THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY

Emel Kızılok Kara

THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY

Abstract

This study aims to explore the dependence structure between magnitude and frequency for Turkey earthquake data. In the literature, the Gutenberg Richter (GR) model based on lineer regression is often used to determine this dependence. The dependence structure is evaluated using copula models in this study. Copulas are useful statistical tool for modeling the dependence structure so it does not require assumptions such as linearity and normality. Therefore, as well as GR model, various copula functions are used to determine the magnitude-frequency relationship of earthquakes. An application is given to illustrate that the copulas can be used as alternatives to the GR model. The best copula models are selected by goodness of fit tests. Additionally, the probabilities of earthquake occurrence and the bivariate return periods are estimated for these selected copula models. It is seen that the probabilities of earthquakes occurrence for GR and copula models are almost identical, whereas the return periods based on copula models is more realistic than GR approach.

Keywords

References

[1] Gutenberg, B. and Richter, C.F., (1954) Seismicity of the Earth and Related Phenomena. Second Printed, Princeton University Press, Princeton.
[2] Nelsen R.B., (2006) An Introduction to Copulas (second ed), Springer, New York.
[3] Yücemen M.S., Akkaya A., (1995) Stochastic models for the estimation of seismic hazard and their comparison, In: Proceedings of the 3rd Earthquake Engineering Conference, İstanbul, Turkey, pp. 466–477.
[4] Altınok Y., Kolçak D., (1999) An application of the semi-Markov model for earthquake occurrences in North Anatolia, Turkey. J Balkan Geophys Soc 2: 90–99.
[5] Kasap R., Gürlen Ü., (2003) Obtaining the return period of earthquake magnitudes: as an example Marmara Region. Doğuş Üniversitesi Dergisi 4: 157–166 (article in Turkish with English abstract).
[6] Sayıl N., Osmanşahin İ., (2005) Investigation of seismicity of the Marmara Region. In: Proceedings of the Earthquake Symposium, 23–25 March 2005, Kocaeli, Turkey, pp. 1417– 1426.
[7] Çobanoğlu İ., Bozdağ Ş., Dinçer İ., Erol H., (2006) Statistical approaches to estimating the recurrence of earthquakes in the Eastern Mediterranean Region. İstanbul Üniv Müh Fak Yerbilimleri Dergisi 19: 91–100.
[8] Kahraman S., Baran T., Saatçi İ.A., and Şalk M., (2008) The Effect of Regional Borders when Using the Gutenberg-Richter Model, Case Study: Western Anatolia, Pure Appl. Geophys., 165, 331-347.

[9] Firuzan E., (2008) Statistical Earthquake Frequency Analysis for Western Anatolia, Turkish Journal of Earth Sciences, 17, 741-762.
[10] Çobanoğlu I. and Alkaya D., (2011) Seismic risk analysis of Denizli (Southwest Turkey) region using different statistical models. International Journal of Physical Sciences, 6(11), 2662-2670.
[11] Bayrak Y., and Bayrak E., (2012) An evaluation of earthquake hazard potential for different regions in Western Anatolia using the historical and instrumental earthquake data. Pure and applied geophysics, 169(10), 1859-1873.
[12] Ünal S., Çelebioğlu S., Özmen B., (2014) Seismic hazard assessment of Turkey by statistical approaches, Turkish J Earth Sci, 23, pp.350-360.
[13] Pınar R., Akçığ Z., Demirel F., (1989) The investigation of Western Anatolia seismicity by the Markov method. Jeofizik 3: 56–66 (article in Turkish with English abstract).
[14] Ulutaş E., Özer F.M., (2000) Seismic hazard estimation of Çukurova Region by using Markov model. Jeofizik 14: 103–112 (article in Turkish with English abstract).
[15] Ünal S., Çelebioğlu S., Özmen., B., (2014) Seismic hazard assessment of Turkey by statistical approaches, Turkish J Earth Sci, 23, pp.350-360.
[16] Chen L., Singh V., Shenglian G., Hao Z., and Li T., (2012) Flood Coincidence Risk Analysis Using Multivariate Copula Functions J. Hydrol. Eng., 17 (6), pp. 742–755.
[17] Genest C., Favre A.C., (2007) Everything you always wanted to know about copula modeling but were afraid to ask, Journal of Hydrologic Engineering, 12, pp.347–368.
[18] Genest C., Remillard B., and Beaudoin D., (2009) Goodness-of fit-tests for copulas: A review and power study. Insurance: Mathematics and Economics, 44, pp. 199-213.
[19] Sraj M., Bezak N. and Brilly M., (2015) Bivariate flood frequency analysis using the copula function: A case study of the Litija station on the Sava River, Hydrological Processes, 29(2), pp.225-238.
[20] Fan Y.R., Huang W.W., Huang G.H., Huang K., Li Y.P., and Kong X.M., (2015) Bivariate hydrologic risk analysis based on a coupled entropy-copula method for the Xiangxi River in the Three Gorges Reservoir area, China, Theoretical and Applied Climatology, pp. 1-17.
[21] De Michele C., Salvadori G., Canossi M., Petaccia A. and Rosso R., (2005) Bivariate statistical approach to check adequacy of dam spillway. Journal of Hydrologic Engineering 10, pp.50-57.
[22] Yue S. and Rasmussen P., (2002) Bivariate frequency analysis: Discussion of some useful concepts in hydrological applications, Hydrol. Processes, 16, pp. 2881 – 2898.
[23] Cossette H., Gaillardetz P., Marceau E., Rioux J., (2002) On two dependent individual risk models. Insurance: Mathematics and Economics, 30, pp.153–166.
[24] Yücemen M.S., Yilmaz C., Erdik M., (2008) Probabilistic assessment of earthquake insurance rates for important structures: Application to Gumusova-Gerede motorway, Structural Safety, 30, pp.420–435.
[25] Frees E., Carriere J. and Valdez E. (1996) Annuity Valuation with Dependent Mortality, Journal of Risk and Insurance, 63, pp. 229-261.
[26] Frees E.W., Valdez E., (1998) Understanding relationships using copulas, North American Actuarial Journal, 2, pp. 1-25.
[27] Li N., Liu X., Xie W., Wu J. and Zhang P., (2013) The return period analysis of natural disasters with statistical modeling of bivariate joint probability distribution, Risk Analysis, 33(1), 134-145.
[28] Goda K. and Ren J., (2010) Assessment of seismic loss dependence using copula. Risk analysis, 30(7), 1076-1091.
[29] Nikoloulopoulos A.K., and Karlis D., (2008) Fitting copulas to bivariate earthquake data: the seismic gap hypothesis revisited, Environmetrics, 19(3), 251-269.
[30] Aki K., (1965) Maximum likelihood estimate of b in the formula logN = a-bM and its confidence limits, Bull. Earthquake Res. Inst., Tokyo Univ. 43, 237-239.
[31] Özmen B., (2013) Probability of Earthquake Occurrences to Ankara, Bulletin of the Earth Sciences Application and Research Centre of Hacettepe University 34.1: 141-168.
[32] Gençoğlu S., (1972) Kuzey Anadolu Fay Hattının Sismisitesi ve Bu Zon Üzerindeki Sismik Risk Çalışmaları. Kuzey Anadolu Fayı ve Deprem Kuşağı Sempozyumu, MTA Enstitüsü, Ankara (article in Turkish with English abstract).
[33] Sklar A., (1959) Fonctions de répartitions à n dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris. 8, 229-231.
[34] Cherubini U., Luciano E., Vecchiato W., (2004) Copula methods in finance West Sussex: John Wiley and Sons.
[35] Joe H., (1997) Multivariate Models and Dependence Concepts, Chapman and Hall, London.
[36] Akaike H., (1974) A new look at the statistical model identification. Automatic Control. IEEE Transactions on 19, pp. 716–723.
[37] Schwarz G., (1978) Estimating the dimension of a model. Annals of Statistics 6, pp. 461–464.
[38] Salvadori G., De Michele C., Kottegoda N.T. and Rosso R (2007) Extremes in nature: an approach using copula, Springer, Dordrencht, pp. 292.
[39] Yen B.C., (1970) Risk Analysis in design of engineering projects. J Hydrol Eng 96(4), pp. 959–966.
[40] Bogazici University Kandilli Observatory and Earthquake Research Institute National Earthquake Observation Centre Database, www.koeri.boun.edu.tr. (Access date: 02.08.2014).

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Emel Kızılok Kara This is me
Türkiye

Publication Date

June 1, 2017

Submission Date

August 8, 2016

Acceptance Date

February 8, 2017

Published in Issue

Year 2017 Volume: 35 Number: 2

IZ

https://izlik.org/JA75AJ94AS

Cite

RIS / Bibtex

APA

Kızılok Kara, E. (2017). THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY. Sigma Journal of Engineering and Natural Sciences, 35(2), 187-200. https://izlik.org/JA75AJ94AS

AMA

1.Kızılok Kara E. THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY. SIGMA. 2017;35(2):187-200. https://izlik.org/JA75AJ94AS

Chicago

Kızılok Kara, Emel. 2017. “THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY”. Sigma Journal of Engineering and Natural Sciences 35 (2): 187-200. https://izlik.org/JA75AJ94AS.

EndNote

Kızılok Kara E (June 1, 2017) THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY. Sigma Journal of Engineering and Natural Sciences 35 2 187–200.

IEEE

[1]E. Kızılok Kara, “THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY”, SIGMA, vol. 35, no. 2, pp. 187–200, June 2017, [Online]. Available: https://izlik.org/JA75AJ94AS

ISNAD

Kızılok Kara, Emel. “THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY”. Sigma Journal of Engineering and Natural Sciences 35/2 (June 1, 2017): 187-200. https://izlik.org/JA75AJ94AS.

JAMA

1.Kızılok Kara E. THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY. SIGMA. 2017;35:187–200.

MLA

Kızılok Kara, Emel. “THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY”. Sigma Journal of Engineering and Natural Sciences, vol. 35, no. 2, June 2017, pp. 187-00, https://izlik.org/JA75AJ94AS.

Vancouver

1.Emel Kızılok Kara. THE EARTHQUAKE RISK ANALYSIS BASED ON COPULA MODELS FOR TURKEY. SIGMA [Internet]. 2017 Jun. 1;35(2):187-200. Available from: https://izlik.org/JA75AJ94AS