The NASA Crustal Dynamics Project (CDP) has been using VLBI on intercontinental baselines to measure tectonic plate motions since 1979. We report on measurements between sites on the North American plate (Haystack/Westford, MA; Owens Valley and Mojave, CA; Ft. Davis, TX and Gilmore Creek, AK), the Eurasian plate (Onsala, Sweden; Wettzell, West Germany, and Shanghai, China), the Pacific plate (Kauai, HI; Kwajalein in the Marshall Islands, and Vandenberg AFB, CA), the African plate (Hartebesthoek, RSA), and Japan (Kashima).

We address the requirements that must be met by space-geodetic systems to place useful, new constraints on horizontal secular motions associated with the geological deformation of the earth's surface. Plate motions with characteristic speeds of about 50 mm/yr give rise to displacements that are easily observed by space geodesy. However, in order to improve the existing plate-motion models, the tangential components of relative velocities on interplate baselines must be resolved to an accuracy of < 3 mm/yr. Because motions considered small from a geodetic point of view have rather dramatic geological effects, especially when taken up as compression or extension of continental crust, detecting plate deformation by space-geodetic methods at a level that is geologically unresolvable places rather stringent requirements on the precision of the measurement systems: the tangential components on intraplate baselines must be observed with an accuracy of < 1 mm/yr. Among the measurements of horizontal secular motions that can be made by space geodesy, those pertaining to the rates within the broad zones of deformation characterizing the active continental plate boundaries are the most difficult to obtain by conventional ground-based geodetic and geological techniques. Measuring the velocities between crustal blocks to ± 5 mm/yr on 100-km to 1000-km length scales can yield geologically significant constraints on the integrated deformation rates across continental plate-boundary zones such as the western United States. However, baseline measurements in geologically complicated zones of deformation are useful only to the extent that the endpoints can be fixed in a local kinematical frame that includes major crustal blocks. For this purpose, the establishment of local geodetic networks around major VLBI and SLR sites in active areas should receive high priority.

The standard against which VLBI measurements of continental drift and plate motions are compared are self-consistent global models of “present-day” plate motions determined from geophysical data: marine magnetic anomalies at oceanic spreading centers, azimuths of transform faults, and orientations of earthquake slip vectors on transform faults and at subduction zones. Past global plate motion models have defined regions where the assumption that plates behave rigidly has apparently lead to systematic misfits, sometimes exceeding 10 mm/yr, of plate motion data. Here, we present some of the results from NUVEL-1, a new, self-consistent global model of present-day relative plate motions determined from a compilation and analysis of existing and new geophysical data. These data and new techniques have allowed us to eliminate nearly all statistically significant systematic misfits identified by earlier models, suggesting that the rigid-plate assumption is an excellent approximation when plate motions are averaged over several million years. Beside improving estimates of the motion on previously identified plate boundaries, we have also identified and determined motions on other boundaries whose subtle morphologies, lack of seismicity, and very slow (< 10 mm/yr) relative motions have made them difficult to detect. Here we focus on the application of VLBI measurements to help resolve plate tectonic problems and then briefly outline our results for Pacific-North America motion and plate motions in the Indian Ocean.

To accommodate the relative motion across the North American-Pacific plate boundary predicted by global plate solutions, significant deformation on faults other than the San Andreas is necessary. In central California, this deformation is thought to include distributed compression perpendicular to the San Andreas as well as right-lateral strike-slip motion parallel to the San Andreas on faults such as the San Gregorio/Hosgri system. A self-consistent set of VLBI observations from experiments beginning in October 1982 is used to determine the vector rate of change of station position at central California VLBI sites Ovro, Mojave, Vandenberg, Fort Ord, Presidio, and Point Reyes. To estimate VLBI station positions, a procedure is used that minimizes the uncertainties in defining a reference frame by including a priori geologic and geodetic information. The vector rate of change of station positions provides constraints on the integrated deformation rates between stations. Geologic and geophysical data suggest that the rate and mode of deformation varies on both local and regional scales. Thus, the VLBI derived results are interpreted in the context of an overall tectonic framework by examining geologic and ground-based geodetic data.

Since the late 1970's, NASA's Crustal Dynamics Project has been using Mark III VLBI to study plate tectonic motion, plate boundary deformation and earth dynamics. One major thrust has been the study of crustal motions in the western continental United States. For this effort, several relatively large, fixed antennas (Mojave, Owens Valley, Hatcreek, Ft. Davis and Vandenberg) have been used along with two small, highly mobile VLBI systems which have periodically visited sites of tectonic interest.

The VLBI group in NASA's Crustal Dynamics Project (CDP) maintains an integrated system for analyzing geodetic VLBI data. This system includes: CALC, calibration programs, SOLVE, GLOBL, and the Data Base System. CALC is the program which contains the models used to calculate the theoretical delay. SOLVE is used to analyze single experiments. GLOBL is used to analyze large groups of experiments. The Data Base System is a self-documenting data storage system used to pass data between programs and archive the data. Kalman filtering is being investigated for operational use in geodetic data analysis.

The geodetic IRIS-network is a transatlantic 5-station VLBI-array dedicated to monitor variations of the earth's rotation (e.g. Carter et al., 1985). In a 5 day cycle 14 extragalactic radio sources are observed in regular intervals, covering a GST-range of up to 24 hours, using the MkIII-system in Mode C at 3.6cm (X-band) and 13cm (S-band) wavelength. As this database provides a great potential to monitor source structures and their changes with mas-resolution (the sample contains at least 7 “superluminals”), we have initiated a project to obtain radio maps at both frequencies and to determine, how accurate physical parameters like component flux densities and separations can be measured. Early results are published in Schalinski (1985) and Schalinski et al. (1986). In addition to astrophysical applications, we investigate the influence of structure phases on phase- and group-delay corrections (s. Campbell et al., this vol.).

A National Crustal Motion Network for the United States using VLBI and GPS technologies is being developed. Implementation of both the VLBI and GPS components of the network is underway.

Earth orientation series are linked to the terrestrial reference frame in which the observing site locations are measured. The effect of tectonic motion is a simple rotation for any given plate, but the overall effect depends on the distribution of sites. The magnitude of this motion is large enough to be evident in the data. For example, the coefficient of rotation for the North American plate around the Earth's Y-axis is −0.8 millarcseconds per year in the AMO-2 plate motion model of Minster and Jordan. The VLBI analysis system at NASA/GSFC for computing earth orientation series has recently been enhanced by including the Minster and Jordan model for a priori tectonic effects. Tests indicate that the weighted-root-mean-square residual of observations to the solution is decreased by using this model.

The problem of understanding the deformation occurring along the Pacific-North American plate boundary in the western United States depends upon understanding the forces which drive the plates in this region. One of the primary sources of our knowledge concerning these forces lies in their manifestation as relative displacements which occur throughout the broad zone of deformation surrounding the San Andreas fault system. It is information concerning the spatial and temporal distribution of these motions which will be of greatest benefit in helping to determine which of several possible mechanisms is responsible for driving contemporary plate motions in this region.

We have used very-long-baseline interferometry (VLBI) to make twenty-two independent measurements, between September 1984 and December 1986, of the length of the 3900-km baseline between the Mojave site in California and the Haystack/Westford site in Massachusetts. These experiments differ from the typical geodetic VLBI experiments in that a large fraction of observations are obtained at elevation angles between 4° and 10°. Data from these low elevation angles allows the vertical coordinate of site position, and hence the baseline length, to be estimated with greater precision. For the sixteen experiments processed thus far, the weighted root-mean-square scatter of the estimates of the baseline length is 8 mm. We discuss these experiments, the processing of the data, and the resulting baseline length estimates.

Tectonic motions will, in general, change the orientation as well as the length of baselines used in Very Long Baseline Interferometry (VLBI), and will thus cause slow divergences between Earth orientation results obtained with different VLBI networks, as well as between VLBI results and those obtained by Satellite Laser Ranging (SLR) and Lunar Laser Ranging (LLR). Such drifts (on the order of a milliarcsecond /year) are inherently interesting as well as being significant in combinations of orientation results from different sources. The geodetic study of tectonic motions is also closely connected to research into the nature and causes of systematic errors in data from the modern techniques of space geodesy. We describe both a special coordinate system found to be of use in the analysis of VLBI data and tectonic motion estimates for a VLBI baseline stretching from California to Australia.

The application of very–long–baseline interferometry (VLBI) to the study of the nutations of the earth has yielded unprecedented accuracy for the experimental determination of the coefficients of the nutation series. The analysis of six years of VLBI data has yielded corrections to the coefficients of the seven largest terms in the IAU 1980 nutation series with periods of one year or less, with accuracies approaching the truncation error of this nutation series (0.1 mas). The nutation series coefficients computed from the VLBI data, and those obtained from theoretical considerations (the IAU 1980 nutation series), are in excellent agreement. The largest corrections are to the coefficients of the retrograde annual nutation [2.0 ± 0.1 mas], the prograde semiannual nutation [(0.5 - ι 0.4) ±0.1 mas], and the prograde 13.7 day nutation [−0.4 ± 0.1 mas]. (The imaginary term for the semiannual nutation represents a term 90° out–of–phase with the arguments of the nutation series.) The geophysical implications of these results are currently under active investigation. We discuss the methods used to extract the nutation information from the VLBI data, the calculations of the uncertainties of the resultant corrections to the coefficients of the nutation series, and the current research into the nutations of the earth.

The core-mantle boundary (CMB), separating the molten metallic core from the overlying solid silicate mantle, marks the largest discontinuity in mechanical properties within the Earth. The ∼ 200 km thick region just above the CMB, named D″ by Bullen (1950), is characterized by an anomalous gradient in seismic velocity versus depth. D″ was originally interpreted as a region with a strong compositional gradient due to the accumulation of dense material at the base of the mantle. Subsequently, the anomalous gradient was interpreted as the result of a strong temperature gradient in a hot thermal boundary layer at the base of the mantle, an interpretation motivated by the requiremnet that heat involved in generating the geodynamo must be transported out of the core and through the mantle by convection.

Models describing earth's nutations can be separated into two major components, plus several small perturbations, of which ocean tides and solid friction are the most significant. The primary element of a successful model is an accurate rigid earth nutation theory. The effect of mantle elasticity and differential nutation of the fluid core is then obtained as a correction factor which multiplies the rigid body result. Wahr's (1981) theory is certainly the most sophisticated elastodynamic response model. However, we have found that the simple model of Sasao et al., (1980) differs from Wahr's theory term by term by less than 0.3mas if a modern earth structure model (1066B) is used to evaluate the nutation structure constants.

The rotation of the earth is variable at a number of time scales, from a few days to thousands of years and longer. Variations occur in the rotation rate, in the geographical position of the rotation axis (referred to as polar motion), and in the position of the axis relative to inertial space (referred to as nutation and precession). The interpretations of the various observations have implications for the dynamical behavior and structure of the earth's deep interior, and for various aspects of meteorology and oceanography. These are reviewed below. Also included is an Appendix describing a model of the diurnal resonance in nutation for a non-hydrostatically pre-stressed earth.

Project IRIS (International Radio Interferometric Surveying) was set up under the IAG and COSPAR to provide an operational system that would employ Very-Long-Baseline Interferometry (VLBI) techniques to monitor variations in the rotation of the Earth. Currently the IRIS-A network, with stations at Westford, MA, Ft. Davis, TX, Richmond, FL, and Wettzell, FRG, conducts 24-hour observing sessions every five days to produce determinations of pole position, UT1, and nutation in addition to other parameters of geophysical and astrometric interest. The resulting Earth orientation parameters (EOP) have been shown to have an accuracy of 1 to 2 milliseconds of arc in pole position, and 0.05 to 0.1 milliseconds of time in UT1. In order to observe the relatively large higher frequency variations in UT1, daily 45-minute observing sessions are conducted using the single baseline between Westford and Wettzell. Intercomparison of the UT1 values from the daily and the 5-day series indicates that the accuracy of the daily values is better than 0.1 millisecond of time.

The longer term objectives of the IRIS project include improving the monitoring of Earth orientation by increasing the sampling rate and accuracy of the observations. In April, 1987, the IRIS-P network, with stations in Kashima, Japan, Fairbanks, AK, Ft, Davis, TX, and Richmond, FL began monthly 24-hour observing sessions, and a second series of daily UT1 observing sessions was begun using the stations in Richmond and Bologna, Italy. The additional networks will provide redundancy that will improve the reliability of the system and allow the accuracy of the EOP values to be estimated.

The IRIS UT1 time series provides, for the first time, sufficient accuracy and temporal resolution to look for the few percent increase in k/C caused by the anelastic response of the mantle. Initial results presented here suggest that improved methods of accounting for the dynamics of the oceans and atmosphere may be required before the intertwined variations in UT1 can be fully separated.

The variability in the earth's rotation rate not due to known solid body tides is dominated on time scales of about four years and less by variations in global atmospheric angular momentum (M), as derived from the zonal wind distribution. Among features seen in the length of day (Δl.o.d.) record produced by atmospheric forcing are the strong seasonal cycle, quasi-periodic fluctuations around 40–50 days, and an interannual signal forced by a strong Pacific warming event, known as the El Niño. Momentum variations associated with these time scales arise in different latitudinal regions. Furthermore, winds in the stratosphere make a particularly important contribution to seasonal variability.

Other related topics discussed here are (i) comparisons of the M series from wind fields produced at different weather centers, (ii) the torques that dynamically link the atmosphere and earth, and (iii) longer-term non-atmospheric effects that can be seen upon removal of the atmospheric signal. An interesting application for climatological purposes is the use of historical earth rotation series as a proxy for atmospheric wind variability prior to the era of upper-air data. Lastly, results pertaining to the role of atmospheric pressure systems in exciting rapid polar motion are presented.

A two-symmetric-rigid-rotators model of the Earth has been studied, under the hypothesis of elasto-viscous coupling. The free Eulerian equation of motion has been solved in the linear approximation related to small wobbling amplitudes. Under these hypotheses, polar motion is stable, and the angular velocity of the Earth is the sum of three vectors rotating with different frequencies and damped amplitudes. One of these terms turns out to be retrograde with a quasidiurnal frequency and could be identified with a similar term appearing in liquid core models of the Earth. The other two terms are identified with the Chandler wobble and the annual term according to observational data. The elastic coupling produces, in the time variation of L.O.D., a periodic term whose frequency is about one year. It could be hypothesized that the “decade fluctuation” could be partially attributed to the free oscillation of the Earth.

The basic observables of VLBI for geophysics are the delay and the delay rate. These two basic observables depend on relative geometric relations between the baseline vector and the source vector. The transformation of baseline orientation from the terrestrial coordinate system, in which the stations are located, to the celestial coordinate system, in which VLBI observables are calculated, involves a number of models. One of them is the rotation model.