Statistical Analysis of Seismicity in the Fiji-Tonga Region: Integrating Classical and Circular Methods

Abstract

This study presents a comprehensive exploratory and directional analysis of 1,000 georeferenced earthquake events from the seismically active Fiji–Tonga region, based on the classical quakes dataset in R. Integrating both multivariate and circular statistical methods, the analysis investigates the spatial, depth-dependent, and directional structure of seismicity along a complex subduction zone. Classical techniques—including kernel-based density estimation, spatial point process modeling, and correlation analysis—reveal a distinctly bimodal depth distribution and a strong linear relationship between magnitude and the number of reporting stations. The estimated spatial intensity surface highlights seismic hotspots consistent with subduction interfaces and tectonic boundaries. To capture directional behavior, a unified circular statistical framework is introduced, incorporating bearing computation, uniformity tests (Rayleigh, Kuiper, Watson), circular-linear regression, and finite mixture modeling using mixed von Mises distributions. This enables decomposition of complex directional patterns into interpretable fault-related clusters and identification of depth-direction coupling. Applied to the Fiji trench, the method detects SW–NE bimodality, a dominant orientation near 127◦, a secondary cluster near 292◦, and significant regression effects ( ˆβ = 0.036, p < 0.001). The findings underscore the utility of classical datasets for modern geostatistical workflows and highlight the value of open-access seismic data in understanding global tectonic processes. All analyses were performed using reproducible code.

Journal of Statistical Research 2025, Vol. 59, No. 2, pp. 145-166.