Deprem Büyüklüklerinin Benford Yasası’na Uygunluğu: Kahramanmaraş Depremleri Örneği

Öz

Bu çalışmada, deprem büyüklüklerinin Benford Yasası’na uygun olup olmadığının tespit edilmesi amaçlanmıştır. Bu amaç doğrultusunda 6 Şubat 2023 Kahramanmaraş depremleri incelenmiş ve 01.01.2023–27.02.2023 dönemi boyunca Türkiye’de gerçekleşen 14.565 adet depremin büyüklük verisi Benford Yasası rakamsal dağılımıyla karşılaştırılarak analiz edilmiştir. Analizden elde edilen sonuçlara göre, deprem büyüklüğü rakamlarının Benford Yasası’na uyum sağladığı ve çok küçük sapmalarla birlikte Benford Yasasını yakından takip ettiği belirlenmiştir. Söz konusu küçük sapmaların ise; büyüklük verilerinin tek ondalık basamağa yuvarlanarak açıklanmasından, yerin belirli derinliğinden daha ilerisinde oluşan çok küçük büyüklükteki depremlerin tespit edilememesinden veya mevcut verilerdeki çok küçük ölçüm hatalarından kaynaklanabileceği düşünülmektedir. Dolayısıyla, deprem oluşumlarının doğal süreçler sonucu ortaya çıktığı ve deprem büyüklüklerinin doğru olarak tespit edildiği söylenebilir.

Anahtar Kelimeler

• Benford Yasası
• Rakamsal analiz
• Deprem büyüklükleri
• Kahramanmaraş Depremleri
• Sismik kümeler

Conformity of Earthquake Magnitudes to Benford's Law: the Case of Kahramanmaras Earthquakes

Öz

The aim of this study is to determine whether the earthquake magnitude data comply with Benford's Law. To this end, magnitude data of 14.565 earthquakes that occurred in Turkey between January 1, 2023, and February 27, 2023, were analyzed by comparing them with the numerical distribution of Benford's Law. According to the results obtained from the analysis, it has been determined that the earthquake magnitude digits conform to Benford's Law and closely follow Benford's Law with very small deviations. These small deviations are thought to arise from the rounding of magnitude data to a single decimal place, the inability to detect very small magnitude earthquakes occurring deeper than a certain depth, or very small measurement errors in the existing data. Therefore, it can be said that earthquake occurrences occur as a result of natural processes and earthquake magnitudes are determined correctly.

Anahtar Kelimeler

• Benford’s Law
• Numerical analysis
• Earthquake magnitudes
• Kahramanmaras Earthquakes
• Seismic clusters

Kaynakça

1. AFAD, 2023. Deprem Kataloğu, Afet ve Acil Durum Yönetimi Baskanlıği, Türkiye Cumhuriyeti İçişleri Bakanlığı, Erişim adresi: https://deprem.afad.gov.tr/event-catalog
2. Benford F., 1938. The law of anomalous numbers, American Philosophical Society, 78/4, 551-572.
3. Bouzoubaa M., El Qadi A., Razzouk A., 2013. Benford's law and its application to the detection of earthquake magnitude falsification, Journal of Seismology, 17(2), 367-378.
4. De A.S., Sen U., 2011. Benford's law detects quantum phase transitions similarly as earthquakes, Europhysics Letters, 95(5), 5008.
5. Deveci A., Kilicarslan Z., Ates A., 2013. Benford’s law and its application on Turkish seismic data, Journal of the Faculty of Engineering and Architecture of Gazi University, 28(2), 371-378.
6. Diaz J., Gallart J., Ruiz M., 2015. On the ability of the Benford's law to detect earthquakes and discriminate seismic signals, Seismological Research Letters, 86(1), 192-201, doi: 10.1785/0220140131.
7. Kanamori H., 2005. The nature of seismicity patterns before large earthquakes. Proceedings of the Japan Academy, Series B, 81(9), 271-283.
8. Kanamori H., 2009. Historical perspective on the 1960 Chilean earthquake. Earthquake Spectra, 25(1), 1-13.

9. Karagün V., Taşdemir E., 2019. Benford Yasası'nın Denetimde Kullanımı ve Bir Uygulama. Ekonomi ve Yönetim Araştırmaları Dergisi, 8(2), 120-137.
10. Morikawa N., Fujimoto M., Koketsu K., Abe K., 2012. Importance of accurate and rapid determination of earthquake magnitude for prompt tsunami warning: the 2011 Tohoku earthquake case, Earthquake Spectra, 28(S1), S369-S383.
11. Nastos P.T., Kazantzidou-Firtinidou D., Kassaras I.A., 2017. Benford's law and distribution functions of earthquake magnitude, Physica A: Statistical Mechanics and its Applications, 465, 263-270.
12. National Research Council, 2003. Living on an active earth: Perspectives on earthquake science, National Academies Press.
13. Newcomb S., 1881. Note on the frequency of the use of digits in natural numbers, American Journal of Mathematics, 4, 39-40.
14. Pietronero L., Tosatti E., Tosatti V., Vespignani A., 2001. Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf, Physica A: Statistical Mechanics and its Applications, 293, 297-304, Erişim adresi: https://doi.org/10.1016/S0378-4371(00)00633-6.
15. Pinkham RS.,1961. On the distribution of first significant digits. Ann Math Stat, 32(4):1223–1230.
16. Richter C.F.,1935. An instrumental earthquake magnitude scale. Bull. Seism. Soc. Am., 25: 1-32.
17. Sambridge M., Tkalčić H., Jackson A., 2010. Benford's law in natural sciences, Geophys. Res. Letonya, 37, DOI: 10.1029/2010GL044830.
18. Scholz C.H., 2002. The mechanics of earthquakes and faulting, Cambridge University Press.
19. Sottili G., Palladino D.M., Giaccio B., 2012. Benford’s law in time series analysis of seismic clusters, Math Geosci 44, 619–634. Erişim adresi: https://doi.org/10.1007/s11004-012-9398-1
20. Stein S., Wysession M., 2003. An introduction to seismology, earthquakes, and earth structure. Blackwell Publishing.
21. Toledo P., Riquelme S., Campos J., 2015. Earthquake source parameters which display first digit phenomenon, Nonlinear Processes in Geophysics Discussions, 2. 811-832. DOI: 10.5194/npgd-2-811-2015.
22. Turcotte D.L., Schubert G., 2002. Geodynamics, Cambridge University Press, 2.
23. Zeng Z., Yang C., Zhou Z., Chen W., 2019. The Application of Benford's law in earthquake magnitude data: A Comparative Study on the 2008 Wenchuan Earthquake in China, Mathematical Geosciences, 51(1), 119-134.
24. Zhou Y., Wu Y., 2019. Seismic magnitude estimation with convolutional neural network, Geophysical Research Letters, 46(2), 798-807.