The modeling of frequency-magnitude of earthquakes in Indonesia using Poisson regression

The occurrence of earthquakes is increasing almost every year in Indonesia. From January 2014 to December 2017, there was around 16,645 earthquakes with magnitude ≥4 Richter Scale occurred. This study is the first part of earthquake risk modeling that we conducted. This study aims to analyze the relationship of frequency and magnitude of the earthquakes by using Poisson Regression and Generalized Poisson Regression. The data used in this study is frequency and magnitude data of earthquakes occurred in Indonesia. The data were selected by selecting earthquakes with magnitude ≥4 Richter Scale in the period January 2014 to December 2017 (4 years). The dependent variable is frequency, meanwhile the magnitude is independent. The frequency of earthquakes is the rounded value of natural log (Ln) transformation of cumulative frequency of earthquakes occurred in time period, and tested that it follows poisson distribution. The Poisson Regression analysis was done for the first, then the analysis continued by using Generalized Poisson Regression to observe whether there is equidispersion effect. The result of two models was compared then continued by selecting the best model based on the smallest of Akaike Information Criterion (AIC). According to the result of Poisson Regression as well as Generalized Poisson Regression, the magnitude is significantly affect the frequency. Based on AIC, the best model of frequency-magnitude relationship is presented by Poisson Regression model, μ = exp (4.048 - 0.3935x).