Chapter
The gradiometricgeodynamic boundary value problem
DOI: 10.1007/3540269320_61

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ABSTRACT: Spherical harmonic synthesis (SHS) of gravity field functionals at the Earth’s surface requires the use of heights. The present study investigates the gradient approach as an efficient yet accurate strategy to incorporate height information in SHS at densely spaced multiple points. Taylor series expansions of commonly used functionals quasigeoid heights, gravity disturbances and vertical deflections are formulated, and expressions of their radial derivatives are presented to arbitrary order. Numerical tests show that firstorder gradients, as introduced by Rapp (J Geod 71(5):282–289, 1997) for degree 360 models, produce cm to dmlevel RMS approximation errors over rugged terrain when applied with EGM2008 to degree 2190. Instead, higherorder Taylor expansions are recommended that are capable of reducing approximation errors to insignificance for practical applications. Because the height information is separated from the actual synthesis, the gradient approach can be applied along with existing highly efficient SHS routines to compute surface functionals at arbitrarily dense grid points. This confers considerable computational savings (above or well above one order of magnitude) over conventional pointbypoint SHS. As an application example, an ultrahigh resolution model of surface gravity functionals (EurAlpGM2011) is constructed over the entire European Alps that incorporates height information in the SHS at 12,000,000 surface points. Based on EGM2008 and residual topography data, quasigeoid heights, gravity disturbances and vertical deflections are estimated at ~200m resolution. As a conclusion, the gradient approach is efficient and accurate for highdegree SHS at multiple points at the Earth’s surface.Journal of Geodesy 09/2012; 86(9). DOI:10.1007/s001900120550y · 3.92 Impact Factor 
Acta Geodaetica et Geophysica Hungarica 06/2007; 42(2). DOI:10.1556/AGeod.42.2007.2.2 · 0.35 Impact Factor
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