International Terrestrial Reference Frame Research Articles

The expanding Earth at present: evidence from temporal gravity field and space-geodetic data

The Earth expansion problem has attracted great interest, and the present study demonstrates that the Earth has been expanding, at least over the recent several decades. Space-geodetic data recorded at stations distributed globally were used (including global positioning system data, very-long-baseline interferometry, satellite laser ranging stations, and stations for Doppler orbitography and radiopositioning integrated by satellite), which covered a period of more than 10 years in the International Terrestrial Reference Frame 2008. A triangular network covering the surface of the Earth was thus constructed based on the spherical Delaunay approach, and average-weighted vertical variations in the Earth surface were estimated. Calculations show that the Earth is expanding at present at a rate of 0.24 ± 0.04 mm/yr. Furthermore, based on the Earth Gravitational Model 2008 and the secular variation rates of the second-degree coefficients estimated by satellite laser ranging and Earth mean-pole data, the principal inertia moments of the Earth (A, B, C) and in particular their temporal variations, were determined: the simple mean value of the three principal inertia moments (i.e., [A+B+C]/3) is gradually increasing. This clearly demonstrates that the Earth has been expanding, at least over the recent decades, and the data show that the Earth is expanding at a rate ranging from 0.17 ± 0.02 mm/yr to 0.21 ± 0.02 mm/yr, which coincides with the space geodetic evidence. Hence, based on both space geodetic observations and gravimetric data, we conclude that the Earth has been expanding at a rate of about 0.2 mm/yr over recent decades.

Accuracy of the International Terrestrial Reference Frame origin and Earth expansion

The International Terrestrial Reference Frame (ITRF) is a fundamental datum for high?precision orbit tracking, navigation, and global change monitoring. Accurately realizing and maintaining ITRF origin at the mean Earth system center of mass (CM) is critical to surface and spacecraft based geodetic measurements including those of sea level rise and its sources. Although ITRF combines data from satellite laser ranging (SLR), Very Long Baseline Interferometry (VLBI), Global Positioning System (GPS), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), its origin is currently realized by the single technique of SLR. Consequently, it is difficult to independently evaluate the origin accuracy. Also, whether the solid Earth is expanding or shrinking has attracted persistent attention. The expansion rate, if any, has not been accurately determined before, due to insufficient data coverage on the Earth's surface and the presence of other geophysical processes. Here, we use multiple precise geodetic data sets and a simultaneous global estimation platform to determine that the ITRF2008 origin is consistent with the mean CM at the level of 0.5 mm yr?1, and the mean radius of the Earth is not changing to within 1? measurement uncertainty of 0.2 mm yr?1.

Strategies to mitigate aliasing of loading signals while estimating GPS frame parameters

Although GNSS techniques are theoretically sensitive to the Earth center of mass, it is often preferable to remove intrinsic origin and scale information from the estimated station positions since they are known to be affected by systematic errors. This is usually done by estimating the parameters of a linearized similarity transformation which relates the quasi-instantaneous frames to a long-term frame such as the International Terrestrial Reference Frame (ITRF). It is well known that non-linear station motions can partially alias into these parameters. We discuss in this paper some procedures that may allow reducing these aliasing effects in the case of the GPS techniques. The options include the use of well-distributed sub-networks for the frame transformation estimation, the use of site loading corrections, a modification of the stochastic model by downweighting heights, or the joint estimation of the low degrees of the deformation field. We confirm that the standard approach consisting of estimating the transformation over the whole network is particularly harmful for the loading signals if the network is not well distributed. Downweighting the height component, using a uniform sub-network, or estimating the deformation field perform similarly in drastically reducing the amplitude of the aliasing effect. The application of these methods to reprocessed GPS terrestrial frames permits an assessment of the level of agreement between GPS and our loading model, which is found to be about 1.5 mm WRMS in height and 0.8 mm WRMS in the horizontal at the annual frequency. Aliased loading signals are not the main source of discrepancies between loading displacement models and GPS position time series.

ITRF2008: an improved solution of the international terrestrial reference frame

ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16 years of observations, respectively. The input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb at epoch 2005.0 and 0.049 ± 0.010 ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005 using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins are defined by SLR) indicates differences at epoch 2005.0, namely: −0.5, −0.9 and −4.7 mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3 mm/yr. The estimated formal errors of these parameters are 0.2 mm and 0.2 mm/yr, respectively. The high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits a Z-translation drift of 1.8 mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level of its agreement with ITRF2005 is believed to be at the level of 1 cm over the time-span of the SLR observations. Considering the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2 ppb (8 mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008 is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties in co-location sites and space geodesy estimates.

Verification of heights above global mean sea level from high-degree global geopotential models by using leveling data

The dedicated satellite gravity missions CHAllenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity field and steady-state Ocean Circulation Explorer (GOCE) and their recent and expected Global Geopotential Models (GGMs) present new opportunities for the determination of gravity-related heights. Global Positioning System (GPS), the recent GGMs, and reference value W0 are used to study the construction of different height systems and verify high-degree global geopotential models. This approach matches well with all theoretical basics of height systems. The presented numerical strategy is independent of height anomaly and geoid undulation computation. Using the International Terrestrial Reference Frame (ITRF) coordinates at 47 GPS stations of the Turkish National Vertical Control Network (TNVCN), the gravity potential values are computed based on new-generation GGMs. The computed gravity potentials are converted into different height systems. A global mean sea level represented by a geoid potential has been taken as reference for the heights. The GGM-derived geopotential numbers, Helmert orthometric, and Molodensky normal heights at the GPS stations are compared against the results from precise leveling. The numerical application demonstrates that three types of gravity-related heights can be determined with a similar accuracy level (12 cm). When long-term deformations such as tectonic activity and possible land subsidence/uplift effects on the heights of benchmarks of the TNVCN are taken into account, the obtained results are significant, and also, under the light of the dedicated satellite gravity missions, high-resolution GGMs such as EGM2008 have an important potential for the realization of a unified height system. The experimental study shows a datum bias of 38 2 cm between the TNVCN datum and the global datum.

Updating Thai Reference Frame to ITRF2005 Using GPS: Diversion Between ITRF2000 and 2005 in Southeast Asia

The Thai geodetic network has been regularly observed with Global Positioning System (GPS) since 1994 through several collaborative EU-ASEAN projects such as GEODYSSEA, SEAMERGES and RTSD-Delft. This geodetic network has long been served as a reference frame for Thailand. Previous realisations of the Thai coordinate reference frame were therefore tied to the global International Terrestrial Reference Frame (ITRF) at epochs 1994, 1996 and 2000. After the occurrence of the 9.2 Mw Sumatra-Andaman earthquake on the 26th December 2004, horizontal displacements were evident at different magnitudes in many surrounding countries. The geodetic network within Thailand was also significantly deformed during the earthquake at the centimetre to decimetre level. Large co-seismic horizontal displacements were observed in the southern part of Thailand, while moderate and small displacements were seen in the central and northern parts of Thailand. The Royal Thai Survey Department (RTSD) has been carrying out multiple GPS field campaigns to monitor the post-seismic displacements. This paper will analyse the GPS observations obtained from the RTSD GPS campaigns up to the end of 2008 using the Precise Point Positioning (PPP) strategy of the GIPSY-OASIS II software. It has been demonstrated that by employing the state of the art PPP technique, the users could achieve mm-level of repeatability in the horizontal components and centimetre precision in the vertical direction, for a 24-hr data span from a static site occupied by a geodetic-quality receiver. Coordinate results obtained from each campaign are then mapped to ITRF2000 and ITRF2005 using a number of well-determined global International GNSS service (IGS) sites. By comparing coordinate results between ITRF2000 and ITRF2005, it is evident that there is a significant diversion in the north component at a rate of 1.7 mm per year over Southeast Asia region. Finally, ITRF2005 coordinate results obtained from the latest RTSD GPS campaign (November 2008) will be served as a new coordinate reference frame for Thailand.

Recommendations for construction of a nonlinear international Terrestrial Reference Frame

The problems of ITRF2008, the latest International Terrestrial Reference Frame, are pointed out and analyzed as follows: (1) ITRF is not a mm-level Terrestrial Reference Frame; (2) the origin of ITRF is neither the Earth’s center of mass (CM) nor the center of figure (CF); (3) the scale of ITRF is not a uniform system in the sense of the gravitational theory of relativity. These problems result from the linear hypothesis used in the establishment and maintenance of ITRF, which includes the linear hypothesis of the coordinates definition of the ITRF reference stations, and the seven coordinate transformation parameters (three translation parameters, three rotation parameters, and one scale parameter) when the ITRF combine solution is constructed. The linear hypothesis of the ITRF construction leads to the current terrestrial reference frame only at the cm-level, which cannot satisfy the requirements of monitoring mm-level crust movements as well as the global environment. This article points out that the construction of a mm-level Terrestrial Reference Frame is actually a leap from linear to nonlinear. Therefore, according to the main characteristics of nonlinear changes of the crust’s deformation, the geocenter motion and the overall height fluctuation of the Earth, the new ITRF station coordinates definition and the new observation equations of combined solutions are constructed for the realization of a mm-level nonlinear ITRF, which can solve the problems of the current ITRF.

Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS

We built a new experimental apparatus (the “Satellite/lunar laser ranging Characterization Facility”, SCF) and created a new test procedure (the SCF-Test) to characterize and model the detailed thermal behavior and the optical performance of cube corner laser retroreflectors in space for industrial and scientific applications. The primary goal of these innovative tools is to provide critical design and diagnostic capabilities for Satellites Laser Ranging (SLR) to Galileo and other GNSS (Global Navigation Satellite System) constellations. The capability will allow us to optimize the design of GNSS laser retroreflector payloads to maximize ranging efficiency, to improve signal-to-noise conditions in daylight and to provide pre-launch validation of retroreflector performance under laboratory-simulated space conditions. Implementation of new retroreflector designs being studied will help to improve GNSS orbits, which will then increase the accuracy, stability, and distribution of the International Terrestrial Reference Frame (ITRF), to provide better definition of the geocenter (origin) and the scale (length unit). Our key experimental innovation is the concurrent measurement and modeling of the optical Far Field Diffraction Pattern (FFDP) and the temperature distribution of the SLR retroreflector payload under thermal conditions produced with a close-match solar simulator. The apparatus includes infrared cameras for non-invasive thermometry, thermal control and real-time movement of the payload to experimentally simulate satellite orientation on orbit with respect to both solar illumination and laser interrogation beams. These unique capabilities provide experimental validation of the space segment for SLR and Lunar Laser Ranging (LLR). We used the SCF facility and the SCF-Test to perform a comprehensive, non-invasive space characterization of older generation, back-coated retroreflectors of the GIOVE-A and -B (Galileo In-Orbit Validation Elements) and the GPS-35 and -36 designs. First, using a full GPS flight model at laser wavelengths of 532 and 632 nm, we found its “effective optical cross section” in air, under isothermal conditions, to be six times lower than the Retroreflector Standard for GNSS satellites (100 × 10 6 m 2 at 20,000 km altitude for GPS and 180 × 10 6 m 2 for Galileo at 23,200 km altitude), issued by the International Laser Ranging Service (ILRS). Under the simulated thermal and space conditions of the SCF, we also showed that in some space configurations the “effective optical cross section” is further reduced, by the thermal degradation of the FFDP. Using the same SCF-Test configuration on an individual GIOVE prototype cube, we measured severe thermal degradation in optical performance, which appears to be caused by the retroreflector metal coating and the non-optimized thermal conductance of the mounting. Uncoated retroreflectors with proper mounting can minimize thermal degradation and significantly increase the optical performance, and as such, are emerging as the recommended design for modern GNSS satellites. The COMPASS-M1, GLONASS-115 GNSS satellites use uncoated cubes. They provide better efficiency than those on GPS and GIOVE, including better daylight ranging performance. However, these retroreflectors were not characterized in the laboratory under space conditions prior to launch, so we have no basis to evaluate how well they were optimized for future GNSS satellites. SCF-Testing, under a non-disclosure agreement between INFN-LNF and the European Space Agency (ESA), of prototype uncoated cubes for the first four Galileo satellites to be launched (named “IOV”, In-Orbit Validation satellites) is a major step forward. An SCF-Test performed on a LAGEOS (LAser GEOdynamics Satellite) engineering model retroreflector array provided by NASA, showed the good space performance on what is now a reference ILRS payload standard. The IOV and LAGEOS measurements demonstrated the effectiveness of the SCF-Test as an LRA diagnostic, optimization and validation tool in use by NASA, ESA and ASI.

Global sea-level rise and its relation to the terrestrial reference frame

We examined the sensitivity of estimates of global sea-level rise obtained from GPS-corrected long term tide gauge records to uncertainties in the International Terrestrial Reference Frame (ITRF) realization. A useful transfer function was established, linking potential errors in the reference frame datum (origin and scale) to resulting errors in the estimate of global sea level rise. Contrary to scale errors that are propagated by a factor of 100%, the impact of errors in the origin depends on the network geometry. The geometry of the network analyzed here resulted in an error propagation factor of 50% for the Z component of the origin, mainly due to the asymmetry in the distribution of the stations between hemispheres. This factor decreased from 50% to less than 10% as the geometry of the network improved using realistic potential stations that did not yet meet the selection criteria (e.g., record length, data availability). Conversely, we explored new constraints on the reference frame by considering forward calculations involving tide gauge records. A reference frame could be found in which the scatter of the regional sea-level rates was limited. The resulting reference frame drifted by 1.36 ± 0.22 mm/year from the ITRF2000 origin in the Z component and by −0.44 ± 0.22 mm/year from the ITRF2005 origin. A bound on the rate of global sea level rise of 1.2 to 1.6 mm/year was derived for the past century, depending on the origin of the adopted reference frame. The upper bound is slightly lower than previous estimates of 1.8 mm/year discussed in the IPCC fourth report.

Quality assessment of GPS reprocessed terrestrial reference frame

The International GNSS Service (IGS) contributes to the construction of the International Terrestrial Reference Frame (ITRF) by submitting time series of station positions and Earth Rotation Parameters (ERP). For the first time, its submission to the ITRF2008 construction is based on a combination of entirely reprocessed GPS solutions delivered by 11 Analysis Centers (ACs). We analyze the IGS submission and four of the individual AC contributions in terms of the GNSS frame origin and scale, station position repeatability and time series seasonal variations. We show here that the GPS Terrestrial Reference Frame (TRF) origin is consistent with Satellite laser Ranging (SLR) at the centimeter level with a drift lower than 1 mm/year. Although the scale drift compared to Very Long baseline Interferometry (VLBI) and SLR mean scale is smaller than 0.4 mm/year, we think that it would be premature to use that information in the ITRF scale definition due to its strong dependence on the GPS satellite and ground antenna phase center variations. The new position time series also show a better repeatability compared to past IGS combined products and their annual variations are shown to be more consistent with loading models. The comparison of GPS station positions and velocities to those of VLBI via local ties in co-located sites demonstrates that the IGS reprocessed solution submitted to the ITRF2008 is more reliable and precise than any of the past submissions. However, we show that some of the remaining inconsistencies between GPS and VLBI positioning may be caused by uncalibrated GNSS radomes.

Achievements of the Earth orientation parameters prediction comparison campaign

Precise transformations between the international celestial and terrestrial reference frames are needed for many advanced geodetic and astronomical tasks including positioning and navigation on Earth and in space. To perform this transformation at the time of observation, that is for real-time applications, accurate predictions of the Earth orientation parameters (EOP) are needed. The Earth orientation parameters prediction comparison campaign (EOP PCC) that started in October 2005 was organized for the purpose of assessing the accuracy of EOP predictions. This paper summarizes the results of the EOP PCC after nearly two and a half years of operational activity. The ultra short-term (predictions to 10 days into the future), short-term (30 days), and medium-term (500 days) EOP predictions submitted by the participants were evaluated by the same statistical technique based on the mean absolute prediction error using the IERS EOP 05 C04 series as a reference. A combined series of EOP predictions computed as a weighted mean of all submissions available at a given prediction epoch was also evaluated. The combined series is shown to perform very well, as do some of the individual series, especially those using atmospheric angular momentum forecasts. A main conclusion of the EOP PCC is that no single prediction technique performs the best for all EOP components and all prediction intervals.

DORIS geodesy: A dynamic determination of geocentre location

Geoscience Australia contributed a multi-satellite, multi-year weekly time series to the International DORIS Service combined submission for the construction of International Terrestrial Reference Frame 2008 (ITRF2008). This contributing solution was extended to a study of the capability of DORIS to dynamically estimate the variation in the geocentre location. Two solutions, comprising different constraint configurations of the tracking network, were undertaken. The respective DORIS satellite orbit solutions (SPOT-2, SPOT-4, SPOT-5 and Envisat) were verified and validated by comparison with those produced at the Goddard Space Flight Center (GSFC), DORIS Analysis Centre, for computational consistency and standards. In addition, in the case of Envisat, the trajectories from the GA determined SLR and DORIS orbits were compared. The results for weekly dynamic geocentre estimates from the two constraint configurations were benchmarked against the geometric geocentre estimates from the IDS-2 combined solution. This established that DORIS is capable of determining the dynamic geocentre variation by estimating the degree one spherical harmonic coefficients of the Earth’s gravity potential. It was established that constrained configurations produced similar results for the geocentre location and consequently similar annual amplitudes. For the minimally constrained configuration Greenbelt–Kitab, the mean of the uncertainties of the geocentre location were 2.3, 2.3 and 7.6 mm and RMS of the mean uncertainties were 1.9, 1.2 and 3.5 mm for the X, Y and Z components, respectively. For GA_IDS-2_Datum constrained configuration, the mean of the uncertainties of the geocentre location were 1.7, 1.7 and 6.2 mm and RMS of the mean uncertainties were 0.9, 0.7 and 2.9 mm for the X, Y and Z components, respectively. The mean of the differences of the two DORIS dynamic geocentre solutions with respect to the IDS-2 combination were 1.6, 4.0 and 5.1 mm with an RMS of the mean 21.2, 14.0 and 31.5 mm for the Greenbelt–Kitab configuration and 4.1, 3.9 and 4.3 mm with an RMS 8.1, 9.0 and 28.6 mm for the GA_IDS-2_Datum constraint configuration. The annual amplitudes for each component were estimated to be 5.3, 10.8 and 11.0 mm for the Greenbelt–Kitab configuration and 5.3, 9.3 and 9.4 mm for the GA_IDS-2_Datum constraint configuration. The two DORIS determined dynamic geocentre solutions were compared to the SLR determined dynamic solution (which was determined from the same process of the GA contribution to the ITRF2008 ILRS combination) gave mean differences of 3.3, −4.7 and 2.5 mm with an RMS of 20.7, 17.5 and 28.0 mm for the X, Y and Z components, respectively for the Greenbelt–Kitab configuration and 1.1, −5.4 and 4.4 mm with an RMS of 9.7, 13.3 and 24.9 mm for the GA_IDS-2_Datum configuration. The larger variability is reflected in the respective amplitudes. As a comparison, the annual amplitudes of the SLR determined dynamic geocentre are 0.9, 1.0 and 6.8 mm in the X, Y and Z components. The results from this study indicate that there is potential to achieve precise dynamically determined geocentre from DORIS.

Topographically induced height errors in predicted atmospheric loading effects

Atmospheric pressure variations are known to induce vertical displacements of the Earth's surface with magnitudes large enough to be detected by geodetic observations. Estimates of these loading effects are derived using global reanalysis fields of surface pressure as input. The input surface pressure has a minimum spatial sampling, which does not capture true surface pressure variations due to high topographic variability in some regions. In this paper, we investigate the effect that unmodeled topographic variability has on surface pressure estimates and subsequent estimates of vertical surface displacements. We find that the estimated height changes from the topographic surface pressure can be significant (2–4 mm) for sites in regions of high topographic variability. When we compare the estimated height changes to Global Positioning System residuals from the 2005 International Terrestrial Reference Frame Realization, we find that the heights derived from the topographic surface pressure, versus those from the normal surface pressure, perform better at reducing the scatter on the height coordinate time series.

Estimation of phase center corrections for GLONASS-M satellite antennas

Driven by the comprehensive modernization of the GLONASS space segment and the increased global availability of GLONASS-capable ground stations, an updated set of satellite-specific antenna phase center corrections for the current GLONASS-M constellation is determined by processing 84 weeks of dual-frequency data collected between January 2008 and August 2009 by a worldwide network of 227 GPS-only and 115 combined GPS/GLONASS tracking stations. The analysis is performed according to a rigorous combined multi-system processing scheme providing full consistency between the GPS and the GLONASS system. The solution is aligned to a realization of the International Terrestrial Reference Frame 2005. The estimated antenna parameters are compared with the model values currently used within the International GNSS Service (IGS). It is shown that the z-offset estimates are on average 7 cm smaller than the corresponding IGS model values and that the block-specific mean value perfectly agrees with the nominal GLONASS-M z-offset provided by the satellite manufacturer. The existence of azimuth-dependent phase center variations is investigated and uncertainties in the horizontal offset estimates due to mathematical correlations and yaw-attitude modeling problems during eclipse seasons are addressed. Finally, it is demonstrated that the orbit quality benefits from the updated GLONASS-M antenna phase center model and that a consistent set of satellite antenna z-offsets for GPS and GLONASS is imperative to obtain consistent GPS- and GLONASS-derived station heights.

Higher‐order ionospheric effects on the GPS reference frame and velocities

We describe how GPS time series are influenced by higher‐order ionospheric effects over the last solar cycle (1995–2008) and examine implications for geophysical studies. Using 14 years of globally reprocessed solutions, we demonstrate the effect on the reference frame. Including second‐ and third‐order ionospheric terms causes up to 10 mm difference in the smoothed transformation to the International Terrestrial Reference Frame (ITRF) 2005, with the Z translation term dominant. Scale is also slightly affected, with a change of up to ∼0.05 ppb. After transformation to ITRF2005, residual effects on vertical site velocities are as high as 0.34 mm yr−1. We assess the effect of the magnetic field model on the second‐order term and find a time‐varying difference of 0–2 mm in the Z translation. We also assess the effect of omitting the third‐order term. We find that while the second‐order term is responsible for almost all the Z translation effects, it is the combination of the second‐ and third‐order terms that causes the effect on scale. Comparison of our GPS reprocessing with ITRF2005 suggests that GPS origin rates may vary with time period. For example, we find Z translation rates of −0.82 ± 0.17 mm yr−1 for 1995–2008 and 0.17 ± 0.24 mm yr−1 for 1995–2005. If GPS were to contribute to origin rate definition for future ITRFs, higher‐order ionospheric corrections would need to be applied due to their effect on translation parameters during solar maximum.

Global GPS reference frame solutions of unlimited size

This paper reports on the Dancer project, which is one of three related projects initiated by working group 1 of the International Association of Geodesy. The Dancer project develops JAVA parameter estimation software that runs in the form of a distributed process on the internet, in such a way that each processing node handles the data of a single geodetic instrument. By exchanging a minimum amount of information among all processing nodes, the same global normal equation solution is found by all instruments. The result is a fully scalable least squares solution that has no practical limit to the number of GPS receivers or other tracking devices that may be included in a single reference frame realization. High-end GPS users will also be able to run a Dancer process for their own data, without contributing to the reference frame solution but taking full advantage of its global consistency. This offers direct access to precise International Terrestrial Reference Frame and UTC realizations, anywhere on Earth where there is an internet connection. Mission control centres of low satellites with GPS receivers can run a Dancer process on the incoming data from the orbiting receiver, to introduce strong ties with other techniques such as Satellite Laser Ranging.

GGSP: Realisation and maintenance of the Galileo Terrestrial Reference Frame

The realisation and maintenance of a Galileo Terrestrial Reference Frame (GTRF) is the main function of the Galileo Geodetic Service Provider (GGSP). The GTRF shall be compatible with the latest International Terrestrial Reference Frame (ITRF) within a precision level of 3 cm (2 sigma). The connection to the ITRF is realized and validated by stations of the International GNSS Service (IGS) and by geodetic local ties to stations equipped with other geodetic techniques. It is demonstrated that this GTRF can be maintained by including the Galileo Signal-in-Space data, once Galileo reaches its operational stage. The GGSP will also provide additional products, such as Earth Rotation Parameters, satellites orbits, clock corrections for satellites and stations, which will be offered to the Galileo user community to have most precise access to the GTRF and will be used to monitor the accuracy of the corresponding Galileo Mission Segment. The GGSP was built up in time, and for a final demonstration the full system was operated for an interval of 6 months. During that time also microwave data from the two active GIOVE satellites were used. The GGSP Consortium followed the most up to date IGS standards of weekly processing during seven monthly campaigns (November 2006 to June 2008) and a continuous processing from September 2008 to February 2009 delivering several versions of the GTRF. The latest GTRF solution (GTRF09v01) has an RMS position difference with respect to the ITRF2005 computed over the 71 common stations of 1.1 and 2.9 mm in the horizontal and vertical components, respectively. The RMS velocity differences are 0.3 and 0.6 mm/y, respectively. The GGSP GPS satellite orbits and clock corrections agree with the IGS Final products at a level of 5–11 mm and 0.02–0.03 ns, respectively. The quality of the GIOVE orbits is at a level of 20–30 cm. The Hydrogen-Maser on board of GIOVE-B is nearly one order of magnitude better than the GPS satellite clocks.

The angular velocities of the plates and the velocity of Earth's centre from space geodesy

Using space geodetic observations from four techniques (GPS, VLBI, SLR and DORIS), we simultaneously estimate the angular velocities of 11 major plates and the velocity of Earth's centre. We call this set of relative plate angular velocities GEODVEL (for GEODesy VELocity). Plate angular velocities depend on the estimate of the velocity of Earth's centre and on the assignment of sites to plates. Most geodetic estimates of the angular velocities of the plates are determined assuming that Earth's centre is fixed in an International Terrestrial Reference Frame (ITRF), and are therefore subject to errors in the estimate of the velocity of Earth's centre. In ITRF2005 and ITRF2000, Earth's centre is the centre of mass of Earth, oceans and atmosphere (CM); the velocity of CM is estimated by SLR observation of LAGEOS's orbit. Herein we define Earth's centre to be the centre of mass of solid Earth (CE); we determine the velocity of CE by assuming that the portions of plate interiors not near the late Pleistocene ice sheets move laterally as if they were part of a rigid spherical cap. The GEODVEL estimate of the velocity of CE is likely nearer the true velocity of CM than are the ITRF2005 and ITRF2000 estimates because (1) no phenomena can sustain a significant velocity between CM and CE, (2) the plates are indeed nearly rigid (aside from vertical motion) and (3) the velocity of CM differs between ITRF2005 and ITRF2000 by an unacceptably large speed of 1.8 mm yr−1. The velocity of Earth's centre in GEODVEL lies between that of ITRF2000 and that of ITRF2005, with the distance from ITRF2005 being about twice that from ITRF2000. Because the GEODVEL estimates of uncertainties in plate angular velocities account for uncertainty in the velocity of Earth's centre, they are more realistic than prior estimates of uncertainties. GEODVEL differs significantly from all prior global sets of relative plate angular velocities determined from space geodesy. For example, the 95 per cent confidence limits for the angular velocities of GEODVEL exclude those of REVEL (Sella et al.) for 34 of the 36 plate pairs that can be formed between any two of the nine plates with the best-constrained motion. The median angular velocity vector difference between GEODVEL and REVEL is 0.028° Myr−1, which is up to 3.1 mm yr−1 on Earth's surface. GEODVEL differs the least from the geodetic angular velocities that Altamimi et al. determine from ITRF2005. GEODVEL's 95 per cent confidence limits exclude 11 of 36 angular velocities of Altamimi et al., and the median difference is 0.015° Myr−1. GEODVEL differs significantly from nearly all relative plate angular velocities averaged over the past few million years, including those of NUVEL-1A. The difference of GEODVEL from updated 3.2 Myr angular velocities is statistically significant for all but two of 36 angular velocities with a median difference of 0.063° Myr−1. Across spreading centres, eight have slowed down while only two have sped up. We conclude that plate angular velocities over the past few decades differ significantly from the corresponding angular velocity averaged over the past 3.2 Myr.

ITRF to GDA94 coordinate transformations

The Geocentric Datum of Australia 1994 (GDA94) is a static coordinate datum realised with respect to the International Terrestrial Reference Frame (ITRF) at the reference epoch of 1 January 1994. At this time GDA94 and ITRF were coinci- dent, however, as a consequence of the tectonic mo- tion of the Australian Plate, ongoing refinement of the ITRF and crustal deformation, the two reference frames have diverged and the absolute di¤erence between them is now approximately 1 m. Conse- quently, precise coordinate transformations between ITRF and GDA94 are required for many applica- tions, and in this study these transformations are reviewed, improved and extended. New transforma- tion parameters between ITRF and GDA94 are computed, including the specific ITRF realisations of ITRF1996, ITRF1997, ITRF2000, ITRF2005 and ITRF2008. The two most recent ITRF realisa- tions, ITRF2005 and ITRF2008, after transforma- tion have a root-mean-square di¤erence of less than 10 and 30 mm in the horizontal and vertical compo- nents, respectively, with respect to GDA94 at the Australian Fiducial Network (AFN) stations. How- ever, the magnitude of some residuals exceed 15 and 60 mm in the horizontal and vertical components, respectively, which reflects the accuracy limit of GDA94. Finally, the implications and future strat- egies for managing the di¤erences between GDA94 and ITRF are discussed, including novel coordinate transformation approaches and justifications for the modernisation of GDA.

GPS surveys in the foreland-foredeep tectonic system of Southeastern Sicily:first results

The Hyblean plateau (Southeastern Sicily) is characterised by three main tectonic structural trends: the first, NNW-SSE striking, runs on the easternmost part of the plateau and is linked to the Hyblean-Maltese fault system; the second runs along the western part of the plateau with a NNE-SSW direction and is characterised by a sinistral strike slip motion, like the Scicli fault; the third ENE-WSW striking, characterises the northernmost part of the area, including the Scordia-Lentini graben. We analysed GPS data collected in a dense network located in the northern area of the Hyblean plateau during 1998 and 2000, between the towns of Catania and Syracuse. Data from Noto, Matera and Cagliari IGS stations, were included in the processing to connect this network to the International Terrestrial Reference Frame (ITRF). The comparison between 1998 and 2000 data sets shows an average northward motion of the GPS stations located south of the Gela-Catania foredeep. Site velocities decrease from south to north and show a weak internal deformation of the northernmost part of the Hyblean plateau.