Geophysical research: article

Аnnotation: The article is devoted to the development and study of the methods for deriving an integral model of the Earth's gravitational field in the form of spherical harmonics of the gravity potential (geopotential) by means of optimal, in a certain sense, averaging of the harmonic geopotential coefficients according to the data of existing (previously created) models of this kind. The range of issues under consideration includes: preliminary processing of the initial data, including the agreement of the averaged models according to the parameters of the world-wide ellipsoid, the tidal system and the initial epoch; algorithmization and testing of various averaging methods on real models of the Earth gravitational field; comparative analysis of the effectiveness of these methods using estimates of the accuracy of the integral model for internal and external convergence. Three methods of obtaining an integral model are considered: simple averaging; weighted averaging; polynomial averaging. The latter is based on the polynomial approximation of the averaged array of harmonic coefficients using the least squares method. Experimentally, it is shown that the results of polynomial averaging depend on the method of ordering the original models. A multicriteria approach to choosing the optimal combination of such models is described. Using these methods, three experimental models up to the 360th degree were created, each in its own way, but using the same set of initial data. On these models, a comparative study of various averaging methods was carried out, including a comparison of the model heights of the geoid (quasigeoid) with the data of reverse satellite leveling in five regions of the world (Russia, USA, Germany, France, South Africa). The weighted averaging method proved to be the most balanced and is recommended for use as a basic method of constructing an integral model. Suggestions are given for the practical application of the developed methodology implementing an integral approach to the derivation of a global model of the Earth's gravitational field.