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.

翻译：霍克斯过程是用于研究地震发生自激特性最常用的模型之一。然而，由于地质和应力的非均匀性，地震活动模式具有复杂特征，现有基于霍克斯过程的方法无法完全捕捉这些特征。本研究引入了新型非参数霍克斯过程模型，在三个不同维度上实现灵活性。首先，我们融入了自激地震生产率在空间上的非均匀性。其次，我们考虑了余震发生的各向异性。第三，我们通过不可分离的时空触发结构，反映了余震之间的时空相互作用。在模型估计方面，我们扩展了模型无关随机聚类（MISD）算法，并提出用核方法替代其基于直方图的估计量。通过将所提方法应用于活跃地震活动区域的地震数据，我们验证了其实用性。