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Spectral Combination of Spherical Gradiometric Boundary-Value Problems: A Theoretical Study

机译：球面梯度边值问题的光谱组合：理论研究

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摘要

The Earth's gravity potential can be determined from its second-order partial derivatives using the spherical gradiometric boundary-value problems which have three integral solutions. The problem of merging these solutions by spectral combination is the main subject of this paper. Integral estimators of biased- and unbiased-types are presented for recovering the disturbing gravity potential from gravity gradients. It is shown that only kernels of the biased-type integral estimators are suitable for simultaneous downward continuation and combination of gravity gradients. Numerical results show insignificant practical difference between the biased and unbiased estimators at sea level and the contribution of far-zone gravity gradients remains significant for integration. These contributions depend on the noise level of the gravity gradients at higher levels than sea. In the cases of combining the gravity gradients, contaminated with Gaussian noise, at sea and 250 km levels the errors of the estimated geoid heights are about 10 and 3 times smaller than those obtained by each integral.
机译：可以使用具有三个积分解的球面梯度边界值问题，根据其二阶偏导数来确定地球的重力势。通过光谱组合合并这些解决方案的问题是本文的主要主题。提出了有偏和无偏类型的整体估计量，用于从重力梯度中恢复干扰重力势。结果表明，只有偏差型积分估计器的核适合于同时向下连续和重力梯度的组合。数值结果表明，在海平面上，有偏估计和无偏估计之间的实际差异不明显，远区重力梯度的贡献对于积分仍然很重要。这些贡献取决于重力梯度的噪声水平，该噪声水平高于海洋。在结合受高斯噪声污染的重力梯度的情况下，在海上和250 km高度处，估计大地水准面高度的误差分别比每个积分所获得的误差小10到3倍。

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