Towards the Estimation of a Multi-Resolution Representation of the Gravity Field Based on Spherical Wavelets

Abstract

Usually the gravity field of the Earth is modeled by means of a series expansion in terms of spherical harmonics. However, the computation of the series coefficients requires preferably homogeneous distributed global data sets. Since wavelet functions localize both in the spatial and in the frequency domain, regional and local structures may be modeled by means of a spherical wavelet expansion. Wavelet-based techniques allow the decomposition of a given data set into frequency-dependent detail signals. This paper deals with two methods to achieve a multi-resolution representation, namely a wavelet-only solution and a combined approach. The latter consists of a spherical harmonic expansion for the low-frequency part and a spherical wavelet expansion for the remaining medium- and high-frequency parts of the gravity field. Parameter estimation procedures are presented to determine the unknown series coefficients of both approaches.