SEMI-MARKOV MODELS FOR SEISMIC HAZARD ASSESSMENT IN CERTAIN AREAS OF GREECE
Published:
Jan 25, 2010
Keywords:
Semi-Markov process semi-Markov kernel sojourn times earthquakes
Abstract
The long-term probabilistic seismic hazard is studied through the application of semi-Markov model. In this model a sequence of earthquakes is considered as a Markov process and the waiting time distributions depend only on the type of the last and the next event. The principal hypothesis of the model is the property of one-step memory, according to which the probability of moving to any future state depends only on the present state. The model under consideration defines a continuous-time, discrete-state stationary process in which successive state occupancies are governed by the transition probabilities of the Markov process. The space of states is considered to be finite and the process started far in the past has achieved stationarity. Firstly, a non-parametric method is applied in order to determine the waiting times. Then, the waiting times derived by means of the exponential and Weibull distributions will be compared to each other, as well as with the actual waiting times. Thus, the probability of occurrence of the anticipated earthquakes of a specific magnitude scale is calculated. The models are applied to an historical catalogue for Northern Aegean Sea.
Article Details
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Votsi, I., Limnios, N., Tsaklidis, G., & Papadimitriou, E. (2010). SEMI-MARKOV MODELS FOR SEISMIC HAZARD ASSESSMENT IN CERTAIN AREAS OF GREECE. Bulletin of the Geological Society of Greece, 43(4), 2200–2009. https://doi.org/10.12681/bgsg.11411
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- Seismology
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References
Alvarez, E. E., 2005. Estimation in Stationary Markov Renewal Processes, with Application to
Earthquake Forecasting in Turkey. Methodology and Computing in Applied Probability 7,
-130.
Alvarez, E. E., 2005. Smoothed nonparametric estimation in window censored semi-Markov
processes. Journal of Statistical Planning and Inference 131, 209-229.
Anderson, A. W., Goodman, L. A., 1957. Statistical inference about Markov chains. Ann. Math.
Statist. 28, 89-110.
Andersen, P. K., Borgan, O., Gill, R. D. & Keiding, N., 1993. Statistical Models Based on
Counting Processes. New York: Springer.
Balakrishnan, N., Limnios, N., Papadopoulos, C., 2001. Basic probabilistic models in reliability.
In: Balakrishnan, N., Rao, C. R., eds. Handbook of Statistics 20. Amsterdam: North-Holland.
Cluff, L. S., Patwardhan, A. S. & Coppersmith, K. J., 1980. Estimating the probability of occurrences
of surface faulting earthquakes on the Wasatch fault zone, Utah. Bulletin of Seismological
Society of America 70, 5, 1463-1478.
Console, R., Rhodes, D. A., Murru, M, Evison, F. F., Papadimitriou, E. E. & Karakostas, V. G.,
Comparative performance of time-invariant, long-range and short-range forecasting
models on the earthquake catalogue of Greece. Journal of Geophysical Research 111,
B09304.
Garavaglia, E., Pavani, R, 2009. About Earthquake Forecasting by Markov Renewal Processes.
Methoodol. Comput. Appl. Probab.
Number of Months Probability of next event in
State2 if last event in State 1
Probability of next event in
State 2 if last event in State 2
0.1318 0.0306
0.5546 0.2006
Number of Months Probability of next event in
State 1 if last event in State 1
Probability of next event in
State 1 if last event in State 2
0.0253 0.1076
0.1796 0.4378
XLIII, No 4 – 2208
Greenwood, P. E., Wefelmeyer, W., 1996. Empirical Estimators for Semi-Markov Processes.
Mathematical Methods of Statistics 5, 299-315.
Janssen, J. Limnios, N., (eds). 1999. Semi-Markov Models and Applications. Dordrecht: Kluwer
Academic.
Kiremidjian, A. S., Anagnos, T., 1984. Stochastic slip-predictable model for earthquake occurrences.
Bulletin of Seismological Society of America 72, 2, 739-755.
Limnios, N., Ouhbi, B., 2006. Nonparametric estimation of some important indicators in reliability
for semi-Markov processes, Statistical Methodology 3, 341-350.
Limnios, N., Ouhbi, B., 2003. Nonparametric reliability estimation of semi-Markov processes,
Journal of Statistical Planning and Inference 109, 155-165.
Limnios, N., Ouhbi, B. & Sadek, A., 2005. Empirical estimator of stationary distribution for
semi- Markov processes. Communications in Statistics-Theory and Methods 34, 287-995.
Limnios, N., Opriçan, G., 2001. Semi-Markov Processes and Reliability, Birkhäuser, Boston.
Ouhbi, B., Limnios, N., 2001. Non-parametric Estimation for Semi-Markov Processes Based
on its Hazard Rate Functions. Statistical Inference for Stochastic Processes 2, 151-173.
Limnios, N., Ouhbi, B., 2003. Empirical estimators and related functions for semi-Markov
systems. In: Linqvist, B., Doksum, K., (eds). Mathematical and Statistical Methods in Reliability.
Word Scientific.
Papadimitriou, E. E., Sykes, L. R., 2001. Evolution of the stress field in the northern Aegean
Sea (Greece). Geophysical Journal International 146, 747-759.
