English (pdf)
Article in xml format
Article references
Automatic translation
Send this article by e-mail
Permalink
Ver contenido en pdf
Services on Demand
Journal
Article
Indicators
-
Cited by SciELO -
Access statistics
Related links
-
Similars in
SciELO
Share
Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.22 n.2 San José Jul./Dec. 2015
Articles
Precision of geoid approximation and geostatistics: how to find continuous map of absolute gravity data
Precisión de la aproximación geoide y geoestadística: cómo encontrar un mapa continuo de datos de gravedad absoluta
1Conrad Blucher Institute for Surveying and Science, School of Engineering and Computing Sciences, Texas A&M University- , Corpus Christi United States. E-mail: hongzhi.song@tamucc.edu
2Department of Mathematics & Statistics, Texas A&M University- , Corpus Christi United States. E-mail: alexey.sadovski@tamucc.edu
3Department of Mathematics & Statistics, Texas A&M University- , Corpus Christi United States. E-mail: gary.jeffress@tamucc.edu
An accurate geoid model is needed for surveyors and engineers who require orthometric heights on a common datum, and environment scientists who require elevations relative to present sea level. Airborne gravity data has been collected by the National Geodetic Survey (NGS) under the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project and is available along the coasts of the Gulf of Mexico. For this study we obtained a set of absolute gravity data derived from full-field gravity at altitude/elevation. We used the data to derive free-air gravity anomalies to establish gravity on the geoid. For spatial interpolation we used the kriging method to estimate gravity on the geoid in any location and kriging of the difference between gravity on the ellipsoid of reference and the geoid. Various kriging methods were used for evaluation of errors calculated in this study. The mean precision of the predicted values is around 1.23 cm, a very good result for coastal regions, which traditionally have sparse gravity data sets.
Keywords: geoid; geospatial statistics; kriging; gravity; precision
Los agrimensores e ingenieros necesitan un modelo preciso del geoide ya que requieren alturas ortométricas de datos comunes, y los científicos del ambiente requieren de elevaciones reales del nivel del mar. La Encuesta Nacional Geodética (NGS por sus siglas en inglés) del proyecto Gravedad para la Redefinición del Datum Vertical Americano (GRAV-D, por sus siglas en inglés) ha recogido datos de gravedad en el aire para las costas del Golfo de México. Para este estudio obtuvimos un conjunto de datos de gravedad absoluta derivados de gravedad completa de campo en altitud/elevación. Usamos los datos para derivar anomalías de gravedad de aire libre con el fin de establecer gravedad en el geoide. En la interpolación espacial usamos el método de kriging para estimar la gravedad en el geoide en cualquier lugar y kriging de la diferencia entre gravedad del elpsoide de referencia y el geoide. Varios métodos de kriging se usaron para evaluar los errores calculados en este estudio. La precisión media de los valores predicho ande alrededor de 1.23 cm, un resultado muy bueno para regiones costeras, que tradicionalmente tienen conjuntos de datos de gravedad dispersos.
Palabras clave: geoide; estadística geoespacial; kriging; gravedad; precisión
REFERENCES
Damiani, T.M. (Ed.) (2011) \GRAV-D General Airborne Gravity Data User Manual". Theresa M. Diehl, ed., Version 1. GRAV-D Science Team. http://www.ngs.noaa.gov/GRAV-D/data/NGS_GRAV-D_General_Airborne_Gravity_Data_User_Manual_v1.1.pdf , accessed 04/19/2012. [ Links ]
GRAV-D Science Team (2011) Gravity for the Redefinition of the American Vertical Datum (GRAV-D) Project, Airborne Gravity Data; Block CS01. In: In: http://www.ngs.noaa.gov/GRAV-D/data_cs01.shtml , accessed 04/19/2012. [ Links ]
GRAV-D Science Team (2011) \Gravity for the Redefinition of the American Vertical Datum (GRAV-D) Project, Airborne Gravity Data; Block CS04". In: In: http://www.ngs.noaa.gov/GRAV-D/data_cs04.shtml , accessed 04/19/2012. [ Links ]
GRAV-D Science Team (2012) \Gravity for the Redefinition of the American Vertical Datum (GRAV-D) Project, Airborne Gravity Data; Block CS02". In: In: http://www.ngs.noaa.gov/GRAV-D/data_cs02.shtml , accessed 04/19/2012. [ Links ]
GRAV-D Science Team (2012) \Gravity for the Redefinition of the American Vertical Datum (GRAV-D) Project, Airborne Gravity Data; Block CS03". In: In: http://www.ngs.noaa.gov/GRAV-D/data_cs03.shtml , accessed 04/19/2012. [ Links ]
Hofmann-Wellenhof, B.; Moritz, H. (2006) Physical Geodesy2. Springer, Wien, New York. [ Links ]
Li, X.; Götze, H.J. (2001) \Tutorial ellipsoid, geoid, gravity, geodesy, and geophysics", Geophysics 66(6): 1660-1668. [ Links ]
Moritz, H. (1980) Geodetic reference system 1980, Journal of Geodesy 54(3): 395-405. [ Links ]
National Oceanic and Atmospheric Administration (NOAA); National Ocean Service (NOS); Office of Coast Survey; Strategic Environmental Assessments (SEA); Division of the Office of Ocean Resources Conservation and Assessment (ORCA) (1994) NOS80K -Medium Resolution Digital Vector U.S. Shoreline shapefile for the contiguous United States. In: In: http://coastalmap.marine.usgs.gov/GISdata/basemaps/coastlines/nos80k/nos80k.zip , accessed 01/19/2012. [ Links ]
Paskevich, V. (2005) STATE BOUNDS: internal US state boundaries. In: In: http://pubs.usgs.gov/of/2005/1071/data/background/us_bnds/state_bounds.zip , accessed 01/19/2012. [ Links ]
Reguzzoni, M.; Sansó, F.; Venuti, G. (2005) The theory of general kriging, with applications to the determination of a local geoid, Geophysical Journal International 162(2): 303-314. [ Links ]
U.S. Geological Survey (2003) HYDROGP020 - U.S. National Atlas Water Feature Areas: bays, glaciers, lakes and swamps. In: In: http://coastalmap.marine.usgs.gov/GISdata/basemaps/usa/water/hydrogp020.zip , accessed 01/19/2012. [ Links ]
Received: August 28, 2013; Revised: October 03, 2014; Accepted: October 29, 2014
This is an open-access article distributed under the terms of the Creative Commons Attribution License
