Prediction of the Maximum Expected Earthquake Magnitude in Iran: From a Catalog with Varying Magnitude of Completeness and Uncertain Magnitudes

Abstract

This paper concerns the problem of predicting the maximum expected earthquake magnitude $\mu$ in a future time interval $T_{\text{f}}$ given a catalog covering a time period $T$ in the past. Different studies show the divergence of the confidence interval of the maximum possible earthquake magnitude $m_{ \hbox{max} }$ for high levels of confidence (Salamat et al. 2017). Therefore, $m_{ \hbox{max} }$ should be better replaced by $\mu$ (Holschneider et al. 2011). In a previous study (Salamat et al. 2018), $\mu$ is estimated for an instrumental earthquake catalog of Iran from 1900 onwards with a constant level of completeness $\left( {m_{0} = 5.5} \right)$. In the current study, the Bayesian methodology developed by Zöller et al. (2014, 2015) is applied for the purpose of predicting $\mu$ based on the catalog consisting of both historical and instrumental parts. The catalog is first subdivided into six subcatalogs corresponding to six seismotectonic zones, and each of those zone catalogs is subsequently subdivided according to changes in completeness level and magnitude uncertainty. For this, broad and small error distributions are considered for historical and instrumental earthquakes, respectively. We assume that earthquakes follow a Poisson process in time and Gutenberg–Richter law in the magnitude domain with a priori unknown $a$ and b values which are first estimated by Bayes’ theorem and subsequently used to estimate $\mu$. Imposing different values of $m_{ \hbox{max} }$ for different seismotectonic zones namely Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh and Makran, the results show considerable probabilities for the occurrence of earthquakes with $M_{w} \ge 7.5$ in short $T_{\text{f}}$ , whereas for long $T_{\text{f}}$, $\mu$ is almost equal to $m_{ \hbox{max} }$.