Ege Graben Sistemi Aylık Deprem Frekansları Zaman Serisi için ARMA ve ARIMA Modelleri

Yıl 2025, Cilt: 25 Sayı: 6, 1447 - 1457

İlknur Kaftan , Petek Sındırgı

Öz

Bölgesel ve dünya ölçeğindeki sismik veri tabanlarına dayanarak kurulan zaman serilerinden, belli bir eşiği aşan deprem büyüklüklerini ve/veya frekanslarını tahmin etmek konusunda pek çok çalışma yapılmıştır. Ancak bu çalışmaların çoğu yıllık veri tabanlarına dayanmaktadır. Bu çalışmada, Türkiye’de Ege Graben Sistemi’ni kapsayan ve 37°- 40° enlemleri ile 26°-30° boylamları arasında yer alan, büyüklüğü M≥2.5 olan depremlerin aylık frekanslarını tahmin etmekte yararlanılabilecek ARMA(p,q) ve ARIMA(p,d,q) modelleri geliştirilmiştir. 1975-2024 dönemini kapsayan, 600 ay uzunluğundaki orijinal veri seti, geleneksel modelleme yöntemlerinde öngörülen “normallik varsayımı”nın sağlanması adına, öncelikle logaritmik dönüşümden geçirilmiştir. Çalışmanın sayısal sonuçları, logaritmik dönüşümden geçirilmiş verilerin, p≤3, d=1, ve q=1 olmak üzere, basit ve ekonomik ARMA(p,1) ve ARIMA(p,1,1) formundaki modeller ile oldukça iyi tanımlanabileceğini göstermiştir. Dört aday modelin (ikisi ARMA(p,1), diğer ikisi ARIMA(p,1,1) formunda) tahmin yetenekleri Akaike Bilgi İçeriği (AIC) tabanlı bir çoklu-model seçim prosedürü uygulanarak karşılaştırılmıştır. En başarılı modelin ARMA(3,1) olduğu; hatta, pratik uygulamalarda ARMA(2,1) modelinin dahi kullanılabileceği saptanmıştır. Geliştirilen modellerden, ileride Ege Graben Sistemi ile ilgili yapılacak istatiksel ve fiziksel simülasyon çalışmalarında, zaman serilerinde yığma (aggregation) kuramı çerçevesinde, bir aydan daha uzun dönemlerde (örneğin, 2 aylık, 6 aylık, yıllık gibi), eşik değerini aşan toplam deprem sayılarının zamansal stokastik davranışlarının teşhis edilmesinde ve elbette, yakın gelecekteki kısa-dönem aylık deprem frekanslarının ön kestiriminde faydalanılabilecektir

Anahtar Kelimeler

Deprem frekansı , Ege Graben Sistemi , ARMA , ARIMA , Zaman serileri

ARMA and ARIMA Models for the Monthly Earthquake Frequencies Time Series in Aegean Graben System

Öz

Several studies have been done on predicting magnitudes and/or frequencies of earthquakes above a given threshold value through the use of time series models fitted for regional and worldwide seismic databases. Most of them, however, often consider annual databases. In this paper, we developed those ARMA(p,q) and ARIMA(p,d,q) models that can be utilized for predicting monthly absolute frequencies of earthquakes with magnitudes M≥2.5 in the region covered the Aegean Graben System of Turkiye, which is located in between 37°- 40° N latitudes and 26°-30° E longitudes. The original time series dataset of length 600 months, which covers the period 1975-2024, is eventually log-transformed to meet the usual “normality assumption” made in traditional modeling procedures. The numerical results of the study revealed that the log-transformed data well can be described by considerably simple and parsimonious ARMA(p,q) and ARIMA(p,d,q) models with p≤3, d=1, and q=1. Prediction abilities of the four candidate models (two of them in ARMA(p,1), and the other two in ARIMA(p,1,1) forms) are compared by utilizing a multi-model selection procedure based on Akaike Information Criterion (AIC). We have found that the best-performing model is the ARMA(3,1) and that even the ARMA(2,1) model can be utilized for practical applications. Those models developed herein, can be integrated in statistical and physical simulation studies related to the Aegean Graben System that will be conducted in future. They may also be evaluated, within the scope of temporal aggregation of time series, for the identification of temporal stochastic behaviour of total earthquake numbers exceeding the threshold value for periods longer than one month (e.g. 2-months, 6-months, annual etc.). And, of course, they can essentially be used for forecasting short-term monthly earthquake frequencies in near future.

Anahtar Kelimeler

Earthquake Frequency , Aegean Graben System , ARMA , ARIMA , Time series

Kaynakça

• Akaike, H., 1973. Information Theory as an Extension of the Maximum Likelihood Principle. In B. N. Petrov & F. Csaki (Eds.), Second international Symposium on Information Theory, Akakmiai Kiado, Budapest, 267–281.
• Akaike, H.,1978. On newer statistical approaches to parameter estimation and structure determination. International Federation of Automatic Control Proceedings Volumes, 3, 1877–1884.
• Akaike, H., 1979. A Bayesian extension of the minimum AIC procedure of autoregressive model fitting. Biometrika, 66, 237–242.
• Akkar, S., Azak, T., Çan, T., Çeken, U., Demircioğlu, Tümsa, M.B., Duman, T.Y. vd., 2018. Evolution of seismic hazard maps in Turkey. Bulletin of Earthquake Engineering, 16, 3197–3228.
• Allen, M., Jackson, J., and Walker, R. 2004. Late Cenozoic reorganization of the Arabia‐Eurasia collision and the comparison of short term and long‐term deformation rates. Tectonics, 23(2), 1-16.
• Alptekin, O., Ilkışık, M., Ezen, U. and Uçer, S.B. 1990. Heat flow, seismicity and the crustal structure of western Anatolia. In: Savascin MY & Eronat AH (eds), Proceeding Book of International Earth Sciences Congress on Aegean Regions, Izmir/Turkey, 2, 1–12.
• Amei, A., Fu, W. and Ho, C.H., 2012. Time series analysis for predicting the occurrences of large scale earthquakes. International Journal of Applied Science and Technology, 2(7), 64–75.
• Aslan, E., 1972. Magnitude and time distributions of earthquakes in Turkey. Bulletin of the International Institute of Seismology and Earthquake Engineering, 7, 1–10.
• Bartlett, M.S., 1946. On the theoretical specification and sampling properties of autocorrelated time-series. Supplement to the Journal of the Royal Statistical Society, 8(1), 27–41. https://doi.org/10.2307/2983611
• Bath, M., 1979. Seismic risk in Turkey-a preliminary approach. Tectonophysics, 54, 9–16.
• Bayrak, Y., Öztürk, S., Çınar, H., Kalafat, D., Tsapanos, T.M., Koravos, G.C., Leventakis, G.A., 2009. Estimating earthquake hazard parameters from instrumental data for different regions in and around Turkey. Engineering Geology, 105(3-4), 200–210.
• Bayrak, Y., Yılmazturk, A., Ozturk, S., 2005. Relationships between fundamental seismic hazard parameters for the different source regions in Turkey. Natural Hazards, 36, 445–462.
• Box, G.E.P. and Cox, D.R., 1964. An Analysis of Transformations, Journal of the Royal Statistical Society: Series B (Methodological), 26(2), 211–243, https://doi.org/10.1111/j.2517-6161.1964.tb00553.x
• Box, G.E.P. and Pierce, D.A., 1970. Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models. Journal of the American Statistical Association, 65 (332), 1509–26. https://doi.org/10.2307/2284333
• Box, G.E.P. and Jenkins, G.M., 1976. Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco.
• Brewer, K.R.W.,1973. Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models. Journal of Economics, 1, 33-154.
• Burnham, K.P. and Anderson, D.R., 2002. Model selection and multimodel inference (2nd ed., Editörler: Kenneth P. Burnham, David R. Anderson). Springer, New York, 1-488.
• Cekim, H.O., Tekin, S., Özel, G., 2021. Prediction of the earthquake magnitude by time series methods along the East Anatolian Fault, Turkey. Earth Science Informatics, 14, 1339–1348.
• Cekim, H.O., Karakavak, H.N., Özel, G., Tekin, S., 2023. Earthquake magnitude prediction in Turkey: a comparative study of deep learning methods, ARIMA and singular spectrum analysis. Environmental Earth Sciences, 82, 387. https://doi.org/10.1007/s12665-023-11072-1
• Dewey, J.F., Şengör, A.M.C., 1979. Aegean and surrounding regions-Complex multi-plate and continuum tectonics in a convergent zone. Geological Society of America Bulletin, 90(1), 84-92.
• Erdik, M., Biro, Y.A., Onur, T., Sesetyan, K., Birgoren, G., 1999 Assessment of earthquake hazard in Turkey and neighbouring. Annals Geophysics, 42(6), 1125-1138.
• Hamilton, J.D., 1994. Time series analysis. Princeton University Press, New Jersey.
• Hyndman, R.J. and Athanasopoulos, G., 2018. Forecasting: Principles and Practice. 2nd ed. Melbourne, Australia: OTexts.
• Kaftan, I., Şalk, M. and Şenol, Y., (2017). Processing of earthquake catalog data of Western Turkey with artificial neural networks and adaptive neuro-fuzzy inference system. Arabian Journal of Geosciences, 10, 243. https://doi.org/10.1007/s12517-017-3021-1
• Kasımzade, A., Abrar, O., Atmaca, G. and Kuruoğlu, M., 2020. New structural seismic protection for high-rise building structures. Journal of Vibroengineering, 22(4), 831-848.
• Kay, S.M., 1993. Fundamentals of statistical signal processing: Estimation theory. Prentice-Hall, New Jersey.
• Kayabalı, K. and Akın, M., 2003. Seismic hazard map of Turkey using the deterministic approach. Engineering Geology, 69, 127–137.
• Koçyiğit, A., Yusufoğlu, H., Bozkurt, E., 1999. Evidence from the Gediz graben for episodic two-stage extension in western Turkey. Journal of Geological Society, London, 156(3), 605-616.
• Ljung, G.M. and Box, G.E.P., 1978. On a measure of a lack of fit in time series models. Biometrika, 65(2), 297–303. https://doi.org/10.1093/biomet/65.2.297
• Minke, G., 2001. Construction Manual for Earthquake-resistant Houses Built of Eart. GATE-BASIN at GTZ GmbH, Eschborn, Germany, 1-52.
• Özşahin, B., 2022. Türkiye bina deprem yönetmeliği 2018’de bina doğal titreşim periyodunun belirlenmesi için verilen ampirik formülün donatısız yığma binalar için irdelenmesi. Afyon Kocatepe Üniversitesi, Fen ve Mühendislik Bilimleri Dergisi, 22, 873-892. https://doi.org/10.35414/akufemubid.1076403
• Phillips, P.C.B. and Perron, P., 1988. Testing for unit roots in time series regression. Biometrika, 75, 335–346. https://doi.org/10.2307/2336182
• Reilinger, R., et al. (1997), Global Positioning System measurements of present-day crustal movements in the Arabia-Africa-Eurasia plate collision zone, J. Geophys. Res., 102, 9983-9999.
• Sarıaslan, N., 2010. The effect of temporal aggregation on univariate time series analysis. Yüksek Lisans tezi. Orta Doğu Üniv. Fen Bilimleri Enstitüsü, Ankara, 164 s.
• Shishegaran, A., Taghavizade, H., Bigdeli, A., Shishegaran, A., 2019. Predicting the Earthquake Magnitude along Zagros Fault Using Time Series and Ensemble Model. Journal of Soft Computing in Civil Engineering, 3(4), 67–77.
• Said, S.E., Dickey, D., 1984. Testing for unit roots in autoregressive moving-average models of unknown order. Biometrika, 71, 599–607. https://doi.org/10.2307/2336570
• Sayıl, N. and Osmanşahin, I., 2008. An investigation of seismicity for Western Anatolia. Natural Hazards, 44,51–64.
• Schwarz, G., 1978. Estimating the dimensions of a model. Annals of Statistics 6(2), 461-464.
• Symonds, M.R.E. and Moussali, A., 2011. A brief guide to model selection, multimodel inference and model averaging in behavioral ecology using Akaike’s information criterion. Behavioral Ecology and Sociobiology, 65, 13–21.
• Şengör, A.M.C. 1987. Cross-fault and differential stretching of hanging walls in regions of low-angle normal faulting: examples from western Turkey. Coward, M.P., Dewey, J.F., Hancock, P.L. (Ed.). Continental extensional tectonics. Geological Society Special Publication, 28, 575– 589.
• Todelo, T.L. and Chris Jordan, G.A., 2019. Predictability of earthquake occurrence using autoregressive integrated moving average (ARIMA) model. In: Lecture notes in engineering and computer science: proceedings of the international multiconference of engineers and computer scientists, 13–15.
• Wei, W.W.S., 1994. Time Series Analysis, Univariate and Multivariate Methods, Addison and Wesley Pb.Comp.Inc., Boston, ABD.
• Wessel, P., Luis, J. F., Uieda, L., Scharroo, R., Wobbe, F., Smith, W. H. F., and Tian, D., 2019. The Generic Mapping Tools version 6. Geochemistry, Geophysics, Geosystems, 20 (11), 5556-5564. https://doi.org/10.1029/2019GC008515
• Westaway, R., 1994 Present-day kinematics of the Middle East and Eastern Mediterranean. Journal of Geophysical Research. Solid Earth, 99(B6),12071–12090. Yarar, R., Ergunay, O., Erdik, M., Gulkan, P., 1980. A Preliminary Probabilistic Assessment of the Seismic Hazard in Turkey. Proceedings of the 7th World Conference on Earthquake Engineering, Istanbul. 309–316.
• Xue Yuan, Hu Dan, Ye Qiuyin et al. ARIMA Model Analysis of the Regularities of Earthquake Origin Times in the Longmen Mountain Fault Zone, 13 October 2022, PREPRINT (Version 1) available at Research Square https://doi.org/10.21203/rs.3.rs-2118474/v1
• Boğaziçi Üniversitesi, Kandilli Rasathanesi ve Deprem Araştırma Enstitüsü, Bölgesel Deprem-Tsunami İzleme ve Değerlendirme Merkezi (BDTİM), Deprem Sorgulama Sistemi, 34684, Çengelköy, İstanbul, http://www.koeri.boun.edu.tr/sismo/zeqdb/, (16.05.2025)
• Türkiye Cumhuriyeti İç İşleri Bakanlığı Afet ve Acil Durum Yönetimi Başkanlığı (AFAD) Veritabanı, Ankara, http://www.deprem.gov.tr, (16.05.2025)
• MathWorks (2022). Econometrics Toolbox 6.1, Econometric Modeler App of MATLAB (R2022b), Natick, Massachusetts, United State. https://www.mathworks.com/help/econ/econometricmodeler-app.html, (16.05.2025)
• USGS (2023). Global Earthquake Faults Database. U.S. Geological Survey. https://earthquake.usgs.gov/data/faults, (16.05.2025)