[1] The analytical formulation of the theories of nutation and wobble reveals the combinations of basic Earth parameters that govern the nutation-wobble response of the Earth to gravitational (tidal) forcing by heavenly bodies and makes it possible to estimate several of them through a least squares fit of the theoretical expressions to the high-precision data now available. This paper presents the essentials of the theoretical framework, the procedure that we used for least squares estimation of basic Earth parameters through a fit of theory to nutation-precession data derived from an up-to-date very long baseline interferometry data set, the results of the estimation and their geophysical interpretation, and the nutation series constructed using the estimated values of the parameters. The theoretical formulation used here differs from earlier ones in the incorporation of anelasticity and ocean tide effects into the basic structure of the dynamical equations of the theory and in the inclusion of electromagnetic couplings of the mantle and the solid inner core to the fluid outer core, though this generalization comes at the cost of making some of the system parameters complex and frequency dependent; it is also more complete, as it takes account of nonlinear terms in these equations, including effects of the time-dependent deformations produced by zonal and sectorial tides, which had been traditionally neglected in nonrigid Earth theories. Among the geophysical results obtained from our fit are estimates for the dynamic ellipticity e of the Earth (e = 0.0032845479 with an uncertainty of 12 in the last digit), for the dynamical ellipticity e f of the fluid core (3.8% higher than its hydrostatic equilibrium value, rather than $5% as hitherto), and for the two complex electromagnetic coupling constants. Our best estimates for the RMS radial magnetic fields at the core mantle boundary and at the inner core boundary, based on the estimates for these coupling constants, are~6.9 and 72 gauss, respectively, when the magnetic field configurations are restricted to certain simple classes. The field strength needed at the inner core boundary could be lower if the density of the core fluid at this boundary or the ellipticity of the solid inner core were lower than that for the Preliminary Reference Earth Model. Our estimate for the resonance frequency of the prograde free core nutation mode, with an uncertainty of $10%, constitutes the first firm detection of the resonance associated with this mode; the period found is $1025 days, double that with electromagnetic couplings ignored. (Throughout this work, ''days,'' referring to periods, stands for ''mean solar days.'') A new nutation series (MHB2000) is constructed by direct solution of the linearized dynamical equations (with our best fit values adopted for all the estimated Earth parameters) for each forcing frequency, and adding on the contributions from the nonlinear terms and other effects not included in the linearized equations. This series gives a considerably better...

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The Mark III very-long-baseline interferometry (VLBI) system allows recording and later processing of up to 112 megabits per second from each radio telescope of an interferometer array. For astrometric and geodetic measurements, signals from two radio-frequency bands (2.2 to 2.3 and 8.2 to 8.6 gigahertz) are sampled and recorded simultaneously at all antenna sites. From these dual-band recordings the relative group delays of signals arriving at each pair of sites can be corrected for the contributions due to the ionosphere. For many radio sources for which the signals are sufficiently intense, these group delays can be determined with uncertainties under 50 picoseconds. Relative positions of widely separated antennas and celestial coordinates of radio sources have been determined from such measurements with 1 standard deviation uncertainties of about 5 centimeters and 3 milliseconds of arc, respectively. Sample results are given for the lengths of baselines between three antennas in the United States and three in Europe as well as for the arc lengths between the positions of six extragalactic radio sources. There is no significant evidence of change in any of these quantities. For mapping the brightness distribution of such compact radio sources, signals of a given polarization, or of pairs of orthogonal polarizations, can be recorded in up to 28 contiguous bands each nearly 2 megahertz wide. The ability to record large bandwidths and to link together many large radio telescopes allows detection and study of compact sources with flux densities under 1 millijansky.

We discuss the prospects for using very long baseline interferometry (VLBI) to measure vertical crustal motions. Our analysis of this problem indicates that the main limitations of such VLBI measurements will probably arise from errors in modeling of the propagation delay through the earth's neutral atmosphere and errors in determining the orientation of a “crust fixed” coordinate system in the VLBI (inertial) reference frame. We examine two techniques for assessing the precision of vertical position measurements which can be made with currently available VLBI systems: (1) the repeatability of baseline length measurements, and (2) the repeatability of the vertical site position of one site in a four‐site network when the positions of the other three sites determine the earth orientation parameters. The repeatability of baseline length measurements implies that the precision of the vertical position estimates is ∼8 cm, averaged over 13 sites (separated by 600–8000 km) and 4.5 years of data. The repeatability of vertical position estimates for the Richmond, Florida, site is ∼7 cm for the 42 observing sessions carried out during an 11‐month period. Both of the techniques we have used to estimate the precision of height determinations indicate that the current precision is ∼8 cm for a single 24‐hour VLBI observing session. The effects of errors in the earth orientation parameters will depend on the distances between the VLBI sites and could induce errors as large as the precision given above.