Investigations on the hierarchy of reference frames in geodesy and geodynamics
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Date
1979-08
Journal Title
Journal ISSN
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Publisher
Ohio State University. Division of Geodetic Science
Abstract
Modern high accuracy measurements of the non-rigid earth are to be referred to four-dimensional, i.e., time- and space-dependent, reference frames. Geodynamic phenomena derived from these measurements are to be described in a terrestrial reference frame in which both space- and time-like variations can be monitored. Existing conventional terrestrial reference frames (e.g. CIO, BIR) are no longer suitable for such purposes. The ultimate goal of this study is the establishment of a reference frame, moving with the earth in some average sense, in which the geometric and dynamic behavior of the earth can be monitored, and whose motion with respect to inertial space can also be determined. The study is conducted in three parts. In the first part problems related to reference directions are investigated, the second part deals with the reference origins and the third part with problems related to scale. The approach is based on the fact that reference directions at an observation point on the earth surface are defined by fundamental vectors (gravity, earth rotation, etc.), both space and time variant. These reference directions are interrelated by angular parameters, also derived from the fundamental vectors. The interrelationships between these space- and time-variant angular parameters are illustrated in hierarchic structures or towers, which make the derivations of the various relationships convenient. In order to determine the above parameters from observations using least squares techniques, model towers of triads are also presented to allow the formation of linear observation equations. Although the model towers are also space and time variant, their variations are described by adopted parameters representing our current knowledge of the earth. After the translational and rotational degrees of freedom (origin and orientation) have been discussed, the notion of a length, scale degrees of freedom are introduced and studied under spacelike/ timelike variations. According to the notion of scale parallelism, originated by H. Weyl, scale factors with respect to a unit length are given. Three-dimensional geodesy is constructed from the set of three base vectors (gravity, earth-rotation and the ecliptic normal vector). Space and time variations are given with respect to a polar and singular value decomposition or in terms of changes in translation, rotation, deformation (shear, dilatation or angular and scale distortions).
Description
Prepared for National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland: Grant No. NSG 5265, OSURF Project 711055