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本文以等效电阻率概念为基础,以等效电流偶极子为条件,通过一般积分形式求解。将球体、圆柱体和板状体等规则几何形体的相互变换关系,推导出其E_2和η_s的实用公式。由于不用拉普拉斯二阶偏微分方程求解,因而使问题大大简化,使结果简单、直观和实用。文章最后得出:用等效电流偶极距方法进行积分求解与按位场基本理论求解是一致的;根据导出不同形体的函数表达式,很容易研究各种形体二次场分布形态,指出等效电流偶极距,不但有实际意义,并有具体物理含意。同时指出通过坐标转换或场的分解可求出倾斜地质体的表达式。
In this paper, based on the concept of equivalent resistivity, the equivalent current dipole is used as the condition, and it is solved by the general integral form. The mutual transformation relations of regular geometric shapes, such as spheres, cylinders, and plate-like bodies, are used to derive the practical formulae for E_2 and η_s. Because the Laplacian second-order partial differential equations are not solved, the problems are greatly simplified and the results are simple, intuitive, and practical. Finally, the paper concludes that the use of the equivalent current dipole moment method for integral solution is consistent with the solution of the basic theory of the bit field. According to the function expressions derived from different shapes, it is easy to study the shape of the secondary field distribution of various shapes, etc. The effective current dipole distance not only has practical significance, but also has specific physical meaning. At the same time, it is pointed out that the expression of the inclined geological body can be obtained through coordinate transformation or field decomposition.