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本文将均质的任意二维、三维物体位场的波谱解析表达式的研究成果推广到变密度、变磁化强度的更一般的情形。对密度差随深度呈指数函数衰减或线性变化的模型,获得了任意倾斜多边形质量面、斜平行六面体以及一般的多面体等形体的重力谱的解析表达式。它们的结构与均质体相应表达式一样简单,易于计算。以上结果表明,在很一般的条件下,位场波谱具有指数函数和的形式。
In this paper, we generalize the research results of the spectral analytical expression of the homogeneous two-dimensional and three-dimensional object field to the more general case of variable density and variable magnetization. The gravimetric analysis of the gravitational spectrum of arbitrary tilted polygonal mass planes, oblique parallelepipeds and general polyhedrons is obtained for the model in which the density difference attenuates exponentially with depth or changes linearly. Their structure is as simple as the corresponding representation of a homogeneous body and easy to calculate. The above results show that under very general conditions, the field spectrum has the form of exponential sum.