Flexible Spatio-Temporal Hawkes Process Models for Earthquake Occurrences

TL;DR

This paper develops flexible nonparametric Hawkes process models that better capture complex earthquake patterns by incorporating spatial inhomogeneity, anisotropy, and space-time interactions, improving seismicity analysis.

Contribution

It introduces novel nonparametric Hawkes models with enhanced flexibility for seismic data, extending the MISD algorithm with kernel estimators for better estimation.

Findings

Models effectively capture heterogeneous seismicity patterns.

Kernel-based estimators improve model estimation accuracy.

Application to real seismic data demonstrates practical utility.

Abstract

Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which existing methods with Hawkes process cannot fully capture. This study introduces novel nonparametric Hawkes process models that are flexible in three distinct ways. First, we incorporate the spatial inhomogeneity of the self-excitation earthquake productivity. Second, we consider the anisotropy in aftershock occurrences. Third, we reflect the space-time interactions between aftershocks with a non-separable spatio-temporal triggering structure. For model estimation, we extend the model-independent stochastic declustering (MISD) algorithm and suggest substituting its histogram-based estimators with kernel methods. We demonstrate the utility of the proposed methods by applying them to the seismicity data in regions with active seismic activities.