A system of spherical functions orthogonal in the local segment of the sphere

Abstract

One of the main tasks of modern physical geodesy is to determine the high-frequency part of the Earth’s gravity field (EGF), which inevitably depends on the individual characteristics of a particular computational area. It is well known that in global EGF modeling it is especially convenient to have a spherical function series. However, these series forming a reliable basis for global modeling are unsuitable for approximation in a local area because they lose orthogonality, the most important property of basis functions. The authors describe the possibility of imparting this property to spherical functions in the necessary part of the sphere, which enables further using the habitual apparatus of harmonic series for approximation of EGF in local areas. Of course, the foregoing is only concerned to the most basic concepts of the new direction in modeling the EGF in a local region