三维直流电场积分方程中奇异性的近似处理  

Treatment of Singularity in Integration Equations for 3D D.C. Electrical Field

作　　者：张金会[1] 孙建国[1] 

机构地区：[1]吉林大学地球探测科学与技术学院/国土资源部应用地球物理综合解释理论开放实验室,长春130026

出　　处：《吉林大学学报（地球科学版）》2009年第5期923-928,共6页Journal of Jilin University：Earth Science Edition

基　　金：国家'863'计划项目(2006AA06Z109);国家自然科学基金项目(40574052);国家'973'计划项目(2007CB209603)

摘　　要：直流电场积分方程的核函数是磁并矢格林函数,其数学表达式与电并矢格林函数的数学表达式完全不同。因此,在处理直流电场积分方程的奇异性时不能直接利用文献中针对电并矢格林函数所提出的奇异性消除公式。为了寻求处理磁并矢格林函数奇异性的有效途径,参考文献中针对电并矢格林函数的奇异性消除方法,提出了针对磁并矢格林函数的拟源并矢概念,并求出了当包围奇异点的小邻域为球体、立方体等不同形状时的拟源并矢。如果将这些拟源并矢代入到电场的积分方程中,可以得到只含有正常非奇异积分的数值计算方案。将这个计算方案用于实现关于直流电场的拟解析近似理论,则可以使三维直流电场的快速数值模拟成为可能。In the integral equation for the direct current electrical field the kernel function is the magnetic dyadic Green＇s function. In comparison to the electrical Green＇s function, the magnetic Green＇s function has a different mathematical formulation. As a result, one cannot use the published singularity removal formulas directly to the magnetic Green＇s function, because the formulas are developed solely for the electrical Green＇s function. To find a way for removing the singularity of the magnetic Green＇s function, we present the concept of the quasi-source dyadic for the magnetic Green＇s function, after the corresponding work done for the electrical Green＇s function. Furthermore, we compute the quasi-source dyadic for some forms of neighborhoods of the singular point of the magnetic Green＇s function, such as spheres and cubes. Using the computed quasi-source dyadic in the integral equation for the direct current field, we can establish a numerical scheme only containing regular integrals. If the numerical scheme is used in the quasi-analytical theory on the direct current field, the fast modeling of the direct current electrical field can be carried out.

关 键 词：拟解析近似 直流电场 奇异性 并矢格林函数 拟源并矢 

分 类 号：P631.3[天文地球—地质矿产勘探]