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The Earth and Its Coordinate System
Published in Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard, Thematic Cartography and Geovisualization, 2022
Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard
To compute a geoidal surface requires knowing, among other parameters, the specific nature of the gravitational forces that exist across Earth's surface. These forces, called gravitational anomalies, are not evenly distributed, nor are they equal in their intensity, because Earth's crust contains different rock densities (e.g., metamorphic and igneous rocks are more likely to contain the iron-rich mineral magnetite and thus influence gravity to a greater extent than sedimentary rocks), but the anomalies can be measured and mapped. At every location on Earth's surface, a line can be placed so that it is perpendicular to the local gravitational anomaly. As shown in Figure 7.16, the line perpendicular to the geoid will not coincide with a line that is perpendicular to the chosen reference ellipsoid's surface. A geoidal surface (or equipotential9 surface) can be created from these perpendicular gravitational measurements. In general terms, Earth's crust is thicker over continents, where the geoid typically rises but falls over the oceans, where the crust is thinner. However, even the smooth undulation in the geoid surface has minor highs and lows that can rise as much as 60 meters (196.8 feet) in some areas. Figure 7.17 shows one geoid model (GEOID18) for the conterminous United States developed by the NGS. The “18” part of GEOID18 refers to the year that the datum was realized or published by the National Geodetic Survey. In this case, GEOID18 is the geoid model that was published in 2018.
Geodesy
Published in Basudeb Bhatta, Global Navigation Satellite Systems, 2021
There are many spheroid references that exist, each of which is a local geoid approximation. Geoid, in simple words, is the hypothetical surface of the earth that coincides with sea level everywhere (Bowditch 1995). It is nearly ellipsoidal but a complex surface. The geoid is almost the same as mean sea level, i.e., it may be described as surface coinciding mean sea level in the oceans and lying under the land at the level to which the sea would reach if admitted by small frictionless channels. The geoid on an average coincides with the mean sea level in open oceans. Ambiguity is due to mean sea level not being exactly an equipotential surface or due to periodic changes in the form of the geoid due to earth tides, but these will not be more than a metre. The mean sea level or geoid is the datum for measurement of heights above it. The geoid may depart from the spheroid by varying amounts (Figure 9.5), as much as 200 m or even more. The geoid unfortunately has rather disagreeable mathematical properties. It is a complicated surface with discontinuities of curvature, hence not suitable as a surface on which to perform mathematical computations. Therefore, spheroid is the only option for mathematical calculations.
Electronic charts
Published in Laurie Tetley, David Calcutt, Electronic Navigation Systems, 2007
Since the beginning of mapmaking, local maps were based on the earth's shape in that area and, since the earth is not a perfect sphere, the shape does vary from location to location. Figure 7.5 shows a representation of a vertical slice through the earth. The diagram shows an uneven surface to the earth, a dotted line representing a geoid and a solid line representing an ellipsoid. The geoid represents a surface with equal gravity values and where the direction of gravity is always perpendicular to the ground surface. For mapping purposes it is necessary to use a geodetic datum which is a specifically orientated reference ellipsoid. The surface of a geoid is irregular while that of an ellipsoid is regular.
Geoid determination using band limited airborne horizontal gravimetric data
Published in Journal of Spatial Science, 2022
Kailiang Deng, Guobin Chang, Motao Huang, Huaien Zeng, Xin Chen
The Geoid or Quasi-Geoid is the reference surface of the height system in spatial science. Specifically a geoid model with sufficiently high resolution and precision makes efficient GNSS-leveling possible (Featherstone 2008, Trojanowicz 2015). Determination of the geoid is one of the fundamental tasks of geodetic science and practice. Recently, benefiting from the increased precision of both differential GNSS positioning technology and gravimetry sensor technology, airborne vector gravimetry has emerged as a major progress in the geodetic community, compared to conventional scalar gravimetry Sander and Ferguson 2010, Cai et al. 2013). Vector gravimetry model equations were stated and their error models were derived in Schwarz and Li (1997). The repeated-line precision of results with the AIRGrav airborne gravity system can reach as high as 0.34 and 0.28mGal for the north and east components, respectively (Sander and Ferguson 2010). Results with a strapdown system named SGA-WZ are 1.23 and 1.80mGal, respectively (Cai et al. 2013). These experimental results show that it is now practically possible that incorporating horizontal components of gravity in the determination of the geoid could achieve relatively high resolution and accuracy. However, in recent years, theoretical and practical studies concerning geoid determination were mainly focused on using the vertical component as the only data source (Novák and Heck 2002, Novák et al. 2003). Similar to astronomical levelling theory, a sub-decimeter geoid can be obtained by integrating the horizontal components of vector airborne gravimetry data along the surveying profiles (Jekeli and Kwon 2002, Serpas and Jekeli 2005). However, only a relative geoid can be obtained using this method, which apparently limits its applicability. As a result, determining the absolute geoid using horizontal components of vector airborne gravimetry data, as the main topic of this study, is of significant theoretical and practical importance.