Equivalency of the kholmogorov-wiener optimal interpolation and equivalent sources approximation of the anomalous potential fileds measured at any discrete set of points: theory

Abstract

The article shows that the optimal Kholmogorov-Wiener interpolation (filtration) of the anomalous potential fields that are measured over any discrete set of points in space is equivalent to the sourcelike approximation if the model correlation functions are specially selected. This result is the generalization of the analogous fact that had been proved in papers by V.M.Gordin and co-authors for the special case of the filed measured over a horizontal plane. The discrete analogue of the Wiener-Hoppf equation is constructed. The paper shows the way of selection of the model correlation functions that leads to the above mentioned equivalency. The authors suggest an algorithm for the problem solution. This result is useful for the interpolation and filtration of the Earth’s anomalous potential fields for the irregular measurements at different heights, including the case where the Earth’s sphericity is important.