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

On the estimation of a multi-resolution representation of the gravity field based on spherical harmonics and wavelets

“…Due to the gaps in the polar regions the data of the modern satellite gravity missions are almost globally distributed. Schmidt et al (2005) present the multi-resolution representation of CHAMP disturbing potential data according to Eq. (47) with maximum resolution level I = 4 at satellite altitude.…”

“…For more details concerning this decomposition process see, e.g. Schreiner (1997) or Schmidt et al (2005). But, we finally want to mention again that the Stokes coefficients X R n,m are global parameters, whereas the coefficients d i,k of the levels i = i , .…”

“…., N 1 means the initial step of the so-called pyramid algorithm; see, e.g. Schmidt et al (2005). In the first pyramid step the altogether N I−1 coefficients d I−1,k of level I − 1, related to the computation points P(t I−1,k ) with k = 1, .…”

Regional gravity modeling in terms of spherical base functions

“…(25) is fulfilled if both the point system S N is admissible and the matrix B is positive definite, i.e. the Legendre coefficients B n are restricted to the condition (Schmidt et al 2005a)…”

“…The application of such techniques to real spaceborne and surface gravity data came only recently into fruition, e.g., Fengler et al (2004a,b) and Schmidt et al (2005aSchmidt et al ( ,b, 2006. Besides gravity field modeling, the application of scalar, vector and tensor spherical wavelets has become more and more popular in other fields of geodesy and geophysics, e.g., the analysis of measurements of the surface air temperature (Li 1999), the Earth's magnetic field (Holschneider et al 2003, Maier 2005, Panet et al 2005, the modeling of ionospheric currents (Mayer 2004), atmospheric flows (Fengler 2005) and oceanographic flows .…”