Examining the Markovian structure of eartquakes in Turkey according to their magnitudes using cluster analysis

This study analyzes earthquakes in Turkey between January 1, 1980, and December 31, 2022, based on their magnitudes using Markovian structures and k-means clustering analysis. Turkey's coordinate system was divided into 114 grid cells. The magnitudes within these cells were categorized into three states: 3-4, 4-5, and 5 and above. Due to the insufficient number of earthquakes in the third state (magnitude 5 and above), these areas were consolidated into 65 units by merging up to six grid cells, considering fault lines. Transition matrices were then estimated for these units, and transition probabilities were calculated for each of the 65 units. Transition Matrices, Limit Distributions, and Mean Recurrence Times were derived to prepare these units for clustering analysis. The hierarchical clustering method was used to determine the number of clusters, identified as four using a dendrogram. The study's findings indicate that the clusters formed based on transition matrices showed similarities in transition probabilities across the three states. In the clusters formed by limit distributions, clusters 3 and 4 were prominent. Additionally, in the analysis based on mean recurrence times, three distinct clusters were observed.