Abstract
The paper examines the application of semi-Markov models to the phenomenon of earthquakes in Tehran province. Generally, earthquakes are not independent of each other, and time and place of earthquakes are related to previous earthquakes; moreover, the time between earthquakes affects the pattern of their occurrence; thus, this occurrence can be likened to semi-Markov models. In our work, we divided the province of Tehran into six regions and grouped the earthquakes regarding their magnitude into three classes. Using a semi-Markov model, it proceeds to predict the likelihood of the time and place of occurrence of earthquakes in the province.
Highlights
Forecasting the time and place of earthquakes is considered to be very important in science (Sadeghian 2007)
While forecasting time or place alone cannot help prevent devastation caused by earthquakes, it is helpful if both dimensions are looked at together; it is useful to consider the dimension of magnitude as the third dimension along them
Some researchers have studied on earthquake prediction using a Markov chain model, and few of them have considered the model as semi-Markov (Altinok and Kolcak 1999; Patwardhan et al 1980)
Summary
Forecasting the time and place of earthquakes is considered to be very important in science (Sadeghian 2007). Some researchers have studied on earthquake prediction using a Markov chain model (such as Di Luccio et al 1997; Console et al 2002; Console 2001), and few of them have considered the model as semi-Markov (Altinok and Kolcak 1999; Patwardhan et al 1980). If all holding times in a semi-Markov chain are equal to a constant value, the chain can be studied as a discrete-time Markov chain To describe it completely, we need only to have all transition probabilities. N is the number of time intervals We must specify both the holding time mass functions and the transition probabilities to describe a discrete-time semi-Markov process completely (see Minh 2001; Altinok and Kolcak 1999; Kulkarni 1995; Jenamani et al 2003). These probabilities can be used for studying earthquake hazards (Altinok and Kolcak 1999; Patwardhan et al 1980) and evaluating seismic hazard (Nava et al 2005)
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