Statistical Analysis of the Temporal Pattern of Seismicity in the Zagros Region

Earthquake is one of the major natural disasters that the current knowledge of the human kind is not able to predict it yet; however, it can be partly subjected to risk assessment and recognition of its pattern by using statistical methods. The Zagros region of Iran is known for its high seismic activity. This mountain belt is amongst the world’s most seismically active mountain ranges. This seismogenic zone is the result of the collision between the Arabian and Eurasian plates during the Cenozoic. Seismic activity in this zone is characterized by the occurrence of low to moderate magnitude earthquakes, most of which nucleate on blind (hidden) thrust faults. In this study, the temporal pattern of occurrence of earthquakes in the Zagros region for a period of more than 11 years, from the beginning of 2005 to the end of October 2016, have been examined using statistical methods. In this regard, the matching degree of the examined data with the Poisson distribution was evaluated and time series analysis of the data was carried out.
Methodology and Data Analysis: Randomness in time, space and size is the most obvious property of earthquake occurrence. At the same time, there are ample evidences to suggest that earthquakes do not occur in a completely disordered manner. The randomness of the occurrence of earthquakes in time or space can be evaluated by statistical methods such as Poisson distribution fitting test. In addition, time series analysis has been widely used in many applications, e.g. earthquake forecasting and the temporal pattern of earthquake occurrences, as a stochastic process, can be studied by this method. In this study, by using the goodness of fit test based on the chi-square statistic, the suitability of the Poisson distribution with λ parameter (the average rate of the earthquake occurrence) fitness to seismic data of the region with different ranges was assessed. Additionally, in this research, due to the low randomness degree of the data in time, the time series modeling of the data were carried out to find the productive time pattern model of the data. A sample of 150 data, covering the end part of the catalogue, was selected for the analysis and modeling of time series, and two main attributes of the earthquake data, magnitude and focal depth, as quantitative variables, were included in this modeling.
According to the obtained results, it can be said that temporal distribution of these data do not completely follow the Poisson distribution model, but with increasing the earthquake magnitude, the data probability distribution approaches to the Poisson distribution. Besides, the results of the time series analysis of data show that the temporal pattern of earthquake occurrence based on the magnitude variable has a good correlation with ARMA (1, 1) model. Similarly, considering the focal depth as variable in modeling, the time series models acceptably match ARMA (0, 1) and ARMA (0,2) models. These findings were verified by Box and Pierce method. According to the obtained results of this research, it is concluded that the earthquake occurrence in the Zagros region do not completely show a random pattern, and time series analysis modeling can be acceptably employed for finding the temporal behavior of seismicity in this region. However, the techniques used in this research are data driven and the reliability of the results obtained depends on the quality of the input datasets. Due to the insufficiency and inaccuracy of the studied data catalogue, it is expected that in future, more appropriate and reliable results could be achieved by reducing the seismic data errors and using the data with longer time periods.