用快速汉克尔变换计算各向异性层状介质中点电流源的电位响应  

COMPUTATION OF THE POTENTIAL OF A POINT CURRENT SOURCE IN LAYERED EARTH WITH ARBITRARY ANISOTROPY BY USING OF THE FAST HANKEL TRANFORMATION

作　　者：沈金松[1,2] 苏本玉[1] 

机构地区：[1]中国石油大学资源与信息学院,北京102249 [2]中国石油天然气集团公司物探重点实验室,北京102249

出　　处：《物探化探计算技术》2009年第1期36-43,共8页Computing Techniques For Geophysical and Geochemical Exploration

基　　金：国家重点基础研究发展计划(973计划)(2007CB209607);中国石油天然气集团公司基础研究项目(07A10303)

摘　　要：针对任意各向异性地层,利用快速汉克尔(Hankel)变换导出了点电流源在地下介质中的电位响应关系,计算了各向异性地层的直流电视电阻率,重点分析了电阻率测深方法对地下各向异性介质的探测能力。这里采用二维傅立叶变换,首先导出了均匀各向异性层的电位一般解函数,利用各层界面电位和电流密度垂向分量的连续性及地下电流源的耦合条件,推导出不同层之间电位和电流密度垂向分量的传递函数,建立了空间电位和电流密度的递归计算关系。针对源点附近电位函数的奇异性,采用柱坐标变换,将二维傅立叶变换转化为汉克尔(Hankel)变换,并用快速汉克尔(Hankel)变换计算所有的位函数值。采用均匀各向异性半空间的解析解,验证了文中算法的正确性,给出了多层各向异性地层模型的视电阻率响应曲线,分析了直流电法探测裂缝性地层,估计裂缝分布性状的可能性。The electric potential function of a direct point current to an arbitrary anisotropic layered earth has been calculated through the fast Hankel transformation and the direct current apparent resistivity in the anisotropic formation has been checked against the isotropic formation by using of the Schlumberger sounding configuration,and the capability of detecting the subsurface fractures of the Schlumberger sounding configuration has been examined.In this study,the two-dimensional Fourier transformation has been adopted,to first construct the general solutions of the electric potential in a homogeneous anisotropic formation.The continuity of the vertical component of the current density and electric potential between two layers and the coupling of the source in the M-th layer have been used to derive the propagation functions the electric potential and the vertical component of the current density from the M-th layer to the upper layers and to lower layers,and the recurrent calculation equations of the electric potential and the vertical component of the current density have been deduced.With regard to the singularity of the point source,the cylindrical coordinate system has been adopted and the Hankel transformation has been used to circumvent the source singularity occurring in the implementing the two-dimensional Fourier transformation.The validity of the analytic solution that is implemented by using of the fast Hankel transformation has been checked against an analytic solution of a simple half space anisotropic model.Results of multi-layer models have been shown to assess the feasibility of discerning the fractured formation and predicting the distribution of the fractures by using of the D.C.current survey.

关 键 词：各向异性层状介质 点电流源 快速汉克尔(Hankel)变换 视电阻率 裂缝性地层 

分 类 号：P631.322[天文地球—地质矿产勘探]