MARKOV RENEWAL MODEL APPLIED TO THE ESTIMATION OF EARTHQUAKE OCCURRENCES

The process of earthquake occurrences can be represented with many analytical models (Votsi
et al.[1]). Some models are based on empirical observations of preliminary events, other
models on physical modelling of the earthquake process and some on statistical analysis of
patterns of seismicity.
The theory of Markov processes can ben applied in various fields since the Markov property
is very intuitive. If we know the past and present of a system, then the future development of
the system is only determined by its present state (Listwon and Saint-Pierre[2]). Hence, the
history of the system does not play a role in its future development. It is called as the
memoryless property. However, the Markov property has its limitations. It enforces
restrictions on the distribution of the sojourn time in a state, which is exponentially distributed
in the continuous case. This is a disadvantage when Markov processes are applied in real-life
applications. Therefore, in this study, we use the Markov renewal process to apply a
previously proposed method for seismic disaster detection and specifically to model large
earthquakes consistently using high-intensity earthquake data that occurred in Turkey during
the 20th century. Among the common non-Poisson models, the Markov renewal process
proposed by Garavaglia and Pavani. A mixture of exponential and Weibull distributions is
used for interevent times by R program