caa a22 4500 475737741 CHVBK 20180406123451.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1007/s001900050282 doi (NATIONALLICENCE)springer-10.1007/s001900050282 Improved convergence rates for the truncation error in gravimetric geoid determination [Elektronische Daten] [J. D. Evans, W. E. Featherstone] Abstract.:  When Stokes's integral is used over a spherical cap to compute a gravimetric estimate of the geoid, a truncation error results due to the neglect of gravity data over the remainder of the Earth. Associated with the truncation error is an error kernel defined over these two complementary regions. An important observation is that the rate of decay of the coefficients of the series expansion for the truncation error in terms of Legendre polynomials is determined by the smoothness properties of the error kernel. Previously published deterministic modifications of Stokes's integration kernel involve either a discontinuity in the error kernel or its first derivative at the spherical cap radius. These kernels are generalised and extended by constructing error kernels whose derivatives at the spherical cap radius are continuous up to an arbitrary order. This construction is achieved by smoothly continuing the error kernel function into the spherical cap using a suitable degree polynomial. Accordingly, an improved rate of convergence of the spectral series representation of the truncation error is obtained. Springer-Verlag Berlin Heidelberg, 2000 Key words: Geoid determination - Integration kernels - Truncation error nationallicence Evans J. D. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK e-mail: masjde@maths.bath.ac.uk; Tel.: +44 1225 826994; Fax: +44 1225 826492, GB aut Featherstone W. E. School of Spatial Sciences, Curtin University of Technology, GPO Box U1987, Perth 6845, Australia e-mail: Featherstone_WE@cc.curtin.edu.au; Tel.: +61 8 9266 2734; Fax: +61 8 9266 2703, AU aut https://doi.org/10.1007/s001900050282 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001900050282 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Evans J. D. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK e-mail: masjde@maths.bath.ac.uk; Tel.: +44 1225 826994; Fax: +44 1225 826492, GB aut NATIONALLICENCE 700 1- Featherstone W. E. School of Spatial Sciences, Curtin University of Technology, GPO Box U1987, Perth 6845, Australia e-mail: Featherstone_WE@cc.curtin.edu.au; Tel.: +61 8 9266 2734; Fax: +61 8 9266 2703, AU aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer