核磁共振（SNMR）信号及其资料解释存在重要影响。实际地下水储存结构及其电性分布通常都是复杂的三维构造，若简化含水模型与介质电性结构会降低SNMR技术反演解释结果的准确度与可靠性；单一线圈测量模式也不利于充分挖掘SNMR技术的地下水成像能力。本课题拟研究复杂电性结构下多种线圈模式SNMR三维正反演方法。SNMR三维正演的关键在于回线源激发磁场的计算，其计算拟基于电场总场控制方程，采用非结构化四面体网格矢量有限元法，并结合局部网格加密技术消除场源奇异性影响，最终利用直接矩阵分解技术求解线性方程组获得；反演中对目标函数的最优化采用具有近似二次收敛性的高斯-牛顿法，并联合不同线圈模式提高含水率与弛豫时间反演精度。最终实现实用化的SNMR三维正反演算法，提高SNMR技术在复杂水文地质环境下的应用效果，促进其在地下水探测与水文地质调查等领域发挥更重要作用。

地下介质电性特征与线圈工作模式对地面核磁共振（SNMR）信号及其资料解译存在重要影响。实际地下水储存结构及其电性分布通常都是复杂的三维结构，倘若简化含水模型与介质电性结构必定会降低SNMR技术反演解释结果的准确度与可靠性；另外，不同线圈测量模式具有不同的分辨率特性和抗干扰能力，仅采用单种线圈测量模式也不利于充分挖掘SNMR技术的地下水成像能力。本项目开展了复杂电性结构下多种线圈模式SNMR三维正反演方法研究。SNMR回线源三维激发磁场的正演计算基于电场总场控制方程，采用非结构化四面体网格矢量有限元法，并结合局部网格加密技术较好地消除了场源奇异性影响，最终利用直接矩阵分解技术求解线性方程组获得；反演中对目标函数的最优化采用具有近似二次收敛性的高斯-牛顿法，并联合不同线圈模式提高了含水率与弛豫时间反演精度。最终实现了实用化的SNMR三维正演和二维反演，为提高SNMR技术在复杂水文地质环境下的应用效果、促进其在地下水探测与水文地质调查等领域发挥更重要作用奠定了一定的基础。