A common requirement for all geodynamic investigations is a well-defined coordinate system attached to the earth in some prescribed way, as well as a well-defined inertial coordinate system in which the motions of the terrestrial system can be monitored. This paper deals with the problems encountered when establishing such coordinate systems and the transformations between them. In addition, problems related to the modeling of the deformable earth are discussed.

The use of space techniques for establishing transcontinental and intercontinental distances is progressing very rapidly. We can think of the set of station locations used in either LAGEOS ranging or VLBI measurements as forming the vertices of a polyhedron. After correcting for tectonic plate motions using an adopted model, we expect the geometry of the polyhedron to be fairly stable over periods of the order of a year. However, after some period of time, a new set of station coordinates will be required because of improved data, unexpected station motions, etc. Methods for maintaining agreement with the previous set of station coordinates in some average sense are discussed in this paper. Some of the contributions expected from other new measurement methods also are described.

Many problems of geodynamics depend on spatial relationship of points and their temporal variations. To solve these problems it is convenient, but not necessary, to use a reference frame. To use a reference frame, a scheme is needed by which the coordinates of any point expressed in this frame could be obtained. Coordinates are hardly ever measured directly. Instead, they are computed from measurements of other quantities within the framework of a theory that relates the measured quantities with the coordinates. Such a scheme will be called a reference system. Reference systems have been realized using simple theories and reducing the measurements with the best available, but not always complete, theories. This geometric (static) method has been used to a great extend to define astronomic reference systems (star catalogues) and geodetic reference systems (geodetic datums), With space techniques, a method can be used based on dynamic principles. A space object moving according to a certain theory (assumed to be known) defines in a time dependent way the representative points. A reference system of this type is the WGS 72.

The impact of relativistic theories of space, time and gravitation on the problem of reference systems is reviewed.

First, the concept of inertial systems is discussed from the point of view of the special and the general theory of relativity. Then, relativistic corrections of Doppler, laser and VLBI, and similar effects are reviewed; they are usually on the order of 10-8. Finally, the problem of a possible variation of the gravitational constant G (on the order of 10-11/year) is outlined; such a variation does not occur in special and general relativity, but is implied by certain generalized field theories which are less commonly accepted.

The fundamental properties of kinematic and dynamic reference frames are defined, first as an abstract concept and second in a practical (although idealized) thought experiment. A four dimensional spacetime description in coordinate free notation illustrates the properties, limitations, and relationships between kinematic and dynamic reference frames. Kinematic reference frames can be defined quite rigorously. Dynamic reference frames cannot be defined so well, but are nonetheless very useful. In practice a combination has been generally adopted. Presently we can materialize purely kinematic terrestrial and celestial reference frames.

Changes in reference coordinate systems have major implications well beyond the realm of Earth dynamics. Definitions that serve geodynamic convenience may cause considerable effects for other disciplines. After presenting some typical areas in which coordinate frame definitions are important, recommendations are given for criteria to be considered as boundary conditions in discussing changes. These cover such qualities as observability, complexity, stability, internal coherence and uniqueness.

A celestial reference frame is based on some dynamical or kinematic approximation of an absolute coordinate system and is materialized by a fundamental catalogue of stars. It is characterized by the accuracy of the system and the precision of its stellar realization.

The present situation, marked by the construction of the FK5 system and catalogue, is briefly described. It will be an hybrid system based on the discussion of all existing observations. The prospects for improvement in accuracy are good using lunar laser observations or VLBI determination of the positions of extra-galactic radio-sources. Three procedures that may be used to link such a system to a star catalogue are given. A major improvement in precision is expected from the Hipparcos programme and further extensions include essentially the densification of catalogues with stars of magnitudes 10 to 14 using photoelectric automatic meridian instruments.

Geodetic observations of gravity, body tides, the Earth’s rotation and crustal motion and deformation potentially provide important constraints in the general inversion of geophysical data for determining the structure and evolution of the Earth. More specifically, the geodetic data provide constraints on the rheology of the planet in the frequency range intermediate between geological and seismic frequencies, on the geologically instantaneous kinematics of the Earth and on the mechanisms responsible for the motions within the Earth, results that are intimately related to the plate tectonics hypothesis. The discussion is limited here to only a few aspects of these “geodetic” aspects of this hypothesis, including deformation along plate boundaries, intraplate tectonics and vertical motions.

This talk was intended, I think, to be an opportunity to recite the conventional wisdom of the class of geophysicists who are interested in investigating theoretically the Earth’s wobble and nutation. It has become clear since the Kiev meeting in 1977, however, that we have not yet agreed upon the contents of our conventional wisdom and it would be premature, and presumptuous, of me to pretend to recite it. What I can do is to tell you what I think the conventional wisdom ought to be. In doing so I shall give free rein to my prejudices and little consideration to opposing points of view (they must speak for themselves). Nothing in this talk is noticeably original; virtually all of it is extracted from the work of others or from the folklore of this topic.

This paper examines the question of the definition of the celestial and terrestrial coordinate frames by the technique of long baseline interferometry. It demonstrates how the celestial coordinate frame may be usefully defined in terms of basis 1-forms associated with the advancing phase fronts of the radiation fields from compact radio sources using only interferometer observables. The paper then proceeds to show how the terrestrial coordinate frame could be usefully defined, incorporating fully the effects of plate tectonics and secular motion of the observatories, by an application of the theory of continuum mechanics to interferometer observations.

The rotational motion of the earth is decomposed into spin, polar motion and local motions. The rotation vector components are associated to phenomena such as precession, nutation, diurnal spin, polar motion and local motions. The above decomposition is accomplished without refering to an earth-fixed CIO pole or BIH zero meridian. The time-like variations of the coordinates of a surface point in a geocentric equatorial reference frame are presented as a function of the rotation vector components. In the rigid earth approximation three scalar parameters are necessary for evaluating point coordinate variations, namely spin rate of the earth, polar motion magnitude and spin rate of the polar motion vector. Two numerical examples are given as an illustration.

The definition of a terrestrial reference pole (TRP) and of a Terrestrial Longitude Origin (TLO), by fixing the stations coordinates of an adopted network seems unrealistic. It is proposed that TRP and TLO be the realized origins of some specified service working in accordance with some stated principles. It is also proposed to clarify the definition of UT1 and to base it on some physical properties.

The inaccuracies in the reference frames actually realized by the different techniques for measuring the Earth’s rotation are theoretically investigated. The intercomparison of the available series of measurements provides numerical estimations of these defects. Using data corrected for reference frame effects high frequency fluctuations of UT1 are detected.

The report of the IAU Working Group on Nutation endorsed by Commissions 4, 8, 19 and 31 at the 1979 General Assembly points out that “… the complete theory of the general nutational motion of the Earth about its center of mass may be described by the sum of two components, astronomical nutation, commonly referred to as nutation, which is nutation with respect to a space-fixed coordinate system, and polar motion, which is nutation with respect to a body-fixed system …”. Unlike the situation for the space-fixed frame, there is not an adequate, formally accepted, body-fixed system for this purpose. The Conventional International Origin (CIO) as it is presently defined is no longer acceptable because of recent improvements in observational techniques. The effective lack of this type of terrestrial reference frame limits the complete description of the general nutational motion of the Earth. In the absence of a terrestrial reference frame suitable for specifying the orientation of the Earth, it is suggested that a body-fixed system could be represented formally in a manner analogous to that used to represent the space-fixed frame. This procedure would be quite similar to methods employed currently by the International Polar Motion Service and the Bureau International de l’Heure, and would allow for the use of observations from new techniques in the definition of a terrestrial reference frame to be used to specify the complete nutational motion of the Earth.

The definition and practical realization of the astronomical system of terrestrial coordinates are discussed. In particular, the separation of secular polar motion and nonpolar drift of observatories are touched upon as far as those phenomena are crucially intertwined with the realization of a terrestrial coordinate system.

A short review of the reference pole presently used in polar motion determinations by classical astrometric methods is followed by a discussion of the systematic differences between systems of polar coordinates and the influence of the mean latitude of stations on pole position. The importance of homogenous processing astrometric data is stressed.

Ten frequency components of short period latitude variations and corrections for the declination at an epoch and the proper motion in declination are estimated simultaneously. The short period variations are nearly diurnal and semi-diurnal and are supposed to be due to nutations and Earth tides. Analysis is by the least-squares chain method with weights for individual observations, recently developed by Manabe et al. (1977). Weights are assigned on the assumption that the observational errors follow a normal distribution, whose dispersion changes night by night. Among all possible 1024 combinations of the short period variations, the best is chosen on the basis of the minimum AIC procedure. The data used are the results of the homogeneous recalculation of the ILS observations, 1399-1978. This is considered to be the optimal astrometric data set for investigating nutations, because of its long time-span, homogeneity and size. Declinations are estimated for each of the seven observational periods with mean errors smaller than 001. The mean errors of the proper motions are of the order 0002/y. Among the short period variations, significant estimates are obtained for the terms corresponding to the lunar fortnightly, solar semi-annual and lunar nodal nutations, and the M2 tide. The mean errors are shown to be greatly reduced and the entire data set is analyzed. An effort is made to distinguish the preferred theoretical model.

The ‘decade’ fluctuations in the Earth’s rotation in the period 1620-1978 are derived from astronomical observations. The torques on the mantle which produce these fluctuations attain a magnitude of 1018Nm (1025 dyn cm) around 1900.