eesti teaduste
akadeemia kirjastus
SINCE 1952
Earth Science cover
Estonian Journal of Earth Sciences
ISSN 1736-7557 (Electronic)
ISSN 1736-4728 (Print)
Impact Factor (2021): 0.811
New 3D velocity model of Estonia from GNSS measurements; pp. 107–125
PDF | 10.3176/earth.2021.08

Tarmo Kall, Tõnis Oja, Kätlin Kruusla, Aive Liibusk

The aim of this study was to create a 3D crustal deformation model for Estonia, based on dense Global Navigation Satellite System (GNSS) data (geodetic points with velocities) and validate the existing models of horizontal and vertical crustal deformations with velocities from Estonian GNSS measurements. The observations performed for at least eight years at Estonian GNSS permanent stations and during the GNSS campaign measurements of 1997, 2008 and 2017 on the Estonian 1st-order geodetic reference network were used as input data. Coordinates of the geodetic points were calculated in the ITRF2008 reference frame using the Precise Point Positioning method. Horizontal and vertical velocities (in the North, East and Up directions) were calculated for a total of 22 GNSS points. Models for horizontal and vertical velocities were calculated using the remove–compute–restore method. The model of glacial isostatic adjustment (GIA) of the Nordic Geodetic Commission NKG2016GIA was used as a reference model. Residual velocities of GNSS points showed a good fit with respect to the reference model. The residual velocities were analysed by geostatistical methods and the prediction surfaces of the residual velocities were modelled. After adding the surface of the residual velocities back to the reference model NKG2016GIA, the modelled surface EST2020VEL was obtained. The obtained model was compared with the up-to-date intraplate deformation model NKG_RF17VEL. It was found that recent Fennoscandian intraplate deformation models NKG2016LU and NKG_RF17VEL fitted well with the Estonian GNSS data. However, both models are systematically shifted with respect to the Estonian GNSS data. For applications in Estonia, it is better to use the fitted model EST2020VEL. The uncertainty of the model is estimated to be lower than ±0.5 mm/a.


Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control19, 716–723.

Alothman, A. O., Fernandes, R. M., Bos, M. S., Schillak, S. & Elsaka, B. 2016. Angular velocity of Arabian plate from multi-year analysis of GNSS data. Arabian Journal of Geosciences9, 529.

Altamimi, Z., Collilieux, X. & Métivier, L. 2011. ITRF2008: an improved solution of the international terrestrial reference frame. Journal of Geodesy85, 457–473.

Altamimi, Z., Métivier, L. & Collilieux, X. 2012. ITRF2008 plate motion model. Journal of Geophysical Research: Solid Earth117, B07402.

Bertiger, W., Bar-Sever, Y., Dorsey, A., Haines, B., Harvey, N., Hemberger, D., Heflin, M., Lu, W., Miller, M., Moore, A. W., Murphy, D., Ries, P., Romans, L., Sibois, A., Sibthorpe, A., Szilagyi, B., Vallisneri, M. & Willis, P. 2020. GipsyX/RTGx, a new tool set for space geodetic operations and research. Advances in Space Research66, 469–489.

Bitharis, S., Ampatzidis, D. & Pikridas, C. 2017. An optimal geodetic dynamic reference frame realization for Greece: Methodology and application. Annals of Geophysics60(2), S0221.

Böhm, J., Werl, B. & Schuh, H. 2006. Troposphere mapping functions for GPS and VLBI from ECMWF operational analysis data. Journal of Geophysical Research: Solid Earth111, B02406.

Bos, M. S., Fernandes, R. M. S., Williams, S. D. P. & Bastos, L. 2013. Fast error analysis of continuous GNSS observations with missing data. Journal of Geodesy87, 351–360.

Carrere, L., Lyard, F., Cancet, M., Guillot, A. & Picot, N. 2016. FES 2014, a new tidal model – Validation results and perspectives for improvements. In Proceedings of the ESA Living Planet Symposium, pp. 9–13.

Dong, D., Fang, P., Bock, Y., Webb, F., Prawirodirdjo, L., Kedar, S. & Jamason, P. 2006. Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis. Journal of Geophysical Research: Solid Earth111, B03405.

Ellmann, A., Pihlak, P. & Kollo, K. 2008. Kõrgtäpsed GPS-mõõtmised riigi geodeetilise põhivõrgu aluspunktidel 2008. aasta suvel [GPS remeasurement campaign on national geodetic points in the summer of 2008]. Geodeet, 37(61), 7–12 [in Estonian].

Forsberg, R. & Tscherning, C. C. 2008. An Overview Manual for the GRAVSOFT Geodetic Gravity Field Modelling Programs. DTU-Space, 75 pp. 

Gandolfi, S., Tavasci, L. & Poluzzi, L. 2017. Study on GPS–PPP precision for short observation sessions. GPS Solutions21, 887–896.

Häkli, P., Lidberg, M., Jivall, L., Steffen, H., Kierulf, H., Ågren, J., Vestøl, O. & Lahtinen, S. 2019. New horizontal intraplate velocity model for Nordic and Baltic countries. In Geospatial Information for a Smarter Life and Environmental Resilience, pp. 1–19. FIG, Hanoi, Vietnam.

Hastie, T., Tibshirani, R. & Friedman, J. 2009. The Elements of Statistical Learning: Data Mining, Inference, and Pre­diction. Springer Science & Business Media, 763 pp.

He, X., Montillet, J.-P., Fernandes, R., Bos, M., Yu, K., Hua, X. & Jiang, W. 2017. Review of current GPS methodologies for producing accurate time series and their error sources. Journal of Geodynamics106, 12–29.

Holdahl, S. H. 1978. Models for extracting vertical crustal movements from leveling data. In Proceedings of the GEOP Conference “Applications of Geodesy to Geo­dynamics”. October 25, 1978, pp. 183–190. Ohio State University, Columbus, Ohio. 

Hulisz, P., Piernik, A., Mantilla-Contreras, J. & Elvisto, T. 2016. Main driving factors for seacoast vegetation in the Southern and Eastern Baltic. Wetlands36, 909–919.

Jackson, D. A. & Chen, Y. 2004. Robust principal component analysis and outlier detection with ecological data. Environmetrics: The Official Journal of the International Environmetrics Society15, 129–139.

Jevrejeva, S., Rüdja, A. & Mäkinen, J. 2002. Postglacial rebound in Fennoscandia: new results from Estonian tide gauges. In Gravity Geoid and Geodynamics 2000 (Sideris, M. G., ed.), pp. 193–198. Springer-Verlag, Berlin.

Johnston, G., Riddell, A. & Hausler, G. 2017. The International GNSS Service. In Springer Handbook of Global Navigation Satellite SystemsSpringer Handbooks (Teunissen, P. J. G. & Montenbruck, O., eds), pp. 967–982. Springer International Publishing, Cham.

Kall, T., Oja, T. & Tänavsuu, K. 2014. Postglacial land uplift in Estonia based on four precise levelings. Tectonophysics610, 25–38.

Kall, T., Oja, T., Kollo, K. & Liibusk, A. 2019. The noise properties and velocities from a time-series of Estonian permanent GNSS stations. Geosciences9(5), 1–23.

Kasper, J. F., Jr. 1971. A second‐order Markov gravity anomaly model. Journal of Geophysical Research76, 7844–7849.

Kierulf, H. P. 2017. Analysis strategies for combining con­tinuous and episodic GNSS for studies of neo-tectonics in Northern-Norway. Journal of Geodynamics109, 32–40.

Kierulf, H. P., Steffen, H., Simpson, M. J. R., Lidberg, M., Wu, P. & Wang, H. 2014. A GPS velocity field for Fennoscandia and a consistent comparison to glacial isostatic adjustment models. Journal of Geophysical Research B: Solid Earth119, 6613–6629.

Kierulf, H. P., Valsson, G., Evers, K., Lidberg, M., Häkli, P., Prizginiene, D., Hjelle, G. A., Vestøl, O., Håkansson, M. & Knudsen, P. 2019. Towards a dynamic reference frame in Iceland. Geophysica54, 3–17.

Kollo, K., Metsar, J. & Ellmann, A. 2017. Riigi geodeetilise võrgu I klassi kordusmõõtmised 2017 [Remeasurement campaign in 2017 on 1st-order points of the national geodetic network]. Geodeet, 47(71), 19–23 [in Estonian].

Kruusla, K. 2019. Maakoore liikumised riikliku geodeetilise võrgu GNSS kordusmõõtmistest [Movements of the Earth’s Crust in Estonia Based on GNSS Measurement Campaigns of the National Geodetic Reference Network]. Master’s Thesis, Eesti Maaülikool, Tartu, 110 pp.

Lahtinen, S., Jivall, L., Häkli, P., Kall, T., Kollo, K., Kosenko, K., Galinauskas, K., Prizginiene, D., Tangen, O. & Weber, M. 2019. Densification of the ITRF2014 position and velocity solution in the Nordic and Baltic countries. GPS Solutions23, 95.

Li, Y., Chen, C., Fang, R. & Yi, L. 2019. Accuracy enhancement of high-rate GNSS positions using a complete ensemble empirical mode decomposition-based multiscale multiway PCA. Journal of Asian Earth Sciences169, 67–78.

Lidberg, M., Johansson, J. M., Scherneck, H.-G. & Davis, J. L. 2007. An improved and extended GPS-derived 3D velocity field of the glacial isostatic adjustment (GIA) in Fennoscandia. Journal of Geodesy81, 213–230.

Metsar, J., Kollo, K. & Ellmann, A. 2018. Modernization of the Estonian national GNSS reference station network. Geodesy and Cartography44, 55–62.

Metsar, J., Kollo, K., Ellmann, A., Rüdja, A. & Pihlak, P. 2019. Multi-epoch GNSS campaigns of the national geodetic network in Estonia. Geophysica54, 51–60.

Minasny, B., McBratney, A. B. & Whelan, B. M. 2005. VESPER User Manual. Version 1.6. Australian Centre for Precision Agriculture, 25 pp.

Montillet, J.-P. & Bos, M. S. (eds). 2019. Geodetic Time Series Analysis in Earth Sciences. Springer, 443 pp.

Moritz, H. 1980. Advanced Physical Geodesy. Wichmann, Karlsruhe; Abacus Press, Tunbridge, Wells, Kent, 500 pp. 

Petit, G. & Luzum, B. (eds). 2010. IERS Conventions (2010). IERS Technical Note, 36, Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie, 179 pp.

Poutanen, M. & Häkli, P. 2018. Future of National Reference Frames – from static to kinematic? Geodesy and Cartography67, 119–129.

Rebischung, P., Griffiths, J., Ray, J., Schmid, R., Collilieux, X. & Garayt, B. 2012. IGS08: the IGS realization of ITRF2008. GPS Solutions16, 483–494.

Rosentau, A., Muru, M., Gauk, M., Oja, T., Liibusk, A., Kall, T., Karro, E., Roose, A., Sepp, M. & Tammepuu, A. 2017. Sea-level change and flood risks at Estonian coastal zone. In Coastline Changes of the Baltic Sea from South to East (Harff, J., Furmanczyk, K. & Von Storch, H., eds), pp. 363–388. Springer.

Rüdja, A. 1999. A new ETRS89 system for Estonia. In Report on the Symposium of the IAG Subcommission for the European Reference Frame (EUREF) Held in Prague 25 June 1999. EUREF Publication No. 8, München. 

Rüdja, A. 2004. Geodetic Datums, Reference Systems and Geodetic Networks in Estonia. Doctoral dissertation, University of Helsinki, Helsinki, 331 pp.

Sjöberg, L. E. 2005. A discussion on the approximations made in the practical implementation of the remove–compute–restore technique in regional geoid modelling. Journal of Geodesy78, 645–653.

Suursaar, Ü. & Kall, T. 2018. Decomposition of relative sea level variations at tide gauges using results from four Estonian precise levelings and uplift models. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing11, 1966–1974.

Tarayoun, A., Mazzotti, S., Craymer, M. & Henton, J. 2018. Structural inheritance control on intraplate present-day deformation: GPS strain rate variations in the Saint Lawrence Valley, Eastern Canada. Journal of Geophysical Research: Solid Earth123, 7004–7020.

Teferle, F. N., Williams, S. D. P., Kierulf, H. P., Bingley, R. M. & Plag, H.-P. 2008. A continuous GPS coordinate time series analysis strategy for high-accuracy vertical land movements. Physics and Chemistry of the Earth, Parts A/B/C33, 205–216.

Vallner, L., Sildvee, H. & Torim, A. 1988. Recent crustal move­ments in Estonia. Journal of Geodynamics9, 215–223.

Vestøl, O., Ågren, J., Steffen, H., Kierulf, H. & Tarasov, L. 2019. NKG2016LU: a new land uplift model for Fennoscandia and the Baltic Region. Journal of Geodesy93, 1759–1779.

Vilumaa, K., Ratas, U., Tõnisson, H., Kont, A. & Pajula, R. 2017. Multidisciplinary approach to studying the formation and development of beach-ridge systems on non-tidal uplifting coasts in Estonia. Boreal Environment Research22, 67–81.

Wdowinski, S., Bock, Y., Zhang, J., Fang, P. & Genrich, J. 1997. Southern California permanent GPS geodetic array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake. Journal of Geophysical Research: Solid Earth102, 18057–18070.

Whelan, B. M., McBratney, A. B. & Minasny, B. 2002. Vesper 1.5 – spatial prediction software for precision agriculture. In Precision Agriculture, Proceedings of the 6th Inter­national Conference on Precision Agriculture (Robert, P. C., Rust, R. H. & Larson, W. E., eds), pp. 1–14. ASA/CSSA/SSSA, Madison, WI, USA. 

Wu, D., Yan, H. & Shen, Y. 2017. TSAnalyzer, a GNSS time series analysis software. GPS Solutions21, 1389–1394.

Zhelnin, G. 1966. On the recent movements of the Earth’s surface in the Estonian SSR. Annales Academiae Scientiarum Fennicae90, 489–493.

Zumberge, J. F., Heflin, M. B., Jefferson, D. C., Watkins, M. M. & Webb, F. H. 1997. Precise point positioning for the efficient and robust analysis of GPS data from large networks. Journal of Geophysical Research: Solid Earth102, 5005–5017.

Back to Issue