The Statistical Analysis of the Earthquake Hazard for Turkey by Generalized Linear Models

Yıl 2017, Cilt: 30 Sayı: 4, 584 - 597, 11.12.2017

Emel Kızılok Kara , Kübra Durukan

Öz

In
this paper, 4863 earthquake data of magnitude 4.0 and greater from 1900 to 2014
are statistically analyzed for the earthquake hazardin Turkey. The
magnitude-frequency relationship in earthquake risk analysis is often performed
by Gutenberg-Richter (GR) model. With the use of this model, information about
earthquake potential of any region can be obtained by previous data and by
estimating parameters such as return periods and possibilities of their
occurrence. In this study, the
relationship between earthquake numbers and magnitudes is modelled with the
Generalized Linear Models (GLMs) as an alternative to Gutenberg-Richter (GR)
Model. Generalized Poisson Regression Model (GPR) and Generalized Negative
Binomial Regression Models (GNBR) as GLMs are utilized in the study. GPR is
found as the best model when considering the dispersion parameters and model
selection criteria. Exceeding probabilities and return periods are calculated
for the selected years depending on yearly average occurrence number of earthquakes
estimated with the GR and GPR models. According to the results, GPR model can
be employed for seismic risk modelling in Turkey.

Anahtar Kelimeler

Earthquake, magnitude-frequency, Gutenberg-Richter relationship, Generalized Poisson Regression Model, Generalized Negative Binomial Regression Model, dispersion parameter

Kaynakça

• [1] F. Saroğlu, O. Emre and I. Kuşcu, "The East Anatolian fault zone of Turkey," Ann. Tectonicae, vol. 6, p. 99–125, 1992.
• [2] B. Gutenberg and C. F. Richter, "Seismicity of the earth and related phenomena", Second Printed, Princeton University Press, Princeton, 1954.
• [3] E. Firuzan, "Statistical Earthquake Frequency Analysis for Western Anatolia", Turkish Journal of Earth Sciences, 17, 741-762, 2008.
• [4] G.R. Dargahi-Noubary, "A method for predicting future large earthquakes using extreme order statistics", Physics of the Earth and Planetary International, 42, 241–245, 1986.
• [5] I. Main, "Statistical physics seismogenesis and seismic hazard", Review of Geophysics, 34, 433–462, 1996.
• [6] Y.Y. Kagan, "Statistics of characteristic earthquakes", Bulletin of Seismological Society of America, 83, 7–24, 1993.
• [7] I. Cobanoğlu, Ş. Bozdağ, I. Dinçer and H. Erol, "Statistical approaches to estimating the recurrence of earthquakes in the Eastern Mediterranean Region," Istanbul University Earth Sciences Review, vol. 19, pp. 91-100, 2006.
• [8] Y. Kalyoncuoğlu, "Evaluation of seismicity and seismic hazard parameters in Turkey and surrounding area using a new approach to the Gutenberg Richter relation," Journal of Seismology, no. 11, pp. 131-148, 2007.
• [9] Y. Bayrak, A. Yılmaztürk and S. Öztürk, "Relationships between fundamental seismic hazard parameters for the different source regions in Turkey," Natural Hazards, vol. 36, p. 445–462, 2005.
• [10] S. Öztürk, Y. Bayrak, H. Cınar, G. C. Koravos and T. M. Tsapanos, "A quantitative appraisal of earthquake hazard parameters computed from Gumbel I method for different regions in and around Turkey," Natural hazards, vol. 47, no. 3, pp. 471-495, 2008.
• [11] S. Ünal and S. Çelebioğlu, "A Markov chain modelling of the earthquakes occurring in Turkey," GU J Sci, no. 24, p. 263–274, 2011.
• [12] S. Ünal, S. Çelebioğlu and B. Özmen, "Seismic hazard assessment of Turkey by statistical approaches," Turkish J Earth Sci, no. 23, pp. 350-360, 2014.
• [13] M. S. Yücemen and A. Akkaya, "Stochastic models for the estimation of seismic hazard and their comparison," in In:Proceedings of the 3rd Earthquake Engineering Conference. İstanbul, Turkey, pp. 466–477, İstanbul, Turkey, 1995.
• [14] S. S. Kestel and M. S. Yücemen, "Earthquake reliability of life line networks," Turk J Engin Environ Sci, no. 24, pp. 143-160, 2000.
• [15] A. S. Selçuk and M. S. Yücemen, "Reliability lifeline networks with multiple sources under seismic hazard," Natural Hazards, no. 21, pp. 1-18, 2000.
• [16] R. Kasap and Ü. Gürlen, "Obtaining the return period of earthquake magnitudes: as an example Marmara Region," Doğus University Journal, no. 4, p. 157–166 (article in Turkish with English abstract), 2003.
• [17] M. S. Yücemen, "Probabilistic assessment of earthquake insurance rates for Turkey," Natural Hazards Springer, no. 35, pp. 291-313, 2005.
• [18] B. Özmen, "Probability of earthquake occurrences to Ankara," Bulletin of the Earth Sciences Application and Research Centre of Hacettepe University, vol. 34, no. 1, pp. 23-26 (article in Turkish with English abstract), 2013.
• [19] K. Kayabali, "Modeling of seismic hazard for Turkey using the recent neotectonic data," Eng Geol, vol. 63, p. 221–232, 2002.
• [20] G. C. Koravos, I. G. Main, T. M. Tsapanos and R. M. W. Musson, "Perceptible earthquakes in the broad Aegean area," Tectonophysics, vol. 371, no. 1, pp. 175-186, 2003.
• [21] P. Mäntyniemi, T. M. Tsapanos and A. Kijko, "An estimate of probabilistic seismic hazard for five cities in Greece by using the parametric-historic procedure" Engineering Geology, vol. 72, no. 3, pp. 217-231, 2004.
• [22] Y. Bayrak, S. Öztürk, H. Cınar, D. Kalafat, T. M. Tsapanos, C. G. Koravos and G. A. Leventakis, "Estimating earthquake hazard parameters from instrumental data for different regions in and around Turkey," Eng Geol, vol. 105, p. 200–210, 2009.
• [23] F. Xie, Z. Wang and J. Liu, "Seismic Hazard and Risk Assessments for Beijing–Tianjin–Tangshan, China, Area," Pure and applied geophysics, vol. 168, no. 3-4, pp. 731-738, 2011.
• [24] J. P. Wang, C. W. Lin, H. Taheri and W. S. Chan, "Impact of fault parameter uncertainties on earthquake recurrence probability examined by Monte Carlo simulation—an example in Central Taiwan," Engineering geology, no. 126, pp. 67-74, 2012.
• [25] B. Akol and T. Bekler, "Assessment of the statistical eartquake hazard parameters for NW Turkey," Natural hazards, vol. 68, no. 2, pp. 837-853, 2013.
• [26] J. Liu, F. Xie and Y. Lv, "Seismic hazard assessments for the Ordos Block and its periphery in China," Soil Dynamics and Earthquake Engineering, no. 84, pp. 70-82, 2016.
• [27] P. McCullagh and J. A. Nelder, Generalized linear models, 2nd Ed., London: Chapman and Hall, 1989.
• [28] P. Jong and G. Z. Heller, Generilazed linear models for insurance data, New York: Cambridge University Press, 2008. [29] J. A. Nelder and R. W. M. Wedderburn, "Generalized linear models," J. Roy. Statist. Soc. A, no. 135, pp. 370-384, 1972.
• [30] G. H. Dunteman and M. R. Ho, An introduction to generalized linear models, Thousand Oaks, Calif.: Sage Publications, 2006.
• [31] S. Tüzel and M. Sucu, "Zero-inflated discrete models for claim frequencies," Journal of Statisticians, no. 5, pp. 23-31 (article in Turkish with English abstract), 2012.
• [32] R. H. Myers, D. C. Montgomery and G. G. Vining, Generalized linear models, New York: John Wiley and Sons, 2002.
• [33] J. George, J. Letha, and P. G. Jairaj, “Daily Rainfall Prediction Using Generalized Linear Bivariate Model–A Case Study,” Procedia Technology, vol. 24, pp. 31-38, 2016.
• [34] Bogazici University Kandilli Observatory And Earthquake Research Institute (KOERI), Istanbul, Turkey, http://www.koeri.boun.edu.tr," 2 8 2014. [Online].
• [35] A. Taban and S. Gençoğlu, "Earthquakes and parameters," Earthquake Research Institute, no. 11, pp. 7-83 (article in Turkish), 1975.
• [36] D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to linear regression analysis, 5th Edition, John Wiley and Sons, 2010.
• [37] W. H. Greene, Accounting for excess zeros and sample selection in Poisson and negative binomial regression models, Tech. Rep., NYU Working Paper No. EC-94-10, March 1994.
• [38] D. Giles, Notes on the zero inflated Poisson model, Department of Economics, University of Victoria, 2010.
• [39] J. F. Lawless, "Negative binomial and mixed Poisson regression," The Canadian Journal of Statistics, vol. 15, no. 3, pp. 209-225, 1987.
• [40] F. Famoye, "Restricted generalized Poisson regression model," Communications in Statistics-Theory and Methods, vol. 22, no. 5, pp. 1335-1354, 1993.
• [41] F. Famoye and K. P. Singh, "Zero-Inflated generalized Poisson regression model with an application to domestic violence data," Journal of Data Science, no. 4, pp. 117-130, 2006.
• [42] C. Dean and J. F. Lawless, "Test for defecting overdispersion in Poisson regression models," Journal of American Statistical Association, vol. 84, pp. 467-472, 1989.
• [43] I. Tuksal, Seismicity of the North Anatolia Fault System in the domain of space, time and magnitude, M.S. Thesis. Saint-Louis Universty, Saint-Louis, Missouri (article in Turkish with English abstract), 1976.
• [44] O. Alptekin, "Magnitude–frequency relationships and deformation release for the earthquakes in and around Turkey," Thesis for Promoting to Associate Professor Level, Karadeniz Technical University, p. 107 (in Turkish), 1978.
• [45] H. Akaike, "A new look at the statistical model identification," Automatic Control, IEEE Transactions on 19, p. 716–723, 1974.
• [46] G. Schwarz, "Estimating the dimension of a model," Annals of Statistics, no. 6, p. 461–464, 1978.