Soft clustering of GPS velocities from a homogeneous permanent network in Turkey

  • Soner ÖzdemirEmail author
  • Mahmut Onur Karslıoğlu
Original Article


Global positioning system (GPS) velocities have long and widely been used on various scales in revealing the deformations of the continental lithosphere. We present a homogeneous geodetic velocity field with high precision derived from ~ 10-year-long permanent GPS observations throughout Turkey. Without any apriori information or assumption, the cluster analysis might be applied upon the velocity fields for inspection, before going further in the analyses used prevalently in tectonic studies. We first “hard clustered” the velocities using k-means, hierarchical agglomerative clustering and Gaussian mixture models and examined how the cluster assignments change by tuning the algorithm-specific parameters. The Eurasian and the Arabian blocks which are separated from the Anatolian block with the strike-slip North and East Anatolian faults have been detected immediately. The Anatolian block itself has been divided into three blocks where the cluster assignments of the velocities at the transition zones might differ according to the chosen hard clustering algorithm. We then applied soft clustering using an appropriate Gaussian mixture model fit and created a probability map exhibiting the credibility of the cluster assignments. The detection capability of the cluster analysis has been demonstrated by comparison to various previously published block models of western Turkey. Cluster analysis detected the most pronounced blocks in western Turkey successfully, especially when the initially chosen number of clusters is not too large. The probability map of soft clustering can be used to modify the block boundaries together with the external validation.


Soft clustering Hard clustering Gaussian mixture model Velocity field 



This study would not have been possible without the continuous data of CORS-TR stations operated by the General Directorate of Mapping and the General Directorate of Land Registry and Cadastre, Turkey. We thank the editors and the two anonymous reviewers for their thorough and constructive reviews that helped to improve the manuscript.


  1. Aktug B et al (2009) Deformation of western Turkey from a combination of permanent and campaign GPS data: limits to block-like behavior. J Geophys Res Solid Earth 114(10):1–22. Google Scholar
  2. Aktug B, Parmaksiz E, Kurt M, Lenk O, Kilicoglu A, Gurdal MA, Ozdemir S (2013) Deformation of central anatolia: GPS implications. J Geodyn 67:78–96. CrossRefGoogle Scholar
  3. Aktug B et al (2016) Slip rates and seismic potential on the East Anatolian Fault System using an improved GPS velocity field. J Geodyn 94–95:1–12. CrossRefGoogle Scholar
  4. Altamimi Z, Collilieux X, Métivier L (2011) ITRF2008: an improved solution of the international terrestrial reference frame. J Geodesy 85(8):457–473. CrossRefGoogle Scholar
  5. Altamimi Z, Métivier L, Collilieux X (2012) ITRF2008 plate motion model. J Geophys Res Solid Earth 117(7):1–14. Google Scholar
  6. Arthur D, Vassilvitskii S (2007) K-means ++: the advantages of careful seeding. In: Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms, vol 8, pp 1027–1025.
  7. Ayhan M E, et al (2002) Turkish National Fundamental GPS Network—1999A (TUTGA-99A). Mapping Journal Special Issue 16, General Directorate of Mapping, Ankara. (in Turkish) Google Scholar
  8. Blewitt G, Lavallée D (2002) Effect of annual signals on geodetic velocity. J Geophys Res 107(B7):2145. CrossRefGoogle Scholar
  9. Boehm J, Werl B, Schuh H (2006) Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data. J Geophys Res Solid Earth 111(2):1–9. Google Scholar
  10. Calinski T, Harabasz J (1974) A dendrite method for cluster analysis. Commun Stat 3(1):1–27Google Scholar
  11. Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Anal Mach Intell PAMI-1(2):224–227CrossRefGoogle Scholar
  12. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B Methodol 39(1):1–38. Google Scholar
  13. Dong D, Herring TA, King RW (1998) Estimating regional deformation from a combination of space and terrestrial geodetic data. J Geodesy 72(4):200–214. CrossRefGoogle Scholar
  14. Driver HE, Kroeber AL (1932) Quantitative expression of cultural relationships, vol 31. University of California Publications in American Archaeology and Ethnology, Berkeley, pp 211–256Google Scholar
  15. Emre O, Duman T Y, Ozalp S, Elmaci H, Olgun S, Saroglu F (2013) Active fault map of Turkey with and explanatory text. General Directorate of Mineral Research and Exploration, Special Publication Series-30. AnkaraGoogle Scholar
  16. Ergintav S, Burgmann R, McClusky S, Çakmak R, Reilinger RE, Lenk O, Barka A, Ozener H (2002) Postseismic deformation near the İzmit earthquake (17 August 1999, M 7.5) rupture zone. Bull Seismol Soc Am 92(1):194–207. CrossRefGoogle Scholar
  17. Flerit F, Armijo R, King GCP, Meyer B, Barka A (2003) Slip partitioning in the Sea of Marmara pull-apart determined from GPS velocity vectors. Geophys J Int 154(1):1–7. CrossRefGoogle Scholar
  18. Gerard P, Luzum B (2010) IERS conventions (2010). Bureau International Des Poids Et Mesures Sevres (France), 1–179. Retrieved from Accessed 1 Oct 2018
  19. Goudarzi MA, Cocard M, Santerre R (2014) EPC: matlab software to estimate Euler pole parameters. GPS Solut 18(1):153–162. CrossRefGoogle Scholar
  20. Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning, 2nd edn. Springer, New York, pp 520–528CrossRefGoogle Scholar
  21. Herring T (2003) MATLAB Tools for viewing GPS velocities and time series. GPS Solut 7(3):194–199. CrossRefGoogle Scholar
  22. Herring T A, King R W, Floyd M A and McClusky S C (2015a) GAMIT Reference Manual: GPS Analysis at MIT, release 10.61, Dep. Of Earth, Atmos., and Planet. Sci., Mass. Inst. of Technol., CambridgeGoogle Scholar
  23. Herring TA, Floyd MA, King RW, McClusky SC (2015) GLOBK reference manual: global Kalman filter VLBI and GPS analysis program, release 10.6. Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, CambridgeGoogle Scholar
  24. Kahle H-G, Cocard M, Peter Y, Geiger A, Reilinger R, Barka A, Veis G (2000) GPS-derived strain rate field within the boundary zones of the Eurasian, African, and Arabian Plates. J Geophys Res 105(B10):23353. CrossRefGoogle Scholar
  25. Kaufman L, Rousseeuw PJ (1990) Finding groups in data: an introduction to cluster analysis, 1st edn. Wiley, New YorkCrossRefGoogle Scholar
  26. Lenk O, Türkezer A, Ergintav S, Kurt AI, Belgen A (2003) Monitoring the kinematics of anatolia using permanent GPS network stations. Turk J Earth Sci 12(1):55–65Google Scholar
  27. Lyard F, Lefevre F, Letellier T, Francis O (2006) Modelling the global ocean tides: modern insights from FES2004. Ocean Dyn 56(5–6):394–415. CrossRefGoogle Scholar
  28. Macqueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth berkeley symposium on mathematical statistics and probability, vol 1, No 233, pp 281–297. citeulike-article-id:6083430Google Scholar
  29. McCaffrey R, King RW, Payne SJ, Lancaster M (2013) Active tectonics of northwestern U.S. inferred from GPS-derived surface velocities. J Geophys Res Solid Earth 118(2):709–723. CrossRefGoogle Scholar
  30. McClusky S et al (2000) Global positioning system constraints on plate kinematics and dynamics in the eastern Mediterranean and Caucasus. J Geophys Res Solid Earth 105(B3):5695–5719. CrossRefGoogle Scholar
  31. Melbourne W G (1985) The case for ranging in GPS based geodetic systems. In: Goad C (ed) Proceedings of 1st international symposium on precise positioning with the global positioning system. U.S. Department of Commerce, Rockville. 15–19 April, pp 373–386Google Scholar
  32. Nyst M, Thatcher W (2004) New constraints on the active tectonic deformation of the Aegean. J Geophys Res Solid Earth 109(11):1–23. Google Scholar
  33. Ozdemir S (2016) On the estimation of precise coordinates and velocities of TNPGN and TNPGN-active stations (in Turkish—TUSAGA ve TUSAGA-Aktif Istasyonlarinin Hassas Koordinat ve Hizlarinin Hesaplanmasi Uzerine). Map J, January 2016, Issue 155, General Directorate of Mapping, AnkaraGoogle Scholar
  34. Ozener H, Arpat E, Ergintav S, Dogru A, Cakmak R, Turgut B, Dogan U (2010) Kinematics of the eastern part of the North Anatolian Fault Zone. J Geodyn 49(3–4):141–150. CrossRefGoogle Scholar
  35. Petrie EJ, King MA, Moore P, Lavallee DA (2010) Higher-order ionospheric effects on the GPS reference frame and velocities. J Geophys Res Solid Earth 115(3):1–8. Google Scholar
  36. Reilinger R et al (2006) GPS constraints on continental deformation in the Africa–Arabia–Eurasia continental collision zone and implications for the dynamics of plate interactions. J Geophys Res Solid Earth 111(5):1–26. Google Scholar
  37. Richards JA, Jia X (2006) Remote sensing digital image analysis: an introduction. Springer, Berlin, pp 211–213Google Scholar
  38. Rousseeuw PJ (1987) Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math 20(C):53–65. CrossRefGoogle Scholar
  39. Savage JC, Simpson RW (2013a) Clustering of GPS velocities in the Mojave Block, southeastern California. J Geophys Res Solid Earth 118(4):1747–1759. CrossRefGoogle Scholar
  40. Savage JC, Simpson RW (2013b) Clustering of velocities in a GPS network spanning the Sierra Nevada Block, the Northern Walker Lane Belt, and the Central Nevada Seismic Belt, California–Nevada. J Geophys Res Solid Earth 118(9):4937–4947. CrossRefGoogle Scholar
  41. Savage JC, Wells RE (2015) Identifying block structure in the Pacific Northwest, USA. J Geophys Res Solid Earth 120:7905–7916. CrossRefGoogle Scholar
  42. Schaffrin B, Bock Y (1988) A unified scheme for processing GPS phase observations. Bull Geodesique 62:142. CrossRefGoogle Scholar
  43. Simpson RW, Thatcher W, Savage JC (2012) Using cluster analysis to organize and explore regional GPS velocities. Geophys Res Lett 39(17).
  44. Smith WHF, Wessel P (1990) Gridding with continuous curvature splines in tension. Geophysics 55(3):293–305. CrossRefGoogle Scholar
  45. Thatcher W (2009) How the continents deform: the evidence from tectonic geodesy. Annu Rev Earth Planet Sci 37(1):237–262. CrossRefGoogle Scholar
  46. Tibshirani R, Walther G, Hastie T (2001) Estimating the number of clusters in a data set via the gap statistic. J R Stat Soc Ser B Stat Methodol 63(2):411–423. CrossRefGoogle Scholar
  47. Tregoning P, Watson C (2009) Atmospheric effects and spurious signals in GPS analyses. J Geophys Res Solid Earth 114(9):1–15. Google Scholar
  48. Tukey JW (1977) Exploratory data analysis. AddisonWesley, ReadingGoogle Scholar
  49. Ustun A et al (2015) Land subsidence in Konya Closed Basin and its spatiotemporal detection by GPS and DInSAR. Environ Earth Sci 73(10):6691–6703CrossRefGoogle Scholar
  50. Ward JH Jr (1963) Hierarchical grouping to optimize an objective function. J Am Stat Assoc 58:236–244CrossRefGoogle Scholar
  51. Wubbena G (1985) Software developments for geodetic positioning with GPS using TI 4100 code and carrier measurements. In: Goad C (ed) Proceedings of 1st international symposium on precise positioning with the global positioning system. U.S. Department of Commerce, Rockville. 15–19 April, pp 403–412Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Geodetic and Geographic Information TechnologiesMiddle East Technical UniversityAnkaraTurkey
  2. 2.Department of Civil Engineering, Geomatics Engineering DivisionMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations