On Deflection of the Vertical Components and Their Transformations
Publication: Journal of Surveying Engineering
Volume 140, Issue 2
Abstract
The deflection of the vertical is an important parameter that combines both physical (astronomic) and geometric (geodetic) determined quantities. This paper introduces an alternative didactic approach based on rotations of three-dimensional right-handed local frames that simplifies such concepts as the derivation of Laplace’s equation and facilitates understanding of vertical deflection components and their transformations under different assumptions. Variations in deflections of the vertical as a consequence of geometric changes introduced by the future replacement of the North American Datum of 1983 (NAD 83) are also investigated.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors thank their NGS colleagues X. Li, D. Roman, and D. Smith for reviewing several stages of this paper and for their constructive comments and suggestions. The authors also acknowledge the three anonymous reviewers for critically reviewing the manuscript and for their valuable recommendations.
References
Fury, R. J. (1984). “Prediction of deflections of the vertical by gravimetric methods.” NOAA Tech. Rep. NOS 103 NGS 28, National Geodetic Survey, National Oceanic and Atmospheric Administration (NOAA), Silver Spring, MD.
Heiskanen, W. A., and Moritz, H. (1967). Physical geodesy, W. H. Freeman, San Francisco.
Hirt, C., Bürki, B., Somieski, A., and Seeber, G. (2010). “Modern determination of vertical deflections using digital zenith cameras.” J. Surv. Eng., 1–12.
Jekeli, C. (2012). “Geometric reference systems in geodesy.” 〈http://hdl.handle.net/1811/51274〉 (Jul. 26, 2013).
Leick, A. (2004). GPS satellite surveying, 3rd Ed., Wiley, New York.
Moritz, H. (1992). “Geodetic reference system 1980.” Bull. Geod., 66(2), 187–192.
Mueller, I. I. (1969), Spherical and practical astronomy as applied to geodesy, Frederick Ungar, New York.
Müller, A., Bürki, B., Kahle, H.-G., Hirt, C., and Marti, U. (2005). “First results from new high-precision measurements of deflections of the vertical in Switzerland.” Gravity, geoid and space missions, Vol. 129, Springer, Berlin, 143–148.
Pearson, C., and Snay, R. (2013). “Introducing HTDP 3.1 to transform coordinates across time and spatial reference frames.” GPS Solutions, 17(1), 1–15.
Snay, R. (2012). “Evolution of NAD 83 in the United States: Journey from 2D toward 4D.” J. Surv. Eng., 161–171.
Soler, T. (1976). “On differential transformations between Cartesian and curvilinear (geodetic) coordinates.” Rep. 236, Dept. of Geodetic Science, Ohio State Univ., Columbus, OH.
Soler, T., Carlson, A. E., Jr., and Evans, A. G. (1989). “Determination of vertical deflections using the Global Positioning System and geodetic leveling.” Geophys. Res. Lett., 16(7), 695–698.
Soler, T., and Hothem, L. D. (1988). “Coordinate systems used in geodesy: Basic definitions and concepts.” J. Surv. Eng., 84–97.
Soler, T., and Johnson, S. D. (1987). “Alternative geometric determination of altazimuthal-distance covariance matrices.” J. Surv. Eng., 57–69.
Soler, T., and van Gelder, B. H. W. (1987). “On differential scale changes and the satellite Doppler system z-shift.” Geophys. J. Int., 91(3), 639–656.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 140 • Issue 2 • May 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 19, 2013
Accepted: Oct 23, 2013
Published online: Oct 25, 2013
Published in print: May 1, 2014
Discussion open until: Jul 12, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.