eesti teaduste
akadeemia kirjastus
SINCE 1952
Earth Science cover
Estonian Journal of Earth Sciences
ISSN 1736-7557 (Electronic)
ISSN 1736-4728 (Print)
Impact Factor (2022): 1.1
Vertical crustal movements in Estonia determined from precise levellings and observations of the level of Lake Peipsi; pp. 27–47
PDF | doi: 10.3176/earth.2016.03

Tarmo Kall, Aive Liibusk, Junkun Wan, Rivo Raamat

The aim of this study was to evaluate vertical velocities of the benchmarks and their change over time based on the four precise levellings of the Estonian levelling network from 1933 to 2011, with the mean epochs being 1936.7, 1961.2, 1982.1 and 2006.9. The vertical velocities of the benchmarks were estimated using two mathematical models. Both models gave similar results for almost all levelling combinations. Significant discrepancies between the velocities from two models were found only in two combinations where levelling loops’ closing time was long compared to the time between the mean epochs of levellings. From the analysis of post-adjustment variances of unit weight and the ANOVA test, a significant change in the benchmark velocities between mean epochs of the levellings was detected. However, due to correlation between the second and third levellings it remained unresolved whether the velocity change was a real change or fortuitous when relying only on this correlation. The detected velocity change could also be explained by the levelling error. Iterated variance component estimation assigned most of the error to the first levelling. In addition, level records of Lake Peipsi from 1921 to 2006 were used for the first time to calculate lake tilt between water gauges. Velocities of the benchmarks from the combination of the last three levellings and water gauges of Lake Peipsi were used to compile the map of the vertical crustal movements (EST2015LU). The main feature of the compiled map was the SE–NW directional postglacial land uplift. However, compared to earlier maps for the region, our isolines declined more in the W–E direction, due to the larger influence of the fourth levelling and velocities from lake tilts. Overall fit of the compiled map with the velocities of continuously operating Global Navigation Satellite System reference stations and coastal tide gauges was ± 0.4 to ± 0.5 mm yr–1.


Amiri-Simkooei, A. 2007. Least-squares Variance Component Estimation: Theory and GPS Applications [PhD thesis]. Delft University of Technology, Publication on Geodesy, 64, Netherlands Geodetic Commission, Delft, 208 pp.

Baarda, W. 1968. A Testing Procedure for Use in Geodetic Networks. Netherlands Geodetic Commission, Delft, 97 pp.

Bähr, H., Altamimi, Z. & Heck, B. 2007. Variance Component Estimation for Combination of Terrestrial Reference Frames. Universität Karlsruhe (TH), Karlsruhe, 69 pp.

Bikis, J. 1940. Zemes garozas kustības ietekme precīzās līmetņošanas darbos Baltijas jūras piekrastē [Influence of the Earth’s Crust Movements on the Levelling Work Precision on the Coast of the Baltic Sea]. Riga, Latvijas Universitātes raksti, ser. II, No. 6, 201 pp. [in Latvian].

Brown, L. D. & Oliver, J. E. 1976. Vertical crustal movements from leveling data and their relation to geologic structure in the eastern United States. Reviews of Geophysics, 14, 13–35.

Bruxer, J. & Southam, C. 2008. Review of Apparent Vertical Movement Rates in the Great Lakes Region. Burlington, Report prepared for the International Upper Great Lakes Study, HY-1D, 88 pp.

Carrera, G. H. & Vaníček, P. 1986. Review of techniques for determining vertical ground movements from levelling data. In Proceedings of Third International Symposium on Land Subsidence, pp. 195–202. IAHS Publication, Venice.

Carrera, G. H., Vaníček, P. & Craymer, M. R. 1991. The Compilation of a Map of Recent Vertical Crustal Movements in Canada. Department of Surveying Engineering, University of New Brunswick, Fredericton, N.B., Technical Report, 153, 107 pp.

Caspary, W. 2000. Concepts of Network and Deformation Analysis (Rüeger, J. M., ed.). University of New South Wales, Sydney, Australia, 187 pp.

Cross, P. A., Hannah, J., Hradilek, L., Kelm, R., Mäkinen, J., Merry, C. L., Sjöberg, L. E., Steeves, R. R., Vaníček, P., & Zilkoski, D. B. 1987. Four-dimensional geodetic positioning. Manuscripta Geodaetica, 12, 147–222.

Davis, J. L., Mitrovica, J. X., Scherneck, H.-G. & Fan, H. 1999. Investigations of Fennoscandian glacial isostatic adjustment using modern sea level records. Journal of Geophysical Research: Solid Earth, 104(B2), 2733–2747.

Ekman, M. & Mäkinen, J. 1996. Recent postglacial rebound, gravity change and mantle flow in Fennoscandia. Geophysical Journal International, 126, 229–234.

Ellenberg, J. 1987. The geological treatment of relevellings. Journal of Geodynamics, 8, 235–243.

Förstner, W. 1979. Ein Verfahren zur Schätzung von Varianz-und Kovarianzkomponenten. Allgemeine Vermessung Nachrichten, 86(11–12), 446–453.

Ghilani, C. D. & Wolf, P. R. 2006. Adjustment Computations: Spatial Data Analysis. John Wiley & Sons, Hoboken, N.J., 611 pp.

Giménez, J., Suriñach, E. & Goula, X. 2000. Quantification of vertical movements in the eastern Betics (Spain) by comparing levelling data. Tectonophysics, 317, 237–258.

Hang, T. & Kohv, M. 2013. Glacial varves at Pärnu, south-western Estonia: a local varve chronology and proglacial sedimentary environment. GFF, 135, 273–281.

Hein, G. W. 1986. A Model Comparison in Vertical Crustal Motion Estimation Using Leveling Data. National Oceanic and Atmospheric Administration, National Ocean Service, Charting and Geodetic Services, Rockville, Md., 46 pp.

Helmert, F. R. 1872. Die Ausgleichungsrechnung nach der Methode der kleinsten Quadrate: mit Anwendungen auf die Geodäsie und die Theorie der Messinstrumente. B. G. Teubner, 370 pp.

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 2–5, 1978, pp. 183–190. Ohio State University, Columbus, Ohio.

Jaani, A. 1973. Veerohkus muutub tsükliliselt [Cyclic changes in the abundance of water]. Eesti Loodus, 24, 758–764 [in Estonian].

Jevrejeva, S., Rudja, A. & Makinen, 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, Berlin.

Kääriäinen, E. 1953. On the Recent Uplift of the Earth’s Crust in Finland. Finnish Geodetic Institute, Helsinki, Suomen geodeettisen laitoksen julkaisuja, 42, 106 pp.

Kääriäinen, E. 1963. Land uplift in Finland computed by the aid of precise levellings. Fennia, 89, 15–18.

Kakkuri, J. & Vermeer, M. 1985. The Study of Land Uplift Using the Third Precise Levelling of Finland. Finnish Geodetic Institute, Helsinki, Reports of the Finnish Geodetic Institute, 85:1, 11 pp.

Kall, T. & Jürgenson, H. 2008. Postglacial land uplift in Estonia based on geodetic measurements on Põltsamaa-Lelle levelling line. In The 7th International Conference “Environmental Engineering”, May 22–23, 2008, Selected Papers (Cygas, D. & Froehner, K. D., eds), pp. 1325–1333. Vilnius Gediminas Technical University Press, Technika, Vilnius.

Kall, T. & Oja, T. 2006. Geodetic and geophysical repeated measurements in geodynamic monitoring networks of Estonia. In Geodetic Deformation Monitoring: From Geophysical to Engineering Roles, International Association of Geodesy Symposia (Sanso, F. & Gil, A. J., eds), pp. 222–230. Springer-Verlag Berlin, Jaen, Spain.

Kall, T. & Torim, A. 2003. Vertical movements on the territory of Tallinn. Journal of Geodynamics, 35, 511–519.

Kall, T., Oja, T. & Tänavsuu, K. 2014. Postglacial land uplift in Estonia based on four precise levelings. Tectono­physics, 610, 25–38.

Kalm, V. 2007. The urban geology of Tartu, Estonia. In Applied Quaternary Research in the Central Part of Glaciated Terrain. Proceedings of the INQUA Peribaltic Group Field Symposium 2006, Oulanka Biological Research Station, Finland, September 11.–15. (Johansson, P. & Sarala, P., eds), Geological Survey of Finland, Special Paper, 46, 141–145.

Koch, K. 1978. Schätzung von varianzkomponenten. Allgemeine Vermessungs Nachrichten, 85, 264–269.

Koch, K.-R. 2010. Parameter Estimation and Hypothesis Testing in Linear Models. Springer, Berlin, Heidelberg, 334 pp.

Kohv, M. 2011. Landslides in Clayey Soils of Western Estonia [Doctoral dissertation]. University of Tartu, Tartu, 116 pp.

Kohv, M. & Hang, T. 2013. Pore pressure fluctuations within quasi-stable slopes in south-western Estonia and their influence on slope stability. In Landslide Science and Practice (Margottini, C., Canuti, P. & Sassa, K., eds), pp. 79–85. Springer, Berlin, Heidelberg.

Krarup, T., Juhl, J. & Kubik, K. 1980. Gotterdammerung over least squares adjustment. In International Archives of Photogrammetry (Ackermann, F., Bauer, H., Konecny, G. & Kupfer, G., eds), pp. 369–378. Committee of the XIV International Congress for Photogrammetry and Remote Sensing, Hamburg.

Kuo, C. Y., Shum, C. K., Braun, A. & Mitrovica, J. X. 2004. Vertical crustal motion determined by satellite altimetry and tide gauge data in Fennoscandia. Geophysical Research Letters, 31, L01608 1–4.

Kuo, C.-Y., Shum, C. K., Braun, A., Cheng, K.-C. & Yi, Y. 2008. Vertical motion determined using satellite altimetry and tide gauges. Terrestrial, Atmospheric and Oceanic Sciences, 19, 21–35.

Listra, E. & Talviste, P. 1988. Geotehniline kontroll nõrkade savipinnaste levialal. I köide. Pinnaseomadused ja vajumis­vaatluste analüüs Pärnus [Geotechnical Control in the Areas of Weak Surfaces of Clay and Till. Vol. 1. Subsidence Observations in Pärnu]. National Institute of Building Research, Tallinn, Report from the database of Estonian geological engineering, Thematical research, 24781, 219 pp. [in Estonian].

Lucas, J. R. 1985. A Variance Component Estimation Method for Sparse Matrix Applications. Rockville, MD, NOAA Technical Report; NOS 111 NGS 33, 12 pp.

Lutsar, R. 1965. Smeshchenie reperov nivelirnoj seti goroda Tallina [Displacements of the Bench Marks of the Levelling System Network of the City of Tallinn]. In Sovremennye dvizheniya zemnoj kory, N 2 [Recent Crustal Movements, No. 2] (Parfjonova-Riives, L. J., ed.), pp. 288–293. Academy of Sciences of the Estonian SSR, Tartu [in Russian, with English summary].

Lutsar, R., Saapar, L. & Arbeiter, R. 1973. Izuchenie dvizhenij zemnoj poverkhnosti v gorodakh Éstonskoj SSR [Investigation of the crustal movements within the precinct of towns of the Estonian SSR]. In Sovremennye dvizheniya zemnoj kory, N 5 [Recent Crustal Movements, No. 5], pp. 139–143. Estonian Academy of Sciences, Tartu [in Russian, with English summary].

Mainville, A. & Craymer, M. R. 2005. Present-day tilting of the Great Lakes region based on water level gauges. Geological Society of America Bulletin, 117, 1070–1080.

Mäkinen, J. 2002. A bound for the Euclidean norm of the difference between the best linear unbiased estimator and a linear unbiased estimator. Journal of Geodesy, 76, 317–322.

Mäkinen, J. & Saaranen, V. 1998. Determination of post-glacial land uplift from the three precise levellings in Finland. Journal of Geodesy, 72, 516–529.

Mets, M., Torn, H. & Saapar, L. 2000. Perspectives and problems of geotechnical monitoring in Estonia. In Proceedings of the Ninth Baltic Geotechnical Conference “Baltic Geotechnics IX 2000” (Mets, M., ed.), pp. 226–233. Estonian Geotechnical Society, Tallinn.

Miller, M. 2013. Maapinna vertikaalliikumise iseloom Pärnu linnas perioodil 1987–2010 põhjavee survetaseme muu­tuste taustal [Ground Surface Vertical Movements on the Territory of Pärnu in 1987–2010]. Master’s thesis. Tartu Ülikool, Tartu, 41 pp. [in Estonian, with English summary].

Oja, T., Kollo, K. & Pihlak, P. 2014. GIAst ja maapinna liikumistest Eestis GNSS täppismõõtmiste valguses [About GIA and Earth’s surface movements in Estonia in the light of precise GNSS measurements]. Geodeet, 44, 55–65 [in Estonian].

Pastarus, J.-R. & Sabanov, S. 2005. A method for securing working mining block stability in Estonian oil shale mines. Proceedings of the Estonian Academy of Sciences. Engineering, 11, 59–68.

Pobedonostsev, S. 1975. Analiz vertikal¢nykh dvizhenij poberezh¢ya Pribaltiki [Analysis of vertical crustal move­ments on the coast of the Baltic Sea]. In Sovremennye dvizheniya territorii Pribaltiki [Recent Crustal Movements on the Territory of Baltic States] (Riives, L., ed.), pp. 28–36. Academy of Sciences of the Estonian SSR, Tartu [in Russian, with English summary].

Pobul, E. & Sildvee, H. 1975. O blokovom stroenii kristallicheskogo fundamenta Éstonii [About the block structure of crystalline basement in Estonia]. In Sovremennye dvizheniya territorii Pribaltiki [Recent Crustal Movements on the Territory of Baltic States] (Riives, L., ed.), pp. 64–73. Academy of Sciences of the Estonian SSR, Tartu [in Russian, with English summary].

Raamat, R. 2009. Maakoore vertikaalliikumised Peipsi järve veevaatlusandmete põhjal [Land Uplift on Lake Peipsi Using Water Level Observation Data]. Master’s thesis in Geodesy, Eesti Maaülikool, Tartu, 85 pp. [in Estonian, with English summary].

Randjärv, J. 1968. Kharakter i skorosti sovremennykh dvizhenij zemnoj kory v Pribaltike [The character and velocities of recent crustal movements in Baltic Regions]. In Sovremennye dvizheniya zemnoj kory, N 3 [Recent Crustal Movements of the Earth, No. 3] (Gerasimov, I., ed.], pp. 200–210. USSR Academy of Sciences, Moscow [in Russian, with English summary].

Randjärv, J. 1993. Vertical Movements of the Earth’s Crust in the Baltic Region. Finnish Geodetic Institute, Helsinki, Reports of the Finnish Geodetic Institute, 93:2, 33 pp.

Rao, C. 1971. Estimation of variance and covariance components – MINQUE theory. Journal of Multivariate Analysis, 1, 257–275.

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

Santamaría-Gómez, A., Gravelle, M. & Wöppelmann, G. 2014. Long-term vertical land motion from double-differenced tide gauge and satellite altimetry data. Journal of Geodesy, 88, 207–222.

Sildvee, H. 1973. O svyazi mezhdu razlomov i sovremennymi differentsirovannymi dvizheniyami zemnoj kory na territorii Éstonii [About the connection between the tectonic faults and recent differential vertical movements of the Earth’s crust in Estonia]. In Sovremennye dvizheniya zemnoj kory na geodinamicheskikh poligonakh [Recent Crustal Movements on the Geodynamic Polygons] (Feofilova, V. G., ed.), pp. 173–177. K. I. Satapaev Institute of Geology of the Academy of Sciences of the Kazakhstan SSR, Alma-Ata [in Russian].

Sildvee, H. & Miidel, A. 1978. Nekotorye rezul¢taty inter­pretatsii sovremennykh dvizhenij zemnoj kory v Éstonii [Some results of the interpretation of recent crustal movements in Estonia]. In Sovremennye dvizheniya zemnoj kory (issledovaniya na geodinamicheskikh poligonakh) [Recent Vertical Crustal Movements (Studies on Geodynamic Polygons)] (Fotiadi, E., ed.), pp. 138–143. Nauka, Novosibirsk [in Russian].

Sildvee, H. & Miidel, A. 1980. Opyt primeneniya geologo-geofizicheskikh metodov dlya interpretatsii sovremennykh dvizhenij zemnoj poverkhnosti na territorii Éstonii [An experience of the application of geological-geophysical methods to interpretation of recent crustal movements on the Estonian territory]. In Sovremennye dvizheniya zemnoj kory. Teoriya, metody, prognoz [Recent Crustal Movements. Theory, Methods, Prognosis] (Bulanže, Y., Linnenberg, D. & Podstrigach, Y., eds), pp. 110–114. Nauka, Moscow [in Russian].

Talviste, P., Hang, T. & Kohv, M. 2012. Glacial varves at the distal slope of Pandivere–Neva ice-recessional formations in western Estonia. Bulletin of the Geological Society of Finland, 84(Special Issue 1), 7–19.

Tamisiea, M. E., Mitrovica, J. X., Tromp, J. & Milne, G. A. 2002. Present-day secular variations in the low-degree harmonics of the geopotential: sensitivity analysis on spherically symmetric earth models. Journal of Geo­physical Research B: Solid Earth, 107, ETG 18-1–18-10.

Tavast, E. 2009. Changing factors of the coasts of Lake Peipsi, North-Eastern Europe. Quaternary International, 207, 130–136.

Tavast, E. & Raukas, A. 1982. Rel¢ef korennykh porod Éstonii [The Bedrock Relief of Estonia]. Valgus, Tallinn, 192 pp. [in Russian].

Toomik, A. & Liblik, V. 1998. Oil shale mining and processing impact on landscapes in north-east Estonia. Landscape and Urban Planning, 41, 285–292.

Torim, A. 2004. Maakoore tõusust ja rannajoone muutusest Eestis [About the land uplift and variation of the coastline in Estonia]. Geodeet, 28, 57–62 [in Estonian].

Vallner, L. 1978. Izuchenie blokovogo kharaktera sovremennykh dvizhenij territorii Éstonii geodezicheskim metodom [The Study of the Block Structure of Recent Crustal Movements of the Estonian Territory by the Geodetic Method]. PhD dissertation, Shmidt Institute of Physics of the Earth, Moscow [in Russian].

Vallner, L. & Zhelnin, G. 1975. Novaya karta izobaz territorii ÉSSR [New map of isobases on the territory of the Estonian S.S.R.]. In Sovremennye dvizheniya territorii Pribaltiki [Recent Crustal Movements on the Territory of Baltic States] (Riives, L., ed.), pp. 48–57. Academy of Sciences of Estonian S.S.R., Tartu [in Russian, with English summary].

Vallner, L., Sildvee, H. & Torim, A. 1988. Recent crustal movements in Estonia. Journal of Geodynamics, 9, 215–223.

Vaníček, P. 1976. Pattern of recent vertical crustal movements in Maritime Canada. Canadian Journal of Earth Sciences, 13, 661–667.

Vaníček, P., Castle, R. O. & Balazs, E. I. 1980. Geodetic leveling and its applications. Reviews of Geophysics, 18, 505–524.

Vestøl, O. 2006. Determination of postglacial land uplift in Fennoscandia from leveling, tide-gauges and continuous GPS stations using least squares collocation. Journal of Geodesy, 80, 248–258.

Vilde, S. 2013. Eesti kõrgusvõrgu reeperite stabiilsuse hindamine graafilisel meetodil [Evaluation of Stability of Benchmarks in the Estonian Vertical Network]. Master’s thesis in Geodesy, Eesti Maaülikool, Tartu, 92 pp. [in Estonian, with English summary].

Welsch, W. 1978. A posteriori Varianzschätzung nach Helmert. Allgemeine Vermessungs Nachrichten, 85, 55–63.

Welsch, W. 1984. Grundlagen, Gebrauchsformeln und Anwendungs­beispiele der Schätzung von Varianz- und Kovarianzkomponenten. Vermessung, Photogrammetrie und Kulturtechnik, 82, 296–301.

Witting, R. 1922. Le soulèvement récent de la Fennoscandie. Geografiska Annaler, 4, 458–487.

Yakubovski, O. 1973. Utochnennaya karta vertikal¢nykh dvizhenij zemnoj kory poberezh¢ya Baltijskogo morya [Renewed map of vertical movements of the Earth’s crust on the coasts of the Baltic Sea]. In Sovremennye dvizheniya zemnoj kory, N 5 [Recent Crustal Movements, No. 5], pp. 72–78. Academy of Sciences of the Estonian SSR, Tallinn [in Russian, with English summary].

Zhelnin, G. 1958. Maakoore kerkimine Eestis [Uplift of the Earth’s crust in Estonia]. Eesti Loodus, 5, 269–274 [in Estonian].

Zhelnin, G. 1960. Izuchenie vertikal¢nykh dvizhenij zemnoj kory v ÉSSR metodom povtornykh nivelirovok [Investigations of vertical displacements of the Earth’s crust on the territory of the Estonian S.S.R. by the Method of Repeated Levellings]. In Materialy soveshchaniya po voprosam neotektonicheskikh dvizhenij v Pribaltike [Proceedings of the Conference About the Neotectonic Movements in the Baltic Region] (Orviku, K., ed.), pp. 76–87. Academy of Sciences of the Estonian S.S.R., Tartu [in Russian, with English summary].

Zhelnin, G. 1964. Tochnost¢ i vozmozhnosti metoda povtornogo nivelirovaniya [The accuracy of and prospects for the method of repeated levellings]. In Sovremennye i novejshie dvizheniya zemnoj kory v Pribaltike [Recent and Latest Crustal Movements in the Baltic Region] (Gudelis, V., ed.), pp. 17–24. Department of Geography, Academy of Sciences of the Lithuanian SSR, Vilnius [in Russian, with English summary].

Zhelnin, G. 1966. On the recent movements of the Earth’s surface in the Estonian SSR. Annales Academiae Scientiarum Fennicae. Series A III Geologica-Geographica, 90, 489–493.



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