Improved convergence rates for the truncation error in gravimetric geoid determination |
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| Authors: | J D Evans W E Featherstone |
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| Institution: | (1) 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;(2) 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 |
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| 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.
Received: 21 April 1998 / Accepted: 4 October 1999 |
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| Keywords: | : Geoid determination – Integration kernels – Truncation error |
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