Probabilistic Modeling of Earthquake Interevent Times in Different Regions of Pakistan

Pakistan and its surroundings are among the most seismically active regions in the world. Occurrence of major earthquakes in Pakistan is a real hazard for life. In this study, an attempt has been made to estimate the seismic hazard in terms of earthquake occurrence conditional probabilities in different zones of Pakistan. We assumed that the temporal data of earthquakes, that occurred in different regions of Pakistan follow a certain probability distribution. In present study, the 10 probability models that include the exponential, gamma, generalized Pareto, inverse Pareto, kappa, log-logistic, lognormal, Pareto, transformed gamma and Weibull are used to analyze the interevent times of the earthquakes with $M_w\ge 5.5$ in different regions of Pakistan. In current study, Pakistan territory has been divided into five different seismic zones based on their tectonic settings. Parameters of the considered distributions are estimated by using the maximum likelihood method using the reviewed earthquake catalogue compiled by Centre for Earthquake Studies (CES), Pakistan. The best suitable model in each seismic zone is selected through various model selection criteria. The results show that the log-logistic distribution provides the best representation of earthquake temporal data of plate convergence zones; while the gamma distribution best explains the temporal seismicity of other tectonic regimes including the transform plate boundary, fold and thrust belts and stable plains. The most suitable gamma and log-logistic models are used for the earthquake occurrence probabilities in different regions of Pakistan. The highest $(>96\%)$ and the least $(>30\%)$ earthquake occurrence conditional probabilities are respectively observed for Zones I and V among five seismic zones for different combinations of elapsed time $\left(\tau \right)$ and time interval $\left(\upsilon \right)$. The estimated probability of $M_w\ge 5.5$ event reaches (60–98)% in next (3–9) years time interval without any elapsed time $(\tau =0)$ in Zones II to IV (the time periods corresponding to 3–9 years time interval are 2016–2022, 2020–2026 and 2019–2025 in Zones I, II and III respectively) since the last event occurrence time in each of these seismic zone. The mean values of the interevent time for an earthquake occurrence of $M_w\ge 5.5$ in Zone-I to Zone-V are respectively calculated as 0.90, 1.78, 4.52, 3.35 and 11.76 years, respectively. The results of the present study indicate that Zone-I has potential capability of producing an earthquake of magnitude 5.5 or higher in next 3 years (2019–2021) time interval since the last event occurrence in May 2018. The earthquake hazard curves associated with earthquake occurrence probabilities are also developed in order to understand the current and future earthquake mechanism in the study region.