REFERENCES Abbondanza, C., Z. Altamimi, P. 416 Sarti, M. Negusini, and

L.Vittuari (2009), Local effects of redundant terrestrial and GPS-based tie vectors in ITRF-like combinations, J Geodesy, pp.

DOI 10.1007/s00,190–009–0321–6. Agnew, D. C. (1992), The time-domain behaviour 419 of power-law

noises, Geophys Res Lett, 19, 333–336. Altamimi, Z. (2005), ITRF and Co-location Sites, IERS Tech. Note,

(33), 8–15. Altamimi, Z., X. Collilieux, J. Legrand, B. Garayt, and C. Boucher

(2007a), ITRF2005: A new release of the International Terrestrial Reference Frame based on

time series of station positions and Earth Orientation Parameters, J Geophys Res, 112, B09,401,

doi:10.1029/2007JB004949. Altamimi, Z., P. Sillard, and C. Boucher (2007b), CATREF software:

combination and analysis of terrestrial reference frames, Tech. rep., Laboratoire de Recherche

en Godsie, IGN, Paris, Tech Rep. Beavan, J. (2005), Noise properties of continuous GPS data from

concrete pillar geodetic mon429 uments in New Zealand and comparison with data from U.S. deep

drilled braced monuments, J Geophys Res, 110, B08,410, doi:10.1029/2005JB003642.

Braccesi, A., M. Ceccarelli, G. Colla, R. Fanti, A. Ficarra, G. Gelato, G. Grueff, and G. Sinigaglia (1969), The Italian Cross Radio Telescope. III - Operation of the Telescope, Nuovo Cimento B, 62, 13–19.

Bruyninx, C. (2004), The EUREF Permanent Network; a Multidisciplinary Network Serving

Surveyors as well as Scientists, GEOInformatics, 7 (5), 32–35. Caspary, W. F. (1987), Concepts of network and deformation analysis,

Monograph, vol. 11, The University of New South Wales, Kensington, N.S.W., Australia. Chen, Y. Q. (1983), Analysis of deformation surveys - a generalized

method, Tech. Rep. 94, University of New Brunswick, Fredericton N.B., Canada. Collilieux, X., Z. Altamimi, D. Coulot, J. Ray, and P. Sillard (2007),

Comparison of very long baseline interferometry, GPS and satellite laser ranging height residuals from ITRF2005 using

spectral and correlation methods, J Geophys Res, 112, B12,403, doi:10.1029/2007JB004933.

Dach, R., U. Hugentobler, P. Fridez, and M. Meindl (2007), Bernese GPS Software Version 5.0,

Astronomical Institute, University of Bern. Dawson, J., P. Sarti, G. Johnston, and L. Vittuari (2007), Indirect

approach to invariant point determination for SLR and VLBI systems: an assessment, J Geodesy, 81 (6-8), 433–441.

Demoulin, A. (2004), Reconciling geodetic and geological rates of vertical crustal motion in intraplate regions, Earth Planet Sc Lett, 221, 91–101.

Johnson, H. O., and D. C. Agnew (1995), Monument motion and measurements of crustal velo450

cities, Geophys Res Lett, 21, 2905–2908. Langbein, J. (2008), Noise in GPS displacement measurements from

Southern California and Southern Nevada, J Geophys Res, 113, B05,405,

doi:10.1029/2007JB005247. Langbein, J., and H. Johnson (1997), Correlated errors in geodetic time series: Implications for

time-dependent deformation, J Geophys Res, 102 (B1), 591–603. Lyard, F., F. Lefevre, T. Letellier, and O. Francis (2006), Modelling

the global ocean tides:modern insights from FES2004, Ocean Dynam, 56 (5), 394–415.

Mignard, F. (2005), FAMOUS, Frequency Analysis Mapping On Unusual Sampling, Tech. rep.,

Obs. de la Cote d’Azur Cassiop´ee, Nice, France. Moore, A. M., and R. E. Neilan (2005), The International GPS Service

Tracking Network: Enabling Diverse Studies And Projects Through International

Cooperation, J Geodyn, 40, 461 461–469. Prescott, W. H., M. Lisowski, and J. C. Savage (1981), Geodetic

measurement of crustal defor463 mation on the San Andreas, Hayward and Calaveras faults near San

Francisco, California, J Geophys Res, 86 (B11), 10,853–10,869. Press, W. H., and G. 465 B. Rybicki (1989), Fast algorithm for spectral

analysis of unevenly sampled 466 data, Astrophys J, 338. Ray, J., Z. Altamimi, X. Collilieux, and T. van Dam (2008),

Anomalous harmonics in the spectra of GPS position estimates, GPS Solut, 12.

RER, Servizio Geologico, Sismico e dei Suoli (2006), Cartografia geologica e dei suoli,

http://geo.regione.emilia-romagna.it/carg/viewer.htm. Romagnoli, C., S. Zerbini, L. Lago, B. Richter, D. Simon, F.

Domenichini, C. Elmi, and M. Ghi472 rotti (2003), Influence of soil consolidation and thermal expansion

effects on height and gravity variations, J Geodyn, 35, 521–539. Sarti, P., P. Sillard, and L. Vittuari (2004), Surveying co-located space

geodetic instruments for ITRF computation, J Geodesy, 78 (3), 210–222.

Sarti, P., C. Abbondanza, and L. Vittuari (2009), Gravity dependent signal path variation in

a large VLBI telescope modelled with a combination of surveying methods, J Geodesy, pp.

DOI:10.1007/s00,190–009–0331–4. Sillard, P., and C. Boucher (2001), A review of algebraic constraints in

terrestrial reference frame datum definition, J Geodesy, 75, 63–73. Tomasi, P. (1993), Noto station status report, in Proceedings of the

9th Working Meeting on European VLBI for Geodesy and Astrometry, edited by J. Campbell

and A. Nothnagel, 81, pp. 11–12, Mitteilungen aus den Geoda¨tischen Instituten der Rheinischen Friedrich-Wilhelms-

Universit¨at Bonn. Tomasi, P., F. Mantovani, R. Ambrosini, A. Bombonati, G. Grueff, A.

Nothnagel, and A. Schuh (1988), The First Geodetic VLBI experiment with the Bologna Radio

Telescope, Nuovo Ci487 mento C, 11 (2), 205–208. Williams, S. D. P., Y. Bock, 488 P. Fang, P. Jamason, R. M.

Nikolaidis, L. Prawirodirdjo, M. Miller, and D. J. Johnson (2004), Error analysis of continuous GPS position

time series, J Geophys Res, 109, B03,412, doi:10.1029/2003JB002471. Wyatt, F. (1982), Displacement of Surface Monuments: Horizontal

Motion, J Geophys Res, 87 (B2), 979–989. Wyatt, F. (1989), Displacement of Surface Monuments: Vertical

Motion, J Geophys Res, 94 (B2), 494 1655–1664. Zerbini, S., B. Richter, M. Negusini, C. Romagnoli, S. Dietrich, F.

Domenichini, and W. Schwahn (2001), Height and gravity variations by continuous GPS, gravity and

environmental parameter observations in the southern Po Plain, near Bologna, Italy, Earth

Planet Sc Lett, 192 (3), 267– 279, doi:10.1016/S0012-821X(01)00445-9. Zerbini, S., B. Richter, F. Rocca, T. van Dam, and F. Matonti (2007),

A combination of Space and Terrestrial Geodetic Techniques to Monitor Land Subsidence: Case Study, the Southeastern Po Plain, Italy, J Geophys Res, 112, B05,405, doi:10.1029/2006JB004338.

A THREE CORNER HAT-BASED ANALYSIS OF STATION POSITION TIME SERIES FOR THE ASSESSMENT OF INTER-TECHNIQUE PRECISION AT ITRF CO-LOCATED SITES

C Abbondanza(1), TM Chin(1), RS Gross(1) , MB Heflin(1), KJ Hurst(1), JW Parker(1), X Wu(1), Z Altamimi(2) (1) CalTech – Jet Propulsion Laboratory, US (2) IGN – Laboratoire de recherches en Géodésie, France

claudio.abbondanza@jpl.nasa.gov

3. DATA SETS used

• The entire set of SINEX files submitted by the IVS, IGS, ILRS and IDS for the computation of ITRF2008 has been analysed in this investigation (see Table 1):

(i) Weekly SINEX files of station positions for GPS, SLR, and DORIS (ii) Daily SINEX files of datum-free normal equations for VLBI

1. INTRODUCTION

• Three corner hat (TCH) has been applied to the station position time series of the 4 space-geodetic (SG) techniques (VLBI, GPS, SLR, DORIS) defining the International Terrestrial Reference Frame (ITRF)

• As an alternative to statistics defining the intrinsic precision (e.g. repeatability, standard deviation), TCH can be used in this context to infer the relative/inter-technique precision of station positions through the comparison of the performances of the 4 SG techniques

• If station position time series are acquired from at least 3 co-located SG techniques, the TCH can provide the relative precision of each station included in the co-located site.

• In this study, adopting the data set used for the definition of the current ITRF2008, (i) we assess via the TCH the relative precisions each ITRF co-located site with a sufficiently adequate observing history, (ii) we compare at each site relative vs intrinsic precision (i.e. repeatability of geodetic positioning, standard deviation derived from SINEX files)

2. THREE CORNER HAT

• xi identifies the measured value (i.e, the station position as determined by the i-th technique and expressed in a local geodetic reference frame), s indicates the geophysical signal, i identifies the space-geodetic technique, wi accounts for both the measurement and systematic errors affecting the i-th technique

• The noise processes wi are assumed to be statistically uncorrelated one to another and independent

• We assume that each co-located technique senses the same geophysical signal s

• This way, the pair-wise difference among the measurements eliminates the common signal s and uniquely reflects the differences between the measurement errors of the two techniques

• Under these assumptions, from the evaluation of the empirical variance of the difference process (xi-xj) we can compute the variance of the noise process wi associated with the i-th technique at the co-located site

• In order for the difference process (xi-xj) to be rigorously defined, station position time series of VLBI, GPS, SLR and DORIS have to be (i) expressed in the same reference frame and (ii) aligned in time

DORISGPSSLRVLBIitwtstx ii ,,,=)(+)(=)(

Technique Data Span Solution Constraints # SNX

VLBI 1980 – 2009 Normal Equations Datum Free 3658

GPS 1997 – 2009 Variance - covariance Minimal 653

SLR 1983 - 2009 Variance - covariance Loose 1041

DORIS 1993 - 2009 Variance – covariance Minimal 830

Table 1. Time span, kind of solution provided by IVS, IGS, ILRS and IDS, constraints applied to the solutions and total number of SINEX files considered for each technique.

• Table 1 shows the time span, the kind of solution provided by the 4 official technique services (IVS, IGS, ILRS and IDS) and the number of sinex files considered for each technique in the analysis

4. DATA ANALYSIS • Data Editing. SINEX files have been cleaned with the aim of

removing outliers. The cleaning relies on the stacking of SINEX files for each of the 4 techniques. Outliers w.r.t. a linear model (i.e. stacked reference frame) have been removed from the SINEX files.

• Transformation in ITRF2008. Translations and rotations between each single technique SINEX file and the official ITRF2008 have been estimated. All the SG solutions have been transformed into ITRF2008 applying the estimated rotations and translations. This way, the SG solutions have been consistently expressed w.r.t. the same reference frame and can be therefore inter-compared.

• Extraction of time series at co-located sites. Time series of station positions have been extracted at ITRF co-located sites. GPS, SLR and DORIS provide time series at a weekly resolution, whereas VLBI time series are daily. Time series at co-located sites have been de-trended, removing piecewise linear trends. The station position discontinuities identified for the ITRF2008 computation have been used for the piecewise linear regressions (see Fig 1).

• Temporal alignment. Simultaneous observations among the 4 techniques have been selected. Prior to the temporal alignment, daily VLBI time series have been aggregated into weekly time series and linearly interpolated in order to make them comparable with GPS, SLR and DORIS solutions.

• TCH application. Once de-trended and temporally aligned, the co-located time series can be differentiated. Difference processes have been formed (see Fig 2) and TCH-derived variances have been estimated (see Table 2).

Figure 1. Time Series of station positions for the SLR (8834), the GPS (WTZR) and the VLBI (7224) co-located at WETTZELL as obtained from the transformation in ITRF2008. Linear trend estimates and WRMS (about the linear trend ) are reported for each technique and component.

Figure 2. Time Series of the difference processes for the SLR (8834), the GPS (WTZR) and the VLBI (7224) co-located at WETTZELL. These differences, computed after the linear trend has been removed from the mono-technique time series (see Figure 1), are the input to the TCH algorithm

• 19 ITRF co-located sites with number of simultaneous observations > 30 in the time window 1997-2009 have been selected for the TCH analysis (see Table 2 for results).

• Output of the TCH are the variances of the station position time series for each technique computed on the (North, East, Height) components. Hartebeesthoek proved to be the only 4-way co-location with an adequately large number of simultaneous observations. In that case, the generalised TCH has been applied to infer the relative precision of the 4 SG techniques.

• Table 2 reports for each co-location (i) the obtained with the TCH, (ii) the WRMS (repeatability) computed on the same set of observations used for the TCH, (iii) the difference between WRMS and TCH-derived , (iv) the formal error extracted by the SINEX files transformed into ITRF2008, (v) the number of simultaneous observations among the co-located techniques. The WRMS is computed after the linear trend has been removed from each time series

• In principle, the higher the number of simultaneous observations, the more robust the TCH-derived sigmas (see sites marked in red in Table 2)

• When comparing columns T (TCH-derived sigmas) and (SNX-derived sigmas, i.e. formal errors) in Table 2, one can observe the formal errors are in general overly optimistic (<T): the ratio (T/)2 can thus provide a scaling factor to be applied to the covariance matrix of the SG solutions reported in the SNX files (e.g. the values of T/ for the height component of Hartebeesthoek are 5.3, 5.3, 2.6, 0.8 for VLBI, SLR, DORIS and GPS respectively)

• SG time series used in this study contain the seasonal signature due to non-tidal loading effects, which have not been removed during the SG data reduction. As a result, the WRMS (column W in Table 2) of the time series accounts for the seasonal variability and, in principle, it should be larger than the TCH-derived sigmas (column T in Table 2).

• The reduction (i.e. positive values of the difference W-T) due to the removal of seasonal signatures when computing the inter-technique difference processes is observable uniquely for the Height component of GPS (see rows G in the column W-T for Wettzell, Greenbelt, Concepcion, Arequipa in Table 2).

5. RESULTS and DISCUSSIONS

ABSTRACT REFERENCE NUMBER : 1490763 PAPER NUMBER : G53B-1142

Table 2. Results per components (North, East, Height) of the TCH analysis applied to the ITRF co-location sites. Tc ( technique) : V VLBI, G GPS, D DORIS, S SLR. T : TCH-derived in mm. W : repeatability in mm. : SINEX formal error in mm. W-T : difference between WRMS and TCH in mm. O : number of observations. Sites marked in red identify the co-locations with the largest number of simultaneous observations.

• GPS is characterised by the highest relative precisions (in the TCH sense) in all the three North, East and Height components, followed by VLBI, SLR and DORIS. GPS relative precisions are below the mm level in the horizontal components and attain values of a few mm in the Height component.

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