任意三维地电模型视电阻率异常的边界元法数值解

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。

NUMERICAL SOLUTION OF BOUNDARY ELEMENTMETHOD FOR APPARENT RESISTIVITY ANOMALYOF AN ARBITRARY THREE-DIMENSIONALGEOELECTRIC MODEL

The boundary element method(BEM)is a new numerical method. As it can reduce the dimensionality of the studied potential field problem, this me thod, as compared with FEM and FDM methods, has such advantages as sim plicity and convenience, less data quantity, rapid calculation and high preci sion. In consequence, this method has been successfully used to solve the cal culation for apparent resistivity anomaly or a three-dimensional geoelectric model which can hardly be worked out by FEM and FDM methods.This paper deals with the principle and numerical processing technique of using BEM method to solve the potential fiel dproblem of the three-dimen-sional geoelectric body of a point source field under the condition of horizon tal or undulate suiface with some calculation examples given: numerical solu tion and analytic solution of apparent resistivity over the conductive spheri cal orebody; plane- section curves or apparent resistivity along different survey lines over a conductive spherical orebody; combined profile curve of apparent resistivity over a conductive ellipsoidal orebody and its topographic correction.The consistency between the numerical solution and the analytic solution of BEM method for apparent resistivity and the obvious effects of three-di mensional topographic correction demonstrate that BEM is an effective method for solving potential field problem of an arbitrary three-dimensional geoelectric model. As it has realized the calculation for spatial potential field over an arbitrary three-dimensional geologic body, this method will undoubtely push forward the electrical prospecting research and play an important role in raising geological effects of the electrical prospecting.