The effect of topographical and atmospheric masses on spaceborne gravimetric and gradiometric data

Abstract

Current satellite missions dedicated to global mapping of the Earth's gravity field are providing accurate global models of the geopotential. Harmonic (Stokes) coefficients of the geopotential derived from satellite observations of its functionals, a potential gradient vector and/or gravity gradient tensor, correspond to the (time-averaged) gravitational potential that is generated by the geoid, topography and atmosphere. The manuscript deals with the effect of static topographical and atmospheric masses on spaceborne observations of the potential gradient vector and gravity gradient tensor that should be applied during their inversion into the geopotential at the geoid level. They would allow for derivation of a harmonic representation of the potential generated only by solid masses inside the geoid and ocean, i.e., harmonicity of the geopotential would apply to the entire space outside the geoid. The geopotential could be then synthesized without problems with diverging harmonic series, i.e., the fundamental condition for application of a truncated harmonic series everywhere outside the geoid would be met. Due to its large numerical values, compensation of topographical masses is outlined using a singlelayer potential. Although not entirely sufficient from a geophysical point of view, this model is often applied in geoid-related computations. Corresponding parameters are evaluated in manners that are consistent with spatial resolution and accuracy of current spaceborne data using spherical harmonic representation of topographical heights and corresponding mass distributions. Theoretical formulations are followed by numerical evaluations.

Bathymetric stripping corrections to gravity gradient components

“…It is thus expected that GOCE gravity field solutions will improve our knowledge about the Earth's inner density structure especially beneath oceanic and continental areas where seismic data are not yet available or their accuracy and spatial coverage is insufficient. Novák and Grafarend (2006) evaluated numerically external gravitational fields of topographic and atmospheric masses by using spherical harmonic expansions. Tenzer et al (2008Tenzer et al ( , 2009Tenzer et al ( , 2010 then computed globally the bathymetry-generated gravity field parameters by using the Copy right c The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.…”

Spectral harmonic analysis and synthesis of Earth’s crust gravity field

“…Makhloof [25] derived expressions for computing topographic-isostatic effects on airborne and spaceborne gravimetry, and gradiometry data. Alternative expressions for computing topographic effects in spaceborne gravimetry and gradiometry applications were formulated by Novák and Grafarend [32] and Eshagh and Sjöberg [7,8]. Novák and Grafarend [31] derived the topographic potential and its radial derivative using the ellipsoidal representation of Newton's integral.…”

“…Sjöberg [46] derived expressions in the spectral representation for the atmospheric potential and its radial derivative considering the ellipsoidal layering of the Earth's atmosphere. Atmospheric effects in satellite geodesy applications were discussed by Novák and Grafarend [32] and Eshagh and Sjöberg [8]. Novák and Grafarend [32] proposed a method for computing the gravitational effect of atmospheric masses on spaceborne data based on the spherical harmonic approach with a numerical study in North America.…”

“…Atmospheric effects in satellite geodesy applications were discussed by Novák and Grafarend [32] and Eshagh and Sjöberg [8]. Novák and Grafarend [32] proposed a method for computing the gravitational effect of atmospheric masses on spaceborne data based on the spherical harmonic approach with a numerical study in North America. Eshagh and Sjöberg [8] applied an alternative spherical approach to compute the atmospheric effect on satellite gravity gradiometry data over Fennoscandia.…”

“…In all these studies, a constant value of the seawater density was adopted. Novák [32] computed globally the gravitational potential generated by the ocean saltwater density with a high-degree spectral resolution. Tenzer et al [59,60] facilitated a depth-dependent seawater density model in deriving expressions for computing the bathymetric stripping gravity corrections in order to reduce large errors otherwise presented in results when using only a constant seawater density.…”