Information geometric embedding of temporal Philippine earthquakes distributions

Abstract

Visualization and interpretation of high-dimensional data proves to be challenging in geophysical datasets as certain features of different types: namely spatial, temporal, and magnitudal result in complex interactions that obscure the underlying structure of the manifold. For this study, an information geometric approach is applied to analyze seismic activity. Philippine earthquake events from 2018-2025 were grouped per quarter (3 months) and subjected to nonparametric Kernel Density Estimation to obtain their probability density functions. Afterwards, the distributions were embedded using Fisher Information Nonparametric Embedding (FINE) approximated using Jensen-Shannon divergence (JS) and Bhattacharyya coefficient (BC). These embeddings were compared based on their temporal trajectory and k-nearest neighbors score, with NN_JS = 0.33 > NN_BC = 0.21, indicating local preservation for discrete JS. The coherence of these trajectories revealed considerably smooth paths that suggest gradual evolution in seismic behavior. HDBSCAN was used for further clustering of the PDF points to highlight regimes. Since the groupings were temporal, this resulted in identifying the baseline regime, transitional, and current state. Such regimes effectively reflect the shift in the framework of probability distributions for Philippine earthquakes, offering a data-driven approach for interpreting complex geophysical systems.