Investigation of the correlation of successive earthquakes preceding main shocks in the Greek territory

The Canonical Correlation Analysis (CCA) estimates the correlation between two vector variables by maximizing the correlation of linear combinations of their respective components. Here, the CCA is used to find correlation patterns in the last five successive, per pairs, earthquakes ( $ M \ge 4.0 $ M≥4.0) preceding 271 main shocks ( $ M \ge 5.5 $ M≥5.5) that occurred in the Greek territory during 1964–2018. The vector variables have two components, the earthquake magnitude and interevent time. The statistical significance of CCA is determined by the standard parametric test along with two proposed randomization tests, one using random shuffling of each paired dataset and one using randomly selected pairs of successive earthquakes. Simulations were designed on synthetic data from vector variables having the statistical characteristics of the real observations. The results on uncorrelated variables showed the correct size for the two randomization tests but larger type I error for the parametric significance test for small sample size. For correlated variables, the test power was equally high for both test types. The application of CCA and the significance tests to the Greek seismicity evidence the significant correlation among the last five successive preshocks, proving to be a promising tool in an a posteriori short-term earthquake forecasting.