A Remark on the Computation of the Gravitational Potential of Masses with Linearly Varying Density
A Remark on the Computation of the Gravitational Potential of Masses with Linearly Varying Density
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DOI：
10.1007/1345_2015_138
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发表时间：
2015
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影响因子：
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通讯作者：
M. D'Urso
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文献类型：
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作者：
M. D'Urso
在Holstein（Geophysics 68：157-167，2003）和Hamayun等人（J Geodesy 83：1163-1170，2009）中给出了具有线性变化密度的多面体体的势的两种不同的表达式，尽管在这两篇论文中，推导是从通过经由高斯定理变换原始体积积分而获得的相同的表面积分开始的。相反，我们证明了Hamayun等人（J Geodesy 83：1163-1170，2009）采用的方法的适当修改产生了Holstein（Geophysics 68：157-167，2003）推导的公式。此外，一个额外的表达式的表面积分，这也证明了在本文中，使我们能够得到一个变量的线性部分的潜力，即积分乘以梯度的密度对比度，过滤空的贡献面包含观察点。这个新公式专门适用于棱镜的情况。
The potential of a polyhedral body with linearly varying density has been given two different expressions in Holstein (Geophysics 68:157–167, 2003) and Hamayun et al. (J Geodesy 83:1163–1170, 2009) although in both papers the derivation is started from the same surface integral obtained by transforming the original volume integral via the Gauss theorem. Conversely, we prove that a suitable modification of the approach exploited by Hamayun et al. (J Geodesy 83:1163–1170, 2009) yields the formula derived by Holstein (Geophysics 68:157–167, 2003). Furthermore, an additional expression of the surface integral, which is also proved in this paper, allows us to derive a variant of the linear part of the potential, i.e. the integral multiplying the gradient of the density contrast, which filters the null contribution of faces containing the observation point. The new formula is specialized to the case of a prism.