Kuzey Anadolu Fay Zonunda Deprem OluŞ Zamanlarinin Karma Weibull ...
KUZEY ANADOLU FAY ZONUNDA DEPREM OLUÅž ZAMANLARININ
KARMA WEIBULL DAÄžILIMIYLA MODELLENMESÄ°
Murat ERİŞOĞLU* Tayfun SERVİ* Nazif ÇALIŞ*
Ülkü ERİŞOĞLU* Sadullah SAKALLIOĞLU* Hamza EROL*
ÖZET
Bu çalışmada, 39.000 – 42.000 kuzey enlemleriyle 30.000- 40.000 doğu boylamları
arasında yer alan Kuzey Anadolu Fay Zonunda (KAFZ’nda) meydana gelen depremlerin
oluş zamanları karma Weibull dağılımı ile modellenmiştir. Karma model yaklaşımının
kullanılmasıyla deprem oluş zamanlarının modellenmesinde, klasik yaklaşıma göre daha
iyi sonuçlar elde edilmiştir.
Anahtar Kelimeler: Karma weibull dağılımı, EM algoritması, Deprem tahmini, AIC,
Kolmogorov-Smirnov testi
PROBABILISTIC PREDICTION OF EARTHQUAKE
OCCURRENCE TIMES IN THE NORTH ANATOLIAN FAULTH
ZONE BY MIXTURE OF WEIBULL DISTRIBUTIONS
ABSTRACT
In this study, we modeled the earthquake occurrence time data which were
occurred in the area coordinated 39-42 North latitudes and 30-40 East longitudes in North
Anatolian Faulth Zone (NAFZ) by mixture of Weibull distributions. In case of classical
modeling the earthquake occurrence time data mixture model approach gives better
results.
Key Words: Mixture of weibull distributions, EM algorithm, Earthquake prediction, AIC,
Kolmogorov-Smirnov
* Çukurova Üniversitesi, Fen Edebiyat Fakültesi İstatistik Bölümü Balcalı ,ADANA 01330
merisoglu@cu.edu.tr. (HaberleÅŸme adresi)
Tüm bildiri yazarları aynı üniversitedir.
KAYNAKLAR
BUCAR, T. NAGODE, M. FAJDIGA, M. (2004), Reliability Approximation using Finite
Weibull Mixture Distributions, Reliability Engineering and System Safety, 84, 241-
251.
BOĞAZİÇİ ÜNİVERSİTESİ, Kandilli Rasathanesi ve Deprem Araştırma Enstitüsü,
Ulusal Deprem Ä°zleme Merkezi, 2008. EriÅŸim:
http://www.koeri.boun.edu.tr/sismo/mudim/katalog.asp, 23 Eylül 2008.
CARTA J.A., RAMIREZ P. (2007), Use of finite mixture distributionmodels in the
analysis of wind energy in the Canarian Archipelago, Energy Conversion
Management, 48, 281–291.
DEMPSTER A.P., LAIRD, N.M. and RUBIN, D.B. (1977), Maximum likelihood from
incomplete data via the EM algorithm (with discussion), Journal Royal Statistics
Society B, 39, 1–38
FERRAES, S.G. (2003), The conditional probability of earthquake occurrence and the
next large earthquake in Tokyo, Japan, Journal of Seismology, 7, 145–153
GOMEZ, J.B., and PACHECO A.F. (2004), The minimalist model of characteristic
earthquakes as a useful tool for description of the recurrence of large earthquakes,
Bulletin of the Seismological Society of America, 94, 1960-1967.
GONG, Z. (2006), Estimation of mixed Weibull distribution parameters using the SCEM-
UA algorithm: application and comparison with MLE in automotive reliability
analysis, Reliability Engineering System Safety, 91, 915–922.
HAGIWARA, Y. (1974), Probability of earthquake occurrence as obtained from a
Weibull distribution analysis of crustal strain, Tectonophysics , 23, 323-318.
HUNG, W.L., CHANG, Y.C. and CHUANG, S.C. (2008), Fuzzy Classification Maximum
Likelihood Algorithms for Mixed-Weibull Distributions, Soft Comput., 12, 1013-
1018.
JIANG S, KEÇECİOĞLU D (1992), Maximum likelihhod estiamtes, from censored data,
formixed-Weibull distributions, IEEE Trans Reliab, Vol.41, pp.248–255.
KAGAN Y.Y. and JACKSON D.D. (2000), Probabilistic forecasting of earthquakes,
Geophysical Journal International, 143, 2, 438-453.
KEÇECİOĞLU, D. B. and WANG, W. (1998), Parameter Estimation For Mixed-Weibull
Distribution, Proceedings Annual Reliability and Maintainability Symposium,
1998, 247-252.
LEE, C.P. and Y.B. TSAI (2005), A study of recurrence models of earthquake in Taiwan,
Terrestrial, Atmospheric and Oceanic Sciences, 16, 1, 251-271.
MATTHEWS, M.V., ELLSWORTH, W.L. and REASENBERG, P.A. (2002), A Brownian
model for recurrent earthquakes, Bulletin of the Seismological Society of America,
92, 2233-2250.
MCLACHLAN, G.J., PEEL, D. (2001), Finite mixture models, Wiley, New York.
NISHENKO, S. P., and R. BULAND, (1987), A generic recurrence interval distribution
for earthquake forecasting, Bulletin of the Seismological Society of America, 77,
1382-1399.
OKUMURA, K., YOSHIOKA, v T. and KUSCU Ä°. (1993), Surface Faulting on the North
Anatolian Fault in These two Millennia. U.S., Geological Survey Open-file Report,
94-568, 143-144.
PARVEZ, I.A. and RAM, A. (1997), Probabilistic assessment of earthquake hazards in
the northeast Indian peninsula and Hindukush regions, Pure Applied Geophysics.,
149, 731-746.
RIKITAKE, T. (1974), Probability of an earthquake occurrence as estimated from crustal
strain, Tectonophysics, 23, 299-312.
RIKITAKE, T. (1991), Assessment of earthquake hazard in the Tokyo area, Japan,
Tectonophysics, 199, 121-131.
SEHER T. and MAIN I.G.A. (2004), Statistical Evaluation of a Stress-Forecast
Earthquake, Geophysical Journal International, 157, 1, 187-193.
SHIMAZAKI, K. (2002), Long-term probabilistic forecast in Japan and time-predictable
behavior of earthquake recurrence, Seismotectonics in Convergent Plate Boundary,
37-43.
SYKES, L. R., and NISHENKO S. P. (1984), Probabilities of occurrence of large plate
rupturing earthquakes for the San Andreas, San Jacinto, and Imperial faults,
California, Journal Geophysics Research, 89, 5905-5927.
UDIAS, A., J. RICE (1975), Statistical analysis of microearthquake activity near San
Andreas geophysical observatory, Hollister, California, Bulletin of the
Seismological Society of America, 65, 809-827.
UTSU, T. (1984), Estimation of parameters for recurrence models of earthquakes, Bulletin
Earthquake Research Inst. Univ. Tokyo, 59, 53-66.
YILMAZ V, M. ERÄ°SOGLU, H.E.CELÄ°K (2004), Probabilistic Prediction of the Next
Earthquake in the North Anatolian Fault Zone,Turkey, Dogus University Journal,
5, 2, 243-250.
ZHANG L, LIU C (2006), Fitting irregular diameter distributions of forest stands by
Weibull, modified Weibull, and mixture Weibull models, Journal For Research, 11,
369–372.
