Determination of the parameters of the triaxial earth ellipsoid as derived from present-day geospatial techniques
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ORIGINAL ARTICLE
Determination of the parameters of the triaxial earth ellipsoid as derived from present‑day geospatial techniques Tomás Soler1 · Jen‑Yu Han2 Received: 21 April 2020 / Accepted: 7 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This investigation implements a least-squares methodology to fit a triaxial ellipsoid to a set of three-dimensional Cartesian coordinates obtained from present-day geospatial techniques, materializing the terrestrial frame ITRF2014. To approximate, as much as possible previous research on this topic, the original spatial values of the station coordinates were “reduced” to the surface of the EGM2008 geoid model by introducing a simple and straightforward procedure. The mathematical model adopted in all LS solutions is the standard quadric surface polynomial equation parameterizing a triaxial ellipsoid. Functionally related to these polynomial coefficients are nine geometric parameters: the three ellipsoid semi-axes, its origin location with respect to the current conventional geocentric terrestrial frame, and the three rotations defining its spatial orientation. The final results are compatible with the pioneering work started by Burša in 1970 and, lately, by a recent publication by Panou and colleagues in that incorporates updated geoid models. Keywords Triaxial ellipsoid fitting · ITRF2014 coordinates · Geoid model EGM2008 · Least-squares solution
Introduction Leaving aside the convenience or not of adopting a triaxial ellipsoid as a replacement to the two-parameter rotational ellipsoid GRS80 presently adopted by the International Association of Geodesy (Moritz 1992), scientists have calculated, using different initial assumptions, the parameters of a supposedly best fitting triaxial earth ellipsoid. Table 1 shows, chronologically, the most recent set of semi-axis values ( a,b , c ) that different authors have published to date to specify the size and shape of a presumed triaxial earth ellipsoid. Krasovsky, also known as Krassovsky and Krasovski, mainly published all his work in Russian. His results of 1902 and 1972 were cited in the English geodetic literature by Zhuravlev (1972) and Geodetic Glossary (1986). The * Jen‑Yu Han [email protected] Tomás Soler [email protected] 1
National Geodetic Survey (NGS), National Oceanic and Atmospheric Administration (NOAA), Retired, 13510 Flowerfield Drive, Potomac, MD 20854, USA
Department of Civil Engineering, National Taiwan University, 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan
2
tabulated quantities credited to Eitschberger were recently recounted by Grafarend et al. (2014). Finally, Panou et al. (2020) report a myriad of solutions; their values in Table 1 correspond to the solution derived from the EGM2008 (Earth Gravimetric Earth Model of 2008) geoid model (Pavlis et al. 2012). The final listed triaxial ellipsoid determined by Soler and Han, also based on EGM2008, is presented herein for the first time. It should be mentioned here that triaxial ellipsoids are often used i
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