TY  - JOUR
T1  - Prediction of the earthquake magnitudes with A new estimator via sub-sampling method
AU  - Ünal, Ceren
AU  - Özel Kadılar, Gamze
PY  - 2025
DA  - September
Y2  - 2025
DO  - 10.59313/jsr-a.1687759
JF  - Journal of Scientific Reports-A
JO  - JSR-A
PB  - Kütahya Dumlupinar University
WT  - DergiPark
SN  - 2687-6167
SP  - 12
EP  - 28
IS  - 062
LA  - en
AB  - Türkiye is situated on active fault lines, where significant tectonic movements occur, resulting in earthquakes, and is located in one of the world’s most active earthquake zones, the Alpine-Himalayan seismic belt. We propose an estimator to examine the population mean of the earthquake magnitude using the information of the largest aftershocks among aftershocks via the sub-sampling method under the non-response scheme. The proposed estimator is obtained and the expressions for the bias, mean square error (MSE) and minimum mean square error are also derived to the first order of approximation. We evaluate earthquakes in the Aegean Region of Türkiye between the years 1900 – 2021mbased on different scenarios within the dataset. The results show that the estimation of the population mean is the perfect fit for the real earthquake magnitude population mean via the proposed estimator. By analyzing earthquake data from Türkiye, we successfully highlighted the practical significance and applicability of our proposed estimator in a real-world scenario.
KW  - Aftershock
KW  - Earthquake
KW  - Sub-sampling Method
KW  - Population Mean Estimator
CR  - [1] H. N. Karakavak and C. Kadılar, “INAR(1) and ARIMA models to predict the number of mainshocks and their aftershocks in Turkey,” J Seismol., 2025, doi:10.1007/s10950-025-10302-2.
CR  - [2] TÜBİTAK 1002, “Earthquake Magnitude Prediction with Bidirectional Deep Learning Methods for Western Anatolia Region”, Project No: 124F059, 2024.
CR  - [3] T. Y. Duman et al., "Türkiye sismotektonik haritası ölçek 1:1.250.000," Maden Tetkik ve Arama Genel Müdürlüğü Özel Yayın Serisi, vol. 34, Ankara, 2017.
CR  - [4] KOERI, "06 Şubat 2023 ML7.5 Ekinözü Kahramanmaraş depremi," [Online]. Available: http://www.koeri.boun.edu.tr/sismo/2/06-subat-2023-ml7-5-ekinozu-kahramanmaras-depremi/. Accessed: Feb. 2023.
CR  - [5] A. Öcal, "Natural disasters in Türkiye: Social and economic perspective," Int J Disaster Risk Manag, vol. 1, no. 1, pp. 51–61, 2019.
CR  - [6] S. McClusky et al., "Global Positioning System constraints on plate kinematics and dynamics in the eastern Mediterranean and Caucasus," J. Geophys. Res.: Solid Earth, vol. 105, no. B3, pp. 5695–5719, Mar. 2000.
CR  - [7] M. Erdik, "Report on 1999 Kocaeli and Düzce (Türkiye) earthquakes," in Struct. Control Civ. Infrastruct. Eng., pp. 149–186, 2001.
CR  - [8] B. Ugurhan and A. Askan, "Stochastic strong ground motion simulation of the 12 November 1999 Düzce (Türkiye) earthquake using a dynamic corner frequency approach," Bull. Seismol. Soc. Am., vol. 100, no. 4, pp. 1498–1512, 2010.
CR  - [9] N. Pınar, "Preliminary note on the earthquake of Yenice-G, Türkiye, March 18, 1953," Bull. Seismol. Soc. Am., vol. 43, no. 4, pp. 307–310, 1953.
CR  - [10] İ. H. Çağatay, "Experimental evaluation of buildings damaged in recent earthquakes in Türkiye," Eng. Fail. Anal., vol. 12, no. 3, pp. 440–442, 2005.
CR  - [11] Mitchell, W. A. (1976). Reconstruction after disaster: The Gediz earthquake of 1970. Geographical Review, 296-313.
CR  - [12] AFAD Earthquake Department, "30 October 2020 Aegean Sea, Seferihisar (Izmir) offshore (17.26 km) preliminary evaluation report on Mw 6.6 earthquake," 2020.
CR  - [13] A. Karadaş and E. Öner, "Effects of the alluvial geomorphology on the damage of the Sisam earthquake in the Bornova plain," J. Geogr., vol. 42, pp. 139–153, 2021.
CR  - [14] C. Ünal, G. Özel, and T. Eroğlu Azak, "Markov chain approach for earthquake sequencing in the Aegean Graben system of Türkiye," Earth Sci. Inf., vol. 16, no. 2, pp. 1227–1239, Apr. 2023.
CR  - [15] S. Ünal, S. Çelebioğlu, and B. Özmen, "Seismic hazard assessment of Türkiye by statistical approaches," Turk. J. Earth Sci., vol. 23, pp. 350–360, 2014.
CR  - [16] E. K. Kara and K. Durukan, "The statistical analysis of the earthquake hazard for Türkiye by generalized linear models," Gazi Univ. J. Sci., vol. 30, no. 4, pp. 584–597, 2017.
CR  - [17] M. S. Yücemen, "Probabilistic assessment of earthquake insurance rates for Türkiye," Nat. Hazards, vol. 35, pp. 291–313, 2005.
CR  - [18] E. Firuzan, "Statistical earthquake frequency analysis for western Anatolia," Turk. J. Earth Sci., vol. 17, no. 4, pp. 741–762, 2008.
CR  - [19] Y. Bayrak et al., "Regional variation of the ω-upper bound magnitude of GIII distribution in and around Türkiye: Tectonic implications for earthquake hazards," Pure Appl. Geophys., vol. 165, no. 7, pp. 1367–1390, Jul. 2008.
CR  - [20] Y. Bayrak et al., "Seismicity assessment for different regions in and around Türkiye based on instrumental data: Gumbel first asymptotic distribution and Gutenberg-Richter cumulative frequency law," Nat. Hazards Earth Syst. Sci., vol. 8, pp. 109–122, 2008.
CR  - [21] T. M. Tsapanos et al., "Analysis of largest earthquakes in Türkiye and its vicinity by application of the Gumbel III distribution," Acta Geophys., vol. 62, pp. 59–82, 2014.
CR  - [22] G. Özel, "A bivariate compound Poisson model for the occurrence of foreshock and aftershock sequences in Türkiye," Environmetrics, vol. 22, no. 7, pp. 847–856, 2011.
CR  - [23] G. Özel, "Ratio estimators using characteristics of Poisson distribution with application to earthquake data," in Proc. 7th Int. Days Stat. Econ., Prague, Sep. 2013.
CR  - [24] P. Sharma, H. K. Verma, N. K. Adichwal, and R. Singh, "Generalized estimators using characteristics of Poisson distribution," Int. J. Appl. Comput. Math., vol. 3, pp. 745–755, 2017.
CR  - [25] S. Khare, R. Singh, and P. Sharma, "Estimation of population mean for logarithmic observation under Poisson distributed study and auxiliary variates," Electron. J. Appl. Stat. Anal., vol. 13, no. 2, pp. 580–593, 2020.
CR  - [26] O. Tan, M. C. Tapırdamaz, and A. Yörük, "The earthquake catalogues for Türkiye," Turk. J. Earth Sci., vol. 17, no. 2, pp. 405–428, 2008.
CR  - [27] R. J. Little and D. B. Rubin, "Maximum likelihood for general patterns of missing data: introduction and theory with ignorable nonresponse," in Statistical Analysis with Missing Data, pp. 164–189, 2002.
CR  - [28] M. H. Hansen and W. N. Hurwitz, "The problem of non-response in sample surveys," J. Am. Stat. Assoc., vol. 41, no. 236, pp. 517–529, 1946.
CR  - [29] H. O. Cekim and C. Kadilar, "In-type estimators for the population variance in stratified random sampling," Commun. Stat. Simul. Comput., vol. 49, no. 7, pp. 1665–1677, 2020.
CR  - [30] H. O. Cekim and C. Kadilar, "Ln-type variance estimators in simple random sampling," Pak. J. Stat. Oper. Res., vol. 16, no. 4, pp. 689–700, 2020.
CR  - [31] H. Cingi and C. Kadilar, Advances in Sampling Theory: Ratio Method of Estimation, Bentham Science Publishers, 2009.
CR  - [32] R. S. Solanki, H. P. Singh, and A. Rathour, "An alternative estimator for estimating the finite population mean using auxiliary information in sample surveys," Int. Scholarly Res. Not., pp. 1–14, 2012.
CR  - [33] Z. Yan and B. Tian, “Ratio method to the mean estimation using coefficient of skewness of auxiliary variable,” in International Conference on Information Computing and Applications, Berlin, Heidelberg: Springer, 2010.
CR  - [34] M. Irfan, M. Javed, and Z. Lin, “Efficient ratio-type estimators of finite population mean based on correlation coefficient,” Sci. Iran., vol. 25, no. 4, pp. 2361–2372, 2018.
CR  - [35] A. A. Sifawa and M. Z. Shehu, “Modified ratio-cum-product type estimator for population mean in simple random sampling scheme,” Him. J. Appl. Med. Sci. Res., vol. 2, no. 5, pp. 1–5, 2021.
CR  - [36] A. Gupta and R. Tailor, “Ratio in ratio type exponential strategy for the estimation of population mean,” J. Reliab. Stat. Stud., vol. 14, no. 2, pp. 551–564, 2021.
CR  - [37] R. K. Gangele, G. K. Vishwakarma, and S. K. Choubey, “An efficient class on linear combination of ratio type estimators for estimating the population mean,” Thail. Stat., vol. 20, no. 2, pp. 284–292, 2022.
CR  - [38] J. J. Cai, P. Wan, and G. Özel, “Parametric and non-parametric estimation of extreme earthquake event: the joint tail inference for mainshocks and aftershocks,” Extremes, vol. 24, pp. 199–214, 2021.
CR  - [39] A. M. Chandler, N. Lam, J. Wilson, and G. L. Hutchinson, “Response spectrum modelling for regions lacking earthquake records,” Electron. J. Struct. Eng., vol. 1, no. 1, pp. 60–73, 2001.
CR  - [40] W. G. Cochran, Sampling Techniques, 3rd ed., New York: John Wiley & Sons, 1977.
CR  - [41] R. Singh, M. Kumar, M. K. Chaudhary, and F. Smarandache, “Estimation of mean in presence of non-response using exponential estimator,” arXiv preprint, arXiv:0906.2462, 2009.
CR  - [42] G. N. Singh and M. Usman, “Ratio-to-product exponential-type estimators under non-response,” Jordan J. Math. Stat., vol. 12, no. 4, pp. 593–616, 2019.
CR  - [43] D. Kalafat and E. Görgün, “An example of triggered earthquakes in western Türkiye: 2000–2015 Afyon-Akşehir Graben earthquake sequences,” J. Asian Earth Sci., vol. 146, pp. 103–113, 2017.
CR  - [44] S. Turkan and G. Özel, “Modeling destructive earthquake casualties based on a comparative study for Türkiye,” Nat. Hazards, vol. 72, no. 2, pp. 1093–1110, 2014.
CR  - [45] E. Akgun and M. İnceöz, "Tectonic evolution of the central part of the East Anatolian Fault Zone, Eastern Turkey," Turk. J. Earth Sci., vol. 30, no. 7, pp. 928-947, 2021.
CR  - [46] F. Flerit, R. Armijo, G. King, and B. Meyer, “The mechanical interaction between the propagating North Anatolian Fault and the back-arc extension in the Aegean,” Earth Planet. Sci. Lett., vol. 224, no. 3–4, pp. 347–362, 2004.
CR  - [47] M. Bohnhoff, H. P. Harjes, and T. Meier, “Deformation and stress regimes in the Hellenic subduction zone from focal mechanisms,” J. Seismol., vol. 9, no. 3, pp. 341–364, 2005.
CR  - [48] O. Tan, “Turkish Homogenized Earthquake Catalogue (TURHEC),” Nat. Hazards Earth Syst. Sci., Zenodo, 2021. [Online]. Available:
CR  - [49] F. T. Kadirioglu and R. F. Kartal, “The new empirical magnitude conversion relations using an improved earthquake catalogue for Türkiye and its near vicinity (1900–2012),” Turk. J. Earth Sci., vol. 25, no. 4, pp. 300–310, 2016.
CR  - [50] A. M. C. Şengör, “The North Anatolian transform fault: its age, offset and tectonic significance,” J. Geol. Soc., vol. 136, pp. 269–282, 1979.
CR  - [51] A. M. C. Şengör, “Mid-Mesozoic closure of Permo-Triassic Tethys and its implications,” Nature, vol. 279, pp. 590–593, 1979.
CR  - [52] E. M. Scordilis, “Empirical global relations converting MS and mb to moment magnitude,” J. Seismol., vol. 10, pp. 225–236, 2006.
CR  - [53] J. K. Gardner and L. Knopoff, “Is the sequence of earthquakes in Southern California with aftershocks removed, Poissonian?” Bull. Seismol. Soc. Am., vol. 64, no. 5, pp. 1363–1377, 1974.
CR  - [54] S. Ünal and S. Çelebioğlu, “A Markov chain modelling of the earthquakes occurring in Türkiye,” Gazi Univ. J. Sci., vol. 24, pp. 263–274, 2011.
CR  - [55] H. A. Cohen, C. J. Dart, H. S. Akyüz, and A. Barka, “Syn-rift sedimentation and structural development of the Gediz and Büyük Menderes graben, western Türkiye,” J. Geol. Soc., vol. 152, no. 4, pp. 629–642, 1995.
UR  - https://doi.org/10.59313/jsr-a.1687759
L1  - https://dergipark.org.tr/en/download/article-file/4822457
ER  -