Anomaly detection of earthquakes with Benford’s law and extreme value approach

Türkiye is located on active fault lines where significant tectonic movements occur regularly leading to earthquakes. Western Anatolia, being in the North Anatolian Fault Zone, has a higher earthquake risk. This study focuses on detecting anomalies in earthquake magnitudes in Türkiye, spanning the years 1970 to 2021. The analysis utilizes Benford's Law and the Generalized Extreme Value distribution within the Block Maxima framework to examine the conformity of earthquake magnitude data and identify potential anomalies. This study is one of the first to apply these methods specifically to the Aegean Region, providing new insights into the seismic risk in this tectonically active region. The dataset, comprising 15845 seismic events with magnitudes of 3.0 and above, was evaluated using both statistical methods. Benford's Law indicated that the data conforms to natural patterns, with statistical tests confirming the expected distribution of first digits in the magnitude data. The Generalized Extreme Value distribution, applied through the Block Maxima approach, revealed that the expected magnitude of extreme events increases with longer return periods, with return levels estimated at 4.77 Mw for 2 years, 5.81 Mw for 20 years, and 6.36 Mw for 100 years. These findings highlight the importance of using these statistical methods to assess seismic risks and identify potential anomalies in earthquake data.