Two-State Poisson Hidden Markov Models for Analysis of Seismicity Activity Rates in West Nusa Tenggara

Abstract

Awareness of seismicity activity rates could be learned from modeling the earthquake events by utilizing the record of seismicity events data in NTB over time which is associated with count time series data. Poisson Hidden Markov Model (PHMM) has been widely applied in various fields, including earthquake event. Therefore, it would be interesting to implement PHMM on earthquake case in NTB. The data can be analyze using PHMM as we can ignore the over-dispersion and dependency relationship among data. The model is the development of Markov Model that consists of (a) observed state, which can be observed directly and (b) hidden state, which cannot be observed directly because it is hidden. Hidden state in this research is defined as seismicity activity rates classified into a low rate and high rate (2 states). The count time series data of earthquake events will be more informative when it is classified into the seismicity activity levels. This research applied earthquake event data (magnitude ≤ M4.7 and depth < 60 km) from January 2009 until September 2018, collected from USGS (United States Geological Survey). The parameter estimation method used in this research is the Bayesian method. The objective of this research is to obtain parameters of 2 state Poisson Hidden Markov Model using the Bayesian approach. Model validation measured by MAE (Mean Absolute Error). Based on the result, the average earthquake cases caused by low seismicity activity rate in NTB over time is 1 event whilst the high rate is 18 events. The probability of low seismicity activity rate influenced by the previous rate and the long run behavior (steady state) in NTB is still larger than the high rate. The achieved two-state PHMM is suitable for modeling the earthquake case in NTB with MAE values of 0.4079.