Abstract—The paper addresses issues related to constructing the analytical approximations of geopotential fields based on a modified method of S-approximations which approximates the initial field by a sum of potentials of a simple and a double layer distributed on a set of carriers of mass located below a given relief. Special attention is paid to the application of new highly efficient methods for solving the systems of linear algebraic equations (SLAE) of large and super-large dimensions to which the inverse geophysical and geodetic problems are reduced. An improved block contrasting method is proposed for solving these SLAEs. The underlying idea of the method is to divide the initial domain into the subdomains that are most contrasting by their properties and to subsequently deform the blocks. The results of mathematical experiments on constructing the analytical approximations of anomalous gravity and magnetic fields and separating the fields created by the different sets of the sources are presented.

中文翻译：

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基于修正 S 近似的不同来源产生的势场分离

摘要——本文解决了基于改进的 S 近似方法构建位势场解析近似的相关问题，该方法通过分布在一组质量载流子上的简单层和双层的势之和来近似初始场。低于给定的救济。特别注意应用新的高效方法来求解大维度和超大维度的线性代数方程 (SLAE) 系统，从而减少逆地球物理和大地测量问题。提出了一种改进的块对比方法来解决这些 SLAE。该方法的基本思想是将初始域划分为属性差异最大的子域，然后使块变形。