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边界元法(BEM)是一种新的数值方法。由于该法可以降低所研究场问题的维数,因而边界元法较之域型法(FEM和FDM)具有应用简便、数据量少、计算快、精度高等优点。从而,用该法解决了域型法难以实现的三维地电模型视电阻率异常的计算问题。本文论述了用边界无法求解点源场地表水平和起伏下三维地电体位场问题的方法原理和数值处理技术,并给出了若干算例:导电球状矿体上视电阻率数值解与解析解结果;导电球状矿体上不同测线上视电阻率平剖曲线;三维山脊地形下导电椭球状矿体上视电阻率联剖曲线及其地形改正结果等。由本文内视电阻率的边界元法数值解与解析解结果对比的一致性和三维地形校正的显著效果,表明了边界元法是求解任意三维地电模型上位场问题的有效方法。由于用该法实现了对任意三线地质体上空间位场计算,必将推动三维电法勘探工作的开展与深入研究,无疑会对提高电法勘探的地质效果发挥重要作用。
Boundary Element Method (BEM) is a new numerical method. Because this method can reduce the dimension of the problem under study, the boundary element method has the advantages of simple application, less data, faster calculation and higher precision than the domain method (FEM and FDM). Therefore, this method solves the calculation problem of apparent resistivity anomaly in 3D geoelectric model which is difficult to be realized by domain method. This paper discusses the principle of the method and the numerical processing technique for solving the 3D geoelectric field potential problem with surface boundary and undulation of the point source field by using the boundary conditions. Some examples are given as well: numerical and analytical solutions of the apparent resistivity of the conductive spherical ore body Results: The apparent resistivity profile on different survey lines of conductive spheroidal ore body; the apparent resistivity deconvolution curve and its topographic correction results on conductive ellipsoid ore body under three-dimensional ridge topography. The significant effect of numerical solution and analytical solution results of BEP on the apparent apparent resistivity in this paper and the 3D terrain correction show that the BEM is an effective method to solve the field problem in any 3D geoelectric model. Because this method has realized the calculation of the space field on any three-line geological body, it is bound to promote the development of the three-dimensional electrical prospecting work and further study, which will undoubtedly play an important role in improving the geological effect of electrical prospecting.