Modeling of Quasigeoid Heights in the Earth’s Local Surface Areas Based on the Results of the Expansion in a Generalized Fourier Series

摘要

Abstract Two methods of modeling quasigeoid heights specified discretely in the Earth’s local surface areas using generalized Fourier series are considered. The first method involves modeling of the Earth gravitational field characteristics on a plane; it makes use of a two-dimensional Fourier transform in an orthonormal set of trigonometric functions. The second method implies the expansion of quasigeoid heights in a Fourier series in an orthonormal set of spherical functions on the Earth’s local surface area. The errors in the approximation of the discrete values of the quasigeoid heights obtained within a local area are analyzed. It is shown that with the current state of computer technology, expansion of quasigeoid heights in a Fourier series in an orthonormal set of spherical functions is an accurate and technologically simple method for modeling of quasigeoid heights.