基于格点型有限体积法的大地电磁二维正演  

Two-dimensional magnetotelluric forward modeling based on vertex-centered finite volume method

作　　者：童孝忠[1,2] 谢维[1] TONG Xiao-zhong;XIE Wei(School of Geosciences and Info-physics,Central South University,Changsha 410083,China;Key Laboratory of Non-ferrous Resources and Geological Hazard Detection of Hunan Province,Central South University,Changsha 410083,China)

机构地区：[1]中南大学地球科学与信息物理学院,长沙410083 [2]中南大学有色资源与地质灾害探查湖南省重点实验室,长沙410083

出　　处：《中国有色金属学报》2023年第5期1682-1694,共13页The Chinese Journal of Nonferrous Metals

基　　金：国家自然科学基金资助项目(41674080);湖南省自然科学基金资助项目(2020JJ4697)。

摘　　要：伴随着大地电磁勘探方法的广泛应用,发展精确和快速的正反演算法成为应用地球物理学者和工程师们的研究重点。考虑到在大多数二维地电模型中,大地电磁响应不存在解析解,本文建立了格点型有限体积正演模拟算法。首先,从大地电磁场满足的变系数亥姆霍兹方程边值问题出发,导出了格点型有限体积法控制方程的离散表达式,对边界条件进行近似处理后求解线性方程组,得到大地电磁场数值解。其次,通过对均匀半空间模型和一维介质模型的模拟计算,与解析法计算结果对比,验证了有限体积正演算法的正确性和稳定性,并分析了纵向单元剖分间距对大地电磁响应的影响。然后,利用格点型有限体积算法精确地计算了COMMEMI 2D-1模型的大地电磁响应值,该方法的计算消耗和精度都优于有限差分法。最后,通过对典型二维地电模型的大地电磁响应模拟,总结了异常响应规律,可为实测数据的定性解释提供指导。With wide application of magnetotelluric sounding method,the searching precise,rapid forward and inversion algorithms have become the focus research of geophysicists and engineers.In the most two-dimensional geo-electric model,there were not analytical solutions for magnetotelluric responses,so the vertex-centered finite volume method was developed for numerical results in this paper.Firstly,from the boundary value problem of variable coefficient Helmholtz equation for electric field and magnetic field,the discrete expressions of governing equation is derived from vertex-centered finite volume method.The numerical solutions of electric field and magnetic field are calculated after the approximate treatment on the boundary conditions.Secondly,through the simulation of homogeneous half-space model and one-dimensional model and compared with the analytical results,the correctness and stability of the finite volume forward algorithm are verified,and the accuracy can be affected by grid size.Then,the magnetotelluric response of COMMEMI 2D-1 model is accurately calculated by using the vertex-centered finite volume algorithm.The calculation consumption and accuracy of this numerical method are better than that of the finite difference method.Lastly,by the numerical simulation for a twodimensional model,the magnetotelluric responses is summarized,which can provide for qualitative interpretation of field data.

关 键 词：大地电磁法 正演模拟 有限体积法 格点型 二维模型 

分 类 号：P631[天文地球—地质矿产勘探]