Abstract—A new method for analytical description of time-dependent signals of different nature based on local and regional versions of the method of linear integral representations in spaces of different dimensions is proposed. The inverse problem of finding the field sources is reduced to solving ill-conditioned systems of linear algebraic equations with an approximate right-hand side. The results of a mathematical experiment on finding elements of nonstationary gravity and magnetic fields of the Earth are presented.

中文翻译：

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地球随时间变化的物理场的分析模型：本地版本

摘要—提出了一种基于不同维度空间中线性积分表示方法的局部和区域版本的不同性质的时间相关信号的分析描述的新方法。寻找场源的反问题被简化为求解具有近似右侧的线性代数方程的病态系统。介绍了寻找地球非静止重力和磁场元素的数学实验结果。