Abstract
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.
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References
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. https://doi.org/10.1029/2008JB006000
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. https://doi.org/10.1016/j.jog.2012.05.008
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. https://doi.org/10.1016/j.jog.2016.01.001
Altamimi Z, Collilieux X, Métivier L (2011) ITRF2008: an improved solution of the international terrestrial reference frame. J Geodesy 85(8):457–473. https://doi.org/10.1007/s00190-011-0444-4
Altamimi Z, Métivier L, Collilieux X (2012) ITRF2008 plate motion model. J Geophys Res Solid Earth 117(7):1–14. https://doi.org/10.1029/2011JB008930
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. https://doi.org/10.1145/1283383.1283494
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)
Blewitt G, Lavallée D (2002) Effect of annual signals on geodetic velocity. J Geophys Res 107(B7):2145. https://doi.org/10.1029/2001JB000570
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. https://doi.org/10.1029/2005JB003629
Calinski T, Harabasz J (1974) A dendrite method for cluster analysis. Commun Stat 3(1):1–27
Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Anal Mach Intell PAMI-1(2):224–227
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. https://doi.org/10.2307/2984875
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. https://doi.org/10.1007/s001900050161
Driver HE, Kroeber AL (1932) Quantitative expression of cultural relationships, vol 31. University of California Publications in American Archaeology and Ethnology, Berkeley, pp 211–256
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. Ankara
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. https://doi.org/10.1785/0120000836
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. https://doi.org/10.1046/j.1365-246X.2003.01899.x
Gerard P, Luzum B (2010) IERS conventions (2010). Bureau International Des Poids Et Mesures Sevres (France), 1–179. Retrieved from http://www.iers.org/TN36/. Accessed 1 Oct 2018
Goudarzi MA, Cocard M, Santerre R (2014) EPC: matlab software to estimate Euler pole parameters. GPS Solut 18(1):153–162. https://doi.org/10.1007/s10291-013-0354-4
Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning, 2nd edn. Springer, New York, pp 520–528
Herring T (2003) MATLAB Tools for viewing GPS velocities and time series. GPS Solut 7(3):194–199. https://doi.org/10.1007/s10291-003-0068-0
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., Cambridge
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, Cambridge
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. https://doi.org/10.1029/2000JB900238
Kaufman L, Rousseeuw PJ (1990) Finding groups in data: an introduction to cluster analysis, 1st edn. Wiley, New York
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):55–65
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. https://doi.org/10.1007/s10236-006-0086-x
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:6083430
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. https://doi.org/10.1029/2012jb009473
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. https://doi.org/10.1029/1999JB900351
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 373–386
Nyst M, Thatcher W (2004) New constraints on the active tectonic deformation of the Aegean. J Geophys Res Solid Earth 109(11):1–23. https://doi.org/10.1029/2003JB002830
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, Ankara
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. https://doi.org/10.1016/j.jog.2010.01.003
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. https://doi.org/10.1029/2009JB006677
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. https://doi.org/10.1029/2005JB004051
Richards JA, Jia X (2006) Remote sensing digital image analysis: an introduction. Springer, Berlin, pp 211–213
Rousseeuw PJ (1987) Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math 20(C):53–65. https://doi.org/10.1016/0377-0427(87)90125-7
Savage JC, Simpson RW (2013a) Clustering of GPS velocities in the Mojave Block, southeastern California. J Geophys Res Solid Earth 118(4):1747–1759. https://doi.org/10.1029/2012JB009699
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. https://doi.org/10.1002/jgrb.50340
Savage JC, Wells RE (2015) Identifying block structure in the Pacific Northwest, USA. J Geophys Res Solid Earth 120:7905–7916. https://doi.org/10.1002/2015JB012277
Schaffrin B, Bock Y (1988) A unified scheme for processing GPS phase observations. Bull Geodesique 62:142. https://doi.org/10.1007/BF02519222
Simpson RW, Thatcher W, Savage JC (2012) Using cluster analysis to organize and explore regional GPS velocities. Geophys Res Lett 39(17). https://doi.org/10.1029/2012gl052755
Smith WHF, Wessel P (1990) Gridding with continuous curvature splines in tension. Geophysics 55(3):293–305. https://doi.org/10.1190/1.1442837
Thatcher W (2009) How the continents deform: the evidence from tectonic geodesy. Annu Rev Earth Planet Sci 37(1):237–262. https://doi.org/10.1146/annurev.earth.031208.100035
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. https://doi.org/10.1111/1467-9868.00293
Tregoning P, Watson C (2009) Atmospheric effects and spurious signals in GPS analyses. J Geophys Res Solid Earth 114(9):1–15. https://doi.org/10.1029/2009JB006344
Tukey JW (1977) Exploratory data analysis. AddisonWesley, Reading
Ustun A et al (2015) Land subsidence in Konya Closed Basin and its spatiotemporal detection by GPS and DInSAR. Environ Earth Sci 73(10):6691–6703
Ward JH Jr (1963) Hierarchical grouping to optimize an objective function. J Am Stat Assoc 58:236–244
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 403–412
Acknowledgements
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.
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Özdemir, S., Karslıoğlu, M.O. Soft clustering of GPS velocities from a homogeneous permanent network in Turkey. J Geod 93, 1171–1195 (2019). https://doi.org/10.1007/s00190-019-01235-z
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DOI: https://doi.org/10.1007/s00190-019-01235-z