Faced with a lack the quantitative evidence, the rare nature of large earthquakes leads to the de facto assumption that earthquake main shocks follow a Poisson process. However, recent history reveals high event counts for seismicity between 1960-64 and again during the early 2000s, motivating the re-analysis of whether Poisson assumptions remain statistically valid.
Above Mw7, previous literature does not decisively conclude that earthquakes exhibit random behaviour. The differences between these studies are not easy to address. However, to maintain the potential for long-range interaction in the dataset, this study parameterises its own windowing declustering method. To improve generalisation potential, this compares the instrumental record against synthetic catalogues generated using Monte-Carlo simulation to extend the recent history to 1,200 years of realistic synthetic data, incorporating location and magnitude uncertainty. To generate objective clusters upon which instrumental and synthetic datasets can be compared, this study considers location and size parameters simultaneously, combining a refined Kohonen Self-Organising Map (SOM) network algorithm and hierarchical agglomeration techniques to generate homogeneous groups. This thesis finds that the high frequency anomaly in the early instrumental catalogue renders the pre-1918 data unhelpful in the assessment of spatio-temporal distributions. Further, the overdispersion statistic and Kolmogorov-Smirnoff hypothesis tests are found to be powerful tools for identifying non-random behaviour and the use of the Ward hierarchical agglomeration method generates strong clusters. Finally, this thesis proposes that incorporating the earthquake parameter uncertainty estimates can lead to greater discernment of non-Poisson features, particularly for shallow events between Mw6 and 7.5, as well as for high magnitude events along the Kurile, Japan and Tonga-Kermadec trenches. In conclusion, short-term seismic risk assessment can be improved by incorporating the overdispersive behaviour observed for such events, at least in the western hemisphere.