Abstract
Spline functions have interesting theoretical and practical properties that make them most useful and effective in a great many approximation problems, not least in geodetic problems such as local modelling of the gravity field. The application we consider here is local modelling of the geoid at the hand of given geoid heights (or height anomalies), and given free-air gravity anomalies. This is a problem of the type likely to be encountered if GPS is to be used for levelling, to obtain differences in orthometric height (or differences in normal height) where geoid heights are obtained from GPS measurements at points of known elevation. The gravity anomalies are used to help with the interpolation of the geoid between the GPS-derived geoid heights.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Belsley, D.A., Kuh, E. and Welsch, E. (1980). Regression diagnostics: identifying influential data and sources of collinearity, Wiley, New York.
Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions, Numer. Math., 31, 377–403.
Eubank, R.L. (1984). The hat matrix for smoothing splines, Statist. and Probab. Letters, 2, 9–14.
Eubank, R.L. (1985). Diagnostics for smoothing splines, J. Royal Statist. Soc. B, 47 (2), 332–341.
Freeden, W. (1981a). On approximation by harmonic splines, Manus. Geod., 6 (2), 193–244.
Freeden, W. (1981b). On spherical spline interpolation and approximation, Math. Meth. Appl. Sci., 3, 551–575.
Golub, G.H., Heath, M. and Wahba, G. (1979). Generalized cross—validation as a method for choosing a good ridge parameter, Technometrics, 21 (2), 215–223.
Lelgemann, D. (1981). On numerical properties of interpolation with harmonic kernel functions, Manus. Geod., 5, 157–191.
Merry, C.L. (1983). Gravity survey of degree square 3318, University of Cape Town, Dept. of Surveying, Internal Report G-10.
Robinson, T. and Moyeed, R. (1989). Making robust the cross—validatory choice of smoothing parameter in spline smoothing regression, Comm. Statist. — Theor. Meth., 18 (2), 523–589.
Silverman, B.W. (1985). Some aspects of the spline smoothing approach to non—parametric regression curve fitting (with discussion), J. Roy. Statist. Soc. B, 47 (1), 1–52.
Van Gysen, H. (1986). A relatively precise geoid for the western Cape: preparations for GPS levelling, Proc. Symposium on Geodetic Positioning for the Surveyor, Cape Town, 143–152.
Van Gysen, H. (1988). Splines and local approximation of the earth’s gravity field, University of Cape Town, unpublished PhD thesis.
Wahba, G. (1978). Improper priors, spline smoothing and the problem of guarding against model errors in regression, J. Roy. Statist. Soc. B, 40 (3), 364–372.
Wahba, G. (1983). Bayesian ‘confidence intervals’ for the cross—validated smoothing spline, J. Roy. Statist. Soc. B, 45 (1), 364–372.
Wahba, G. and Wendelberger, J. (1980). Some new mathematical methods for variational objective analysis using splines and cross—validation, Monthly Weather Review, 108, 1122–1143.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag New York Inc.
About this paper
Cite this paper
van Gysen, H., Merry, C.L. (1990). Towards A Cross-Validated Spherical Spline Geoid for the South-Western Cape, South Africa. In: Sünkel, H., Baker, T. (eds) Sea Surface Topography and the Geoid. International Association of Geodesy Symposia, vol 104. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-7098-7_7
Download citation
DOI: https://doi.org/10.1007/978-1-4684-7098-7_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97268-8
Online ISBN: 978-1-4684-7098-7
eBook Packages: Springer Book Archive