Semi-Markov chain modeling on earthquake occurrences in selected areas in Luzon

Hannibal Paul A. Causapin

Department of Mathematics and Computing Science, College of Arts and Sciences, Southern Luzon State University


This study aimed to model earthquake occurrences for the next five (5) years in selected areas in Luzon, Philippines using semi-Markov chain. This research focused on estimating the transition matrix, holding time mass functions and interval transition probability matrix for two defined states: region-to-region and magnitude-to-magnitude. Semi-Markov chain was utilized in modeling the earthquakes with magnitude M≥4.0 from 1930-2015 in selected areas in Luzon. The selected areas (13°-16° North latitude by 120°-122° East longitude) were divided into six (6) regions and was used as a state. In addition, magnitudes were classified and used as states (M1<4.6 ; 4.6≤M2≤5.0 ; M3>5.0). From these, the researcher estimated the transition matrices and holding time mass functions. The necessary probability functions were utilized for the determination of interval transition probability matrix. Different dimensions of earthquake like time, location and magnitude were forecasted for the next five (5) years. Based on the findings of the study, the forecasts implies that earthquakes are most probable to happen in some areas of Mindoro and Batangas (13.00°-13.99° North Latitude to 120.00°-120.99° East Longitude) having a magnitude of M>5.0. 

Keywords Semi-Markov Chain Modeling, Earthquakes, Interval transition probability matrix, Forecasts

Full Text: PDF
Philippine Copyright 2018

Suggested APA Citation:

Causapin, Hannibal Paul A. (2018). Semi-Markov chain modeling on earthquake occurrences in selected areas in Luzon.Tilamsik: The Southern Luzon Journal of Arts and Sciences, 10. 67-90.


Aquino, T. (2014). PHIVOLCS: Metro Manila should prepare for earthquake, tsunamis. Retrieved on October 29, 2016 from

Brimicombe, A. (2010). GIS, Environmental Modelling and Engineering, 2nd edition. London: CRC Press, Taylor & Francis. Retrieved on September 3, 2016 from AndEngineering/Gis%20environmental%20modeling%20and%20engineering.pdf

Dela Cruz, G., Romulo, M. & Santos, R. (2015). MAP: Strongest Earthquakes in the Philippines. Retrieved on October 23, 2016 from

Diola, C. (2015). MAPS: Are you in a Metro Manila Earthquake zone? Retrieved on November 10, 2016 from

Doganer, A. & Calik, S. (2012). Estimates of Earthquakes with Markov Models in the East Anatolian Fault Zone. Turkish Journal of Science & Technology, 8(1), 55-61. Retrieved on January 26, 2016 from handle/11508/8465/Doganer.pdf?sequence=1

Grinstead, C. & Snell, L (2006). Introduction to Probability: Theory and Its Application. USA: American Mathematical Society. 

Hillier, F. S. & Lieberman G. J. (2010). Introduction to Operations Research, 9th edition. New York: McGraw-Hill Companies.

Mostafaei, H. & Kordnoori, S. (2013). The Application of Semi-Markov Model in Predicting the Earthquake Occurrences in Alborz Fault Region, Northern Iran. Earth Science India, 6 (IV), pp. 147 – 159. Retrieved from on January 7, 2016.

Ricci, L. (2011). Markov Chain: Basic Concepts. Dipartimento di Informatica. Retrieved from on February 28, 2016.

Sabordino, L. (2015). Top 10 Strongest Earthquake to hit the Philippines. Retrieved from  on October 21, 2016.

Sadeghian, R. (2012). Forecasting time and place of earthquakes using a semi-Markov model (with case study in Tehran Province). Journal of Industrial Engineering International, 8:20. Retrieved on February 1, 2016.

Unal, S. & Celebioglu, S. (2010). A Markov Chain Modelling of the Earthquakes Occuring in Turkey. Gazi University Journal of Science, 24(2): 263-274. Retrieved from on January 6, 2016.