Abstract
Earthquakes are natural phenomena that can be viewed in three dimensions: time, space and magnitude. Earthquakes can be investigated not only physically, but also mathematically. In this study, semi-Markov models are applied, which can be considered as useful methods to analyze and forecast the occurrence of future earthquakes based on previous earthquake data. In the present study, the target region, Iran, is divided into zones, and each zone is examined as one of the semi-Markov model states. Several methods to determine the levels of forecasting error are then introduced and applied to the target area. The results of the application of these semi-Markov models to investigate and forecast the occurrence of future earthquakes are obtained and analyzed mathematically. A new zoning method is developed and compared with that of Karakaisis, through the proposed forecasting method. Moreover, the effects of the type of zoning and the number of zones on the forecasting error of the next earthquake occurrences are investigated using several algorithms.<br />
Highlights
Earthquakes can be examined both mathematically and physically [Sadeghian 2007]
Markov models have already been applied for earthquake occurrence analysis [Di Luccio et al 1997, Console 2001, Console et al 2002]; in this regard, a few studies have recommended the use of semi-Markov models [Patwardhan et al 1980, Altinok and Kolcak 1999, Sadeghian and Jalali-Naini 2008b, Jalali-Naini and Sadeghian 2009]
An algorithm is presented for mean square error (MSE), which can be used with some changes for both mean absolute deviation (MAD) and method 2
Summary
Earthquakes can be examined both mathematically and physically [Sadeghian 2007]. Stochastic processes represent one of the branches of mathematics that can be applied to probabilistic investigations of these phenomena, and one of the stochastic process models that has been frequently applied over recent years is the Markov model, and especially the semi-Markov model. Semi-Markov models belong to those that can model events that have a relationship with previous events [Jalali-Naini 1997, Minh 2001, Rice 2007, Sadeghian and Jalali-Naini 2008a]. For analyzing of the three temporal, spatial, magnitudinal dimensions of earthquakes, Markov models, including semi-Markov models, can be applied [Patwardhan et al 1980]. Markov models have already been applied for earthquake occurrence analysis [Di Luccio et al 1997, Console 2001, Console et al 2002]; in this regard, a few studies have recommended the use of semi-Markov models [Patwardhan et al 1980, Altinok and Kolcak 1999, Sadeghian and Jalali-Naini 2008b, Jalali-Naini and Sadeghian 2009]. A similar classification has to be used for the magnitudes of the earthquake occurrences too
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
