Parametric Estimation of Expected Number of Earthquakes and Hitting Time Distribution Based on Semi-Markov Model in south of Iran South

Document Type : Original Paper

Authors

1 Department of Statistics, Shiraz University, Shiraz, Iran

2 Department of Geology, Shiraz University, Shiraz, Iran

Abstract

In this paper, a semi-Markov model is applied for description the seismicity patterns in the region within (27 °, -30 °) latitude and (55 °, 58 °) longitude, which includes some portion of the Kerman and Hormozgan provinces. The classification of states of the model is based on magnitudes of earthquakes. Because of the features of Weibull distribution and earthquake characteristics, it is assumed that the crossing times between states are Weibull. Some numerical estimates for the semi-Markov kernel and the mean recurrence times of earthquakes have been presented based on the past information. A new computational method which is on the basis of the inverse Laplace transform approximation have been introduced for estimating the expected number of earthquakes, distribution of hitting time of strongest earthquakes and transition functions. Estimation of above functions are rapid by using this method, with short processing times. The past history has been used for prediction while the probabilities of future earthquakes with different magnitudes and time intervals have been calculated. The obtained results are consistent with the latest recent earthquake in this zone, which shows the validity of the employed model.

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References

[1] Cluff, L.S., Patwardhan, A.S. and Coppersmith, K.J. (1980). Estimating the probability of occurrences of surface faulting earthquakes on the Wasatch fault zone, Utah. Bull. Seism, Soc. Am. 70, 1463–1478. [2] Altinok, Y. and Kolcak, D. (1999). An
 
application of the semi-Markov model for earthquake occurrences in North Anatolia, Turkey. Journal of Balkan Geophysical Society, 2(4), 90-99. [3] Alvarez, E.E. (2005). Estimation in stationary Markov renewal processes with application to earthquake
forecasting in Turkey. Methodology and Computing in Applied Probability, 7, 119–130. [4] Garavaglia, E. and Pavani, R. (2011).
About earthquake forecasting by Markov renewal processes. Methodology and Computing in Applied Probability, 13, 155-169. [5] Vots, I., Limnios, N., Tsaklidis, G. and Papadimitriou, E. (2012). Estimation of the expected number of earthquake occurrences
based on semi-markov models. Methodology and Computing in Applied Probability, 14, 685–703.
Journal of Advanced Mathematical Modeling
Volume 3, Issue 2 - Serial Number 2
November 2014
Pages 1-20

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History

  • Receive Date: 19 August 2013
  • Revise Date: 23 May 2014
  • Accept Date: 10 June 2014

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