ПРО ПРЕДСТАВЛЕННЯ АКФ STHA-ПОЛІНОМАМИ ДЛЯ МОДЕЛЮВАННЯ РЕГІОНАЛЬНОГО ГРАВІТАЦІЙНОГО ПОЛЯ ЗЕМЛІ

Abstract

The current Baltic height system in Ukraine is outdated and requires modernization. The current resolution of Cabinet of Ministers of Ukraine states that the implementation of topographic, geodetic and cartographic works starting from January 1, 2023 will be carried out using UELN/EVRS2000 height system. For successful integration of our height system into European one, it is necessary to construct a high-precision model of geoid surface on territory of Ukraine, which should fit well with European geoid model EGG2015. This will allow using advanced satellite technologies to determine gravity-dependent heights. The main methods of constructing regional gravitational field of Earth include method of geopotential decomposition into series of spherical functions with fractional indices (in particular, STHA-method) and least-squares collocation method. However, to date, no relationship has been established between them. The construction of ACF using STHApolynomials, which wavelength is much shorter than Legendre polynomials and depends on area of studied region, will significantly improve accuracy of regional models of Earth's gravitational field. The approach to construction of ACF using STHA-polynomials can be very promising precisely because wavelength of these functions coincides with area of studied region, and all other properties coincide with properties of Legendre polynomials. That is why it is necessary to perform ACF calculations using Legendre polynomials and STHApolynomials and analyze results. The solution of this problem is realized by constructing and analyzing covariance and cross-covariance functions of geopotential functionals using Legendre polynomials and STHA-polynomials according to Tscherning-Rapp model. A number of covariance and crossover-covariance functions are calculated and compared using Legendre polynomials and STHA-polynomials according to Tscherning-Rapp model. The values of geoid heights obtained from GNSS-observations at points of SGN of I, II and III classes in territory of Lviv region are taken as input data. A method for constructing a local ACF using STHA-polynomials is proposed and tested. STHA-polynomials have been found to be significantly more efficient than Legendre polynomials because their domain coincides with that of region under study. For example, it is shown that for Lviv region decomposition of covariance functions in a series by Legendre polynomials up to order 600 is equivalent to decomposition in a series by STHA-polynomials up to order 8.