Seismicity Insights and Forecasting with Delaunay-Based Hierarchical Models

This paper presents advanced applications of a hierarchical space-time point-process model (HIST-PPM) through the latest implementation examples, based on the seismicity analysis software developed and published by the authors. The model improves the precision of earthquake prediction by incorporating spatial interpolation using Delaunay triangulation meshes, allowing accurate reproduction of local and anisotropic spatial patterns of seismic activity.Characteristic parameters—such as changes in spatial density over transformed time, and variations in the b -value—are captured flexibly and in detail across both time and space, owing to a model structure in which these parameters vary linearly within each triangular unit. The estimation procedure employs empirical Bayesian maximum a posteriori (MAP) estimation, allowing for stable inference in high-dimensional parameter spaces while effectively avoiding overfitting.In particular, the hierarchical space-time ETAS (HIST-ETAS) model, which incorporates spatial anisotropy and regional characteristics, not only enhances the reliability of short-term earthquake forecasts, but also supports mid- to long-term spatial assessments of seismic activity by estimating background seismicity. Moreover, it can be applied to seismic monitoring by visualizing spatial variations in aftershock activity intensity.In addition, the spatiotemporal detection rate model, developed to address the incompleteness of earthquake catalogs—particularly those involving small earthquakes—enables unbiased estimation of seismic activity in both real-time and long-term settings.These technological advancements offer a practical and effective foundation for developing future multi-layered earthquake forecasting systems.