Walsh-Fourier Series Expansion of the Earth’s Gravitational Potential

Abstract

The Earth’ s gravity field model is usually represented by spherical harmonics expansion. In this paper a sequency spectrum representation of potential field has been put forward, and the Walsh-Fourier series expansion of the gravitational potential expressed by spherical coordinates has been derived. The relationship between the spatial domain, frequency and sequency domain forms of gravitational potential field is established; Some basic properties—transformation of coefficient matrixes, characteristic of weight matrix, similarity of expansion, and odd-even symmetry—of the sequency spectrum representation of geopotential field are demonstrated; The adaptabilities of sequency and frequency spectrum representation to study the gravity field are discussed. The sequency spectrum representation of potential field can improve the calculated accuracy and speed the computation up, and more objectively represent the truth of the Earth’ s gravity field.