On the R- approximations of the Earth's surface topography

The determination of a function describing the Earth’s surface topography on a generally irregular grid is important for the interpretation of gravity data, calculation of the corrections for the topography and construction of maps of plumb line deviations. Thus, we have the problem of describing a surface D, or more specifically, the problem of constructing an approximation of a surface D that will be used in the calculation of the function (the derivative of the potential with respect to the coordinate ). We can write where are the observation points. If the model of the plane Earth is adopted, the surface D may be represented by a function of two variables , parametrizing points on an equipotential surface. Then, the correction for topographic masses (the gravity reduction) is calculated by the approximate formula