This article deals with an infinitesimal current source (ICS) in a multilayer conducting medium that consists of air and multilayer soil. Closed-form kernel functions of the spectral-domain Green's function for scalar electric and vector magnetic potentials (Lorentz potentials) were obtained for every layer of the multilayered medium as analytic solutions of the systems of linear equations. Validation of the proposed closed-form expressions is performed by numerical solving of the system of linear equations and by numerical comparison with expressions derived from existing closed-form expressions developed for the source layer of the multilayer dielectric medium. For an arbitrary-oriented ICS, scalar electric potential of its horizontal component is chosen as a unique scalar electric potential. Accordingly, dyadic Green's function of vector magnetic potential is corrected.

中文翻译：

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多层土壤中无穷小电流源的闭式谱域格林函数

本文讨论由空气和多层土壤组成的多层导电介质中的无穷小电流源 (ICS)。对于多层介质的每一层，作为线性方程组的解析解，获得了标量电势和矢量磁势（洛伦兹势）的谱域格林函数的闭式核函数。通过对线性方程组进行数值求解，并通过与为多层电介质源层开发的现有封闭式表达式导出的表达式进行数值比较，来验证所提出的封闭式表达式。对于任意定向的 ICS，选择其水平分量的标量电势作为唯一的标量电势。因此，二元格林'