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Koşullu Otoregresif Bayes Model Yaklaşımı ile Türkiye Deprem Verilerinin Mekânsal Analizi

Year 2022, Volume: 17 Issue: 1, 111 - 127, 27.05.2022
https://doi.org/10.29233/sdufeffd.983296

Abstract

Mekânsal veri türlerinden birisi olan alansal verilerde gözlem değerleri mekâna bağlı olarak değiştiği için gözlem değerleri arasında mekânsal otokorelasyon ortaya çıkar. Mekânsal modellerde mekân bilgisinin modele katılabilmesi için alanların ilişkilerini tanımlayan komşuluk matrisinin oluşturulması gerekir. Bu nedenle mekânsal otokorelasyonu dikkate alan modellerin kullanımı son yıllarda yaygınlaşmıştır. Genelleştirilmiş Doğrusal Modeller (GDM), mekânsal otokorelasyonun modellenmesinde yetersiz kalmaktadır. Koşullu Otoregresif Bayes (CARBayes) modeli ile daha önceden deprem verilerinin modellenmesi ile ilgili bir çalışma yapılmamıştır. Bu yüzden, bu çalışmada 2016 yılında Türkiye’de meydana gelen deprem sayıları kullanılarak CARBayes modelinin kullanımı önerilmiştir. CARBayes modeli Genelleştirilmiş Doğrusal Mekânsal Model (GDMM) formundadır. Verilerde alansal birim olarak “iller” alınmış ve komşuluk matrisleri oluşturulurken idari bölünüş sınırları dikkate alınmıştır. Oluşturulan komşuluk matrisi üzerinden kurulan permütasyon testi sonucunda deprem sayılarında mekânsal ilişki çıkmıştır. Bu yüzden, deprem sayıları ile ortalama deprem büyüklüğü arasındaki ilişki için GDMM’de mekân bilgisi komşuluk matrisi yardımı ile rastgele etki olarak modele eklenmiştir. Böylece artıklardaki otokorelasyon problemi çözülmüş ve tahmin değerleri elde edilmiştir. Tahmin değerlerinden yararlanılarak bir risk değeri hesaplanmış ve haritalandırma aracılığıyla riskli iller belirlenmiştir.

References

  • N. Cressie, Statistics for Spatial Data, Revised Edition, John Wiley & Sons, New York, 1993.
  • R. P. Haining, Spatial Data Analysis: Theory and Practice, Cambridge University Press, Cambridge, 2003.
  • O. Schabenberger and C. A. Gotway, Statistical Methods for Spatial Data Analysis, Chapman & Hall/CRC, Boca Raton/London, 2005.
  • S. R. Bivand, E. Pebesma, and V. Gomez-Rubio, Applied Spatial Data Analysis with R, Second Edition, Springer, 2013.
  • A. D. Cliff and J. K. Ord, Spatial Processes: Models and Applications, Pion, London, 1981.
  • D. Griffith, “What is spatial autocorrelation?,” L’Espace geographique, 21, 265–280, 1992.
  • Y. Chun and D. A. Griffith, Spatial Statistics & Geostatistics, Sage, Thousand Oaks, CA, 2013.
  • A. D. Cliff and J. K. Ord, Spatial Autocorrelation, Pion, London, 1973.
  • M. D. Ward and K. S. Gleditsch, Spatial regression models, Sage, Thousand Oaks, CA, 2008.
  • R. Haining, Spatial Data Analysis in the Social and Environmental Sciences, Cambridge University Press, Cambridge, 1990.
  • T. C. Bailey and A. C. Gatrell, Interactive Spatial Data Analysis, England, Addison Wesley Longman, 1995.
  • W. Kissling and G. Carl, “Spatial autocorrelation and the selection of simultaneous autoregressive models,” Global Ecol. Biogeogr., 17, 59–71, 2008.
  • E. Schiappapietra and J. Douglas, “Modelling the spatial correlation of earthquake ground motion: Insights from the literature, data from the 2016–2017 Central Italy earthquake sequence and ground-motion simulations,” Earth-Sci. Rev., Volume 203, 103139, 2020.
  • P. M. Mai and G. C. Beroza, “A spatial random field model to characterize complexity in earthquake slip,” J. Geophys. Res., 107(B11), 2308, 2002.
  • N. Jayaram and J. W. Baker, “Considering spatial correlation in mixed-effects regression, and impact on ground-motion models,” Bull. Seismol. Soc. Am., 100(6), 3295-3303, 2011.
  • N. Jayaram and J. W. Baker, “Correlation model for spatially distributed round-motion intensities,” Earthquake Engng Struct. Dyn., 38:1687–1708, 2009.
  • D. Lavallée, P. Liu, and R. J. Archuleta, “Stochastic model of heterogeneity in earthquake slip spatial distributions,” Geophys. J. Int., Volume 165(2), 622–640, 2006.
  • Y. Ogata and K. Katsura, “Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues,” Geophys. J. Int., 113(3), 727–738, 1993.
  • V. Sokolov, F. Wenzel, J. Wen-Yu, and W. Kuo-Liang, “Uncertainty and Spatial Correlation of Earthquake Ground Motion in Taiwan,” Terr. Atmos. Ocean. Sci., 21(6), 905-921, 2010.
  • K. Goda and H. P. Hong, “Spatial correlation of peak ground motions and response spectra,” Bull. Seismol. Soc. Am., 98, 354-365, 2008.
  • K. Goda and G. M. Atkinson “Probabilistic characterization of spatially correlated response spectra for earthquakes in Japan”, Bull. Seismol. Soc. Am., 99, 3003-3020, 2009.
  • L. Bakacak, “Genelleştirilmiş doğrusal mekânsal modellere koşullu otoregresif model yaklaşımı,” Yüksek Lisans Tezi, Fen Bilimleri Enstitüsü, Hacettepe Üniversitesi, Ankara, Türkiye, 2018.
  • B. Leroux, X. Lei, and N. Breslow, Estimation of disease rates in small areas: a new mixed model for spatial dependence, Statistical models in epidemiology, the environment and clinical trials, New York, Springer-Verlag, 135–78, 1999.
  • D. Lee, “CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors,” J. Sta.l Softw., Volume 55, Issue 13, 2013.
  • B.Ü. KRDAE Bölgesel Deprem-Tsunami İzleme ve Değerlendirme Merkezi, Avaliable: http://www.koeri.boun.edu.tr/sismo/zeqdb/.
  • R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Avaliable: http://www.R-project.org/.
  • J. Geweke, “Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments,” In Bayesian Statistics, University Press, 169-193, 1992.
  • P. McCullagh and J. A. Nelder, Generalized Linear Models, Second Edition, New York, Chapman & Hall, 1989.

Spatial Analysis of Turkey Earthquake Data with Conditional Autoregressive Bayesian Model Approach

Year 2022, Volume: 17 Issue: 1, 111 - 127, 27.05.2022
https://doi.org/10.29233/sdufeffd.983296

Abstract

Since the observation values in (spatial) areal data, which is one of the spatial data types, change depending on the space, spatial autocorrelation occurs between the observation values. In spatial models, in order for the spatial information to be included in the model, the neighborhood matrix, which defines the relations of the areas, must be created. For this reason, the use of models that take into account spatial autocorrelation has become widespread in recent years. Generalized Linear Models (GLM) are insufficient in modeling spatial autocorrelation. There is no previous study which has been done on modeling earthquake data with the Conditional Autoregressive Bayes (CARBayes) model. Therefore, in this study, the use of CARBayes model has been proposed by using the number of earthquakes occurred in Turkey in 2016. The CARBayes model is in the form of the Generalized Linear Spatial Model (GLSM). In the data set, “provinces” are taken as the spatial unit and administrative division boundaries are taken into account while creating neighborhood matrices. As a result of the permutation test established on the created neighborhood matrix, a spatial relationship is found in the earthquake numbers. Therefore, for the relationship between the number of earthquakes and the average earthquake size, the spatial information in GLSM is added to the model as a random effect with the help of the neighborhood matrix. Thus, the autocorrelation problem in residuals was solved and the predicted values were obtained. A risk value was calculated by using the estimated values and risky provinces were determined by mapping.

References

  • N. Cressie, Statistics for Spatial Data, Revised Edition, John Wiley & Sons, New York, 1993.
  • R. P. Haining, Spatial Data Analysis: Theory and Practice, Cambridge University Press, Cambridge, 2003.
  • O. Schabenberger and C. A. Gotway, Statistical Methods for Spatial Data Analysis, Chapman & Hall/CRC, Boca Raton/London, 2005.
  • S. R. Bivand, E. Pebesma, and V. Gomez-Rubio, Applied Spatial Data Analysis with R, Second Edition, Springer, 2013.
  • A. D. Cliff and J. K. Ord, Spatial Processes: Models and Applications, Pion, London, 1981.
  • D. Griffith, “What is spatial autocorrelation?,” L’Espace geographique, 21, 265–280, 1992.
  • Y. Chun and D. A. Griffith, Spatial Statistics & Geostatistics, Sage, Thousand Oaks, CA, 2013.
  • A. D. Cliff and J. K. Ord, Spatial Autocorrelation, Pion, London, 1973.
  • M. D. Ward and K. S. Gleditsch, Spatial regression models, Sage, Thousand Oaks, CA, 2008.
  • R. Haining, Spatial Data Analysis in the Social and Environmental Sciences, Cambridge University Press, Cambridge, 1990.
  • T. C. Bailey and A. C. Gatrell, Interactive Spatial Data Analysis, England, Addison Wesley Longman, 1995.
  • W. Kissling and G. Carl, “Spatial autocorrelation and the selection of simultaneous autoregressive models,” Global Ecol. Biogeogr., 17, 59–71, 2008.
  • E. Schiappapietra and J. Douglas, “Modelling the spatial correlation of earthquake ground motion: Insights from the literature, data from the 2016–2017 Central Italy earthquake sequence and ground-motion simulations,” Earth-Sci. Rev., Volume 203, 103139, 2020.
  • P. M. Mai and G. C. Beroza, “A spatial random field model to characterize complexity in earthquake slip,” J. Geophys. Res., 107(B11), 2308, 2002.
  • N. Jayaram and J. W. Baker, “Considering spatial correlation in mixed-effects regression, and impact on ground-motion models,” Bull. Seismol. Soc. Am., 100(6), 3295-3303, 2011.
  • N. Jayaram and J. W. Baker, “Correlation model for spatially distributed round-motion intensities,” Earthquake Engng Struct. Dyn., 38:1687–1708, 2009.
  • D. Lavallée, P. Liu, and R. J. Archuleta, “Stochastic model of heterogeneity in earthquake slip spatial distributions,” Geophys. J. Int., Volume 165(2), 622–640, 2006.
  • Y. Ogata and K. Katsura, “Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues,” Geophys. J. Int., 113(3), 727–738, 1993.
  • V. Sokolov, F. Wenzel, J. Wen-Yu, and W. Kuo-Liang, “Uncertainty and Spatial Correlation of Earthquake Ground Motion in Taiwan,” Terr. Atmos. Ocean. Sci., 21(6), 905-921, 2010.
  • K. Goda and H. P. Hong, “Spatial correlation of peak ground motions and response spectra,” Bull. Seismol. Soc. Am., 98, 354-365, 2008.
  • K. Goda and G. M. Atkinson “Probabilistic characterization of spatially correlated response spectra for earthquakes in Japan”, Bull. Seismol. Soc. Am., 99, 3003-3020, 2009.
  • L. Bakacak, “Genelleştirilmiş doğrusal mekânsal modellere koşullu otoregresif model yaklaşımı,” Yüksek Lisans Tezi, Fen Bilimleri Enstitüsü, Hacettepe Üniversitesi, Ankara, Türkiye, 2018.
  • B. Leroux, X. Lei, and N. Breslow, Estimation of disease rates in small areas: a new mixed model for spatial dependence, Statistical models in epidemiology, the environment and clinical trials, New York, Springer-Verlag, 135–78, 1999.
  • D. Lee, “CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors,” J. Sta.l Softw., Volume 55, Issue 13, 2013.
  • B.Ü. KRDAE Bölgesel Deprem-Tsunami İzleme ve Değerlendirme Merkezi, Avaliable: http://www.koeri.boun.edu.tr/sismo/zeqdb/.
  • R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Avaliable: http://www.R-project.org/.
  • J. Geweke, “Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments,” In Bayesian Statistics, University Press, 169-193, 1992.
  • P. McCullagh and J. A. Nelder, Generalized Linear Models, Second Edition, New York, Chapman & Hall, 1989.
There are 28 citations in total.

Details

Primary Language Turkish
Subjects Mathematical Sciences
Journal Section Makaleler
Authors

Leyla Bakacak Karabenli 0000-0001-8968-7221

Serpil Aktaş 0000-0003-3364-6388

Publication Date May 27, 2022
Published in Issue Year 2022 Volume: 17 Issue: 1

Cite

IEEE L. Bakacak Karabenli and S. Aktaş, “Koşullu Otoregresif Bayes Model Yaklaşımı ile Türkiye Deprem Verilerinin Mekânsal Analizi”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 17, no. 1, pp. 111–127, 2022, doi: 10.29233/sdufeffd.983296.