Determination of the parameters of the triaxial earth ellipsoid as derived from present-day geospatial techniques

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 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.

Mechanics of incompressible test bodies moving on λ‐spheres

“…The derived parametrization expresses the z ‐coordinate on the λ ‐sphere with the help of the elliptic integrals of the first, second, and third kind. It can be used, for instance, for construction of some alternatives to ellipsoidal's models of the Earth's shape (see, e.g., previous studies 11,12 ).…”

“…The derived parametrization expresses the z-coordinate on the 𝜆-sphere with the help of the elliptic integrals of the first, second, and third kind. It can be used, for instance, for construction of some alternatives to ellipsoidal's models of the Earth's shape (see, e.g., previous studies 11,12 ). Next, we have discussed the d'Alembert model of the kinetic energy using the two-polar decomposition of the configuration matrix for the incompressible test bodies moving on 𝜆-spheres.…”

“…The main applicative reason that prompted us to analyze and study the problem presented in this paper is to develop the new reference model for the geoid describing the Earth's shape, which is alternative to the traditional ellipsoidal models used currently (see, e.g., previous studies 11,12 ). Faridi and Schucking 1 have introduced λ ‐spheres as deformations of the usual sphere.…”

A triaxial reference ellipsoid for the Earth

“…Earth's triaxiality has been investigated historically via astro-geodetic or gravimetric measurements (Clarke 1861; Heiskanen 1928), and since the advent of the space era, (together with) observed satellite motions (Kaula 1959;Izsak 1961;Kozai 1961). As an approximate equipotential surface, this reference figure, whether a biaxial or triaxial ellipsoid, can be determined as best fits to the geoid derived from the gravitational field model (Burša 1970;Burša and Sima 1980;Tserklevych et al 2016;Panou et al 2020;Soler and Han 2020). This is the same principle as determining the triaxial dimensions of other planetary bodies (Smith et al 1999;Iz et al 2011).…”

“…Granted, a biaxial ellipsoid remains an intuitive and apposite reference for the Earth in near hydrostatic equilibrium. With the measurement precision nowadays far exceeding the (in)distinctness of the equatorial flattening, the triaxial ellipsoid has received renewed attention for being a more accurate and natural reference figure (Panou et al 2020;Soler and Han 2020). This work exploits the innate advantages of the EHs and is among the first to offer a practical solution on the topic.…”