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ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE

Year 2016, Volume: 29 Issue: 3, 635 - 644, 30.09.2016

Abstract

In this study, we build a Markov chain model for the earthquakes in Southwestern China by following the maximum entropy principle, while the states of Markov chain are the co-occurrence of earthquakes with different magnitudes.  In this case an approximation is to focus on just the occurrences of the most serious magnitude earthquakes and neglect the others.  Our approximation to this situation is to take into account all magnitude earthquakes if they occur at least once in any given period.  In order to reveal the feature of this Markov chain in respect of first passage time distributions we run a long term simulation with occurrences of all the 3 categories of earthquakes.  Finally, we give both fitted distributions and multinomial approximations to the distribution of first passage time for some states.

References

  • Huang, Jinli, Dapeng Zhao, and Sihua Zheng. "Lithospheric structure and its relationship to seismic and volcanic activity in southwest China." Journal of Geophysical Research: Solid Earth 107.B10 (2002).
  • Vere-Jones, D. "A Markov model for aftershock occurence." pure and applied geophysics 64.1: 31-42 (1966).
  • Hagiwara, Yukio. "A stochastic model of earthquake occurrence and the accompanying horizontal land deformation." Tectonophysics 26.1: 91-101 (1975).
  • Ogata, Yosihiko. "Statistical models for earthquake occurrences and residual analysis for point processes." Journal of the American Statistical association 83.401: 9-27 (1988).
  • Tsapanos, Theodoros M., and Alexandra A. Papadopoulou. "A discrete Markov model for earthquake occurrences in Southern Alaska and Aleutian Islands." Journal of the Balkan Geophysical Society 2.3: 75-83 (1999).
  • Nava, F. A., Herrera, C., Frez, J., and Glowacka, E. "Seismic hazard evaluation using Markov chains: application to the Japan area." pure and applied geophysics 162.6-7: 1347-1366 (2005).
  • Herrera, C., F. A. Nava, and C. Lomnitz. "Time-dependent earthquake hazard evaluation in seismogenic systems using mixed Markov Chains: An application to the Japan area." Earth, planets and space 58.8: 973-979 (2006).
  • Cavers, M. S., and K. Vasudevan. "Insight into earthquake sequencing: analysis and interpretation of time-series constructed from the directed graph of the Markov chain model." Nonlinear Processes in Geophysics Discussions 2: 399-424 (2015).
  • Cavers, Michael, and Kris Vasudevan. "Spatio-temporal complex Markov Chain (SCMC) model using directed graphs: Earthquake sequencing." Pure and Applied Geophysics 172.2: 225-241 (2015).
  • Serpil, UNAL., and Salih CELEBIOGLU. "A Markov Chain Modelling Of the Earthquakes Occuring In Turkey." Gazi University Journal of Science 24.2: 263-274 (2011).
  • Harris, Theodore Edward. "First passage and recurrence distributions." Transactions of the American Mathematical Society 73.3: 471-486 (1952).
  • Harrison, Peter G., and William J. Knottenbelt. "Passage time distributions in large Markov chains." ACM SIGMETRICS Performance Evaluation Review. Vol. 30. No. 1. ACM, (2002).
  • Gul, Murat, and Salih Celebioglu. "Distribution of First Passage Times for Lumped States in Markov Chains." Journal of Mathematics and System Science 5.8: 315-329 (2015).
  • Lawler GF Introduction to stochastic process (2/e). Chapman & Hall, London (2006).
  • Çınlar, E., “Introduction to Stochastic Processes”, Englewood Cliffs, New Jersey, 106-277 (1997).
  • Izquierdo, L. R., Izquierdo, S. S., Galán, J. M., & Santos, J. I. Combining Mathematical and Simulation Approaches to Understand the Dynamics of Computer Models. In Simulating Social Complexity (pp. 235-271). Springer Berlin Heidelberg. (2013).
  • Shannon, Claude Elwood. "A mathematical theory of communication." ACM SIGMOBILE Mobile Computing and Communications Review 5.1: 3-55 (2001).
  • Jaynes, Edwin T. "Information theory and statistical mechanics." Physical review 106.4: 620 (1957).
  • Cover, Thomas M., and Joy A. Thomas. Elements of information theory. John Wiley & Sons, (2012).
Year 2016, Volume: 29 Issue: 3, 635 - 644, 30.09.2016

Abstract

References

  • Huang, Jinli, Dapeng Zhao, and Sihua Zheng. "Lithospheric structure and its relationship to seismic and volcanic activity in southwest China." Journal of Geophysical Research: Solid Earth 107.B10 (2002).
  • Vere-Jones, D. "A Markov model for aftershock occurence." pure and applied geophysics 64.1: 31-42 (1966).
  • Hagiwara, Yukio. "A stochastic model of earthquake occurrence and the accompanying horizontal land deformation." Tectonophysics 26.1: 91-101 (1975).
  • Ogata, Yosihiko. "Statistical models for earthquake occurrences and residual analysis for point processes." Journal of the American Statistical association 83.401: 9-27 (1988).
  • Tsapanos, Theodoros M., and Alexandra A. Papadopoulou. "A discrete Markov model for earthquake occurrences in Southern Alaska and Aleutian Islands." Journal of the Balkan Geophysical Society 2.3: 75-83 (1999).
  • Nava, F. A., Herrera, C., Frez, J., and Glowacka, E. "Seismic hazard evaluation using Markov chains: application to the Japan area." pure and applied geophysics 162.6-7: 1347-1366 (2005).
  • Herrera, C., F. A. Nava, and C. Lomnitz. "Time-dependent earthquake hazard evaluation in seismogenic systems using mixed Markov Chains: An application to the Japan area." Earth, planets and space 58.8: 973-979 (2006).
  • Cavers, M. S., and K. Vasudevan. "Insight into earthquake sequencing: analysis and interpretation of time-series constructed from the directed graph of the Markov chain model." Nonlinear Processes in Geophysics Discussions 2: 399-424 (2015).
  • Cavers, Michael, and Kris Vasudevan. "Spatio-temporal complex Markov Chain (SCMC) model using directed graphs: Earthquake sequencing." Pure and Applied Geophysics 172.2: 225-241 (2015).
  • Serpil, UNAL., and Salih CELEBIOGLU. "A Markov Chain Modelling Of the Earthquakes Occuring In Turkey." Gazi University Journal of Science 24.2: 263-274 (2011).
  • Harris, Theodore Edward. "First passage and recurrence distributions." Transactions of the American Mathematical Society 73.3: 471-486 (1952).
  • Harrison, Peter G., and William J. Knottenbelt. "Passage time distributions in large Markov chains." ACM SIGMETRICS Performance Evaluation Review. Vol. 30. No. 1. ACM, (2002).
  • Gul, Murat, and Salih Celebioglu. "Distribution of First Passage Times for Lumped States in Markov Chains." Journal of Mathematics and System Science 5.8: 315-329 (2015).
  • Lawler GF Introduction to stochastic process (2/e). Chapman & Hall, London (2006).
  • Çınlar, E., “Introduction to Stochastic Processes”, Englewood Cliffs, New Jersey, 106-277 (1997).
  • Izquierdo, L. R., Izquierdo, S. S., Galán, J. M., & Santos, J. I. Combining Mathematical and Simulation Approaches to Understand the Dynamics of Computer Models. In Simulating Social Complexity (pp. 235-271). Springer Berlin Heidelberg. (2013).
  • Shannon, Claude Elwood. "A mathematical theory of communication." ACM SIGMOBILE Mobile Computing and Communications Review 5.1: 3-55 (2001).
  • Jaynes, Edwin T. "Information theory and statistical mechanics." Physical review 106.4: 620 (1957).
  • Cover, Thomas M., and Joy A. Thomas. Elements of information theory. John Wiley & Sons, (2012).
There are 19 citations in total.

Details

Journal Section Statistics
Authors

Tianliu Li This is me

Salih Çelebioğlu

Publication Date September 30, 2016
Published in Issue Year 2016 Volume: 29 Issue: 3

Cite

APA Li, T., & Çelebioğlu, S. (2016). ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE. Gazi University Journal of Science, 29(3), 635-644.
AMA Li T, Çelebioğlu S. ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE. Gazi University Journal of Science. September 2016;29(3):635-644.
Chicago Li, Tianliu, and Salih Çelebioğlu. “ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE”. Gazi University Journal of Science 29, no. 3 (September 2016): 635-44.
EndNote Li T, Çelebioğlu S (September 1, 2016) ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE. Gazi University Journal of Science 29 3 635–644.
IEEE T. Li and S. Çelebioğlu, “ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE”, Gazi University Journal of Science, vol. 29, no. 3, pp. 635–644, 2016.
ISNAD Li, Tianliu - Çelebioğlu, Salih. “ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE”. Gazi University Journal of Science 29/3 (September 2016), 635-644.
JAMA Li T, Çelebioğlu S. ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE. Gazi University Journal of Science. 2016;29:635–644.
MLA Li, Tianliu and Salih Çelebioğlu. “ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE”. Gazi University Journal of Science, vol. 29, no. 3, 2016, pp. 635-44.
Vancouver Li T, Çelebioğlu S. ON THE CO-OCCURRENCE OF DIFFERENT MAGNITUDE EARTHQUAKES: SOUTHWESTERN CHINA CASE. Gazi University Journal of Science. 2016;29(3):635-44.