F-approximation of the Earth's surface topography

At the present time, the development and implementation of the new methods of describing the relief (topography) of the Earthis surface is a highly urgent task. It is referred to the construction of the substantially more powerful and more flexible methods of the analytical description of the topography of the Earthis surface: such linear analytical approximations, which are constructed according to the data on the heights of points on the Earthis surface on a sufficiently large set of points in the territory with a sufficiently large area, and which are used for this entire area for the solution of a large set of problems of geodesy, geomorphology and geophysics (in particular, for calculation of the values of topographic corrections in the observed gravity forces). Earlier, on the basis of the method of linear integral representations of V.N. Strakhov, the general theoretical concepts of the F-approximation of the relief of the Earthis surface were developed in the rectangular and spherical coordinates [Strakhov et al., 1999]. In the present paper the special features of the F-approximation of the relief of the Earthis surface are considered in more detail for the relatively small territories, i.e., with the use of the rectangular coordinates, the obtained analytical expressions, and, also, the results of validation on the model and the real topographic materials are presented..