Stephen Wu

Modeling earthquake clustering in space and time is central to understanding seismicity patterns and improving forecasting. The Epidemic‐Type Aftershock Sequence (ETAS) model, grounded in the Hawkes process, has long been the standard approach for describing aftershock triggering through fixed, empirically defined kernel functions. However, these functional forms may limit flexibility in representing the full diversity of real seismic behavior. In this study, we introduce the Spatio‐Temporal Neural Kernel Function (ST‐NKF) model, a neural extension of the ETAS model that replaces empirical kernels with data‐driven function approximators while retaining physical interpretability. Specifically, three fully connected neural networks are used to learn the productivity, temporal, and spatial kernel components directly from earthquake catalogs, enabling flexible estimation of triggering patterns under the same probabilistic structure as ETAS. We evaluate ST‐NKF on the EarthquakeNPP benchmark for California and compare its performance with the ETAS model using marginal temporal and conditional spatial log‐likelihoods. Results show that ST‐NKF achieves comparable performance with ETAS model, demonstrating that neural networks can reproduce empirical ETAS behavior within a unified, interpretable point process framework. Importantly, this represents the first neural model to match ETAS in spatiotemporal seismicity modeling, marking a promising step toward integrating seismological interpretability with the flexibility of deep learning. Future extensions may further improve performance by incorporating nonstationary background rates, multimodal geophysical information, or more expressive neural architectures beyond the Hawkes paradigm.

1. Geotechnical site characterisation is inherently challenged by the scarcity and heterogeneity of borehole measurement data. Reliable prediction of soil mechanical properties–undrained shear stre...

Incomplete earthquake catalogs, especially for early aftershocks, pose challenges for accurate seismological analysis. This study introduces Auto-Biscale Empirical Transformation Application (AutoBETA), a fully automated earthquake data replenishment tool that builds upon previous semiautomated approaches by integrating grid-based density analysis with flexible missing region identification. This tool also supports user-defined polygons and hybrid strategies (union or intersection) to incorporate expert knowledge. We applied AutoBETA to one synthetic incomplete catalog and four real-earthquake catalogs: the 2008 Mw 7.9 Wenchuan, 2024 Mw 7.5 Noto, 2010 M 5.26 Baja California, and 2016 M 6.06 Norcia sequences. The analyses were conducted using magnitude thresholds of M ≥ 3.0, M ≥ 2.0, M ≥ 1.0, and M ≥ 2.0. After 100 fully automated iterations, the method replenished 43.9%, 40.0%, 40.5%, and 44.8% of the final catalogs. These results substantially improve catalog completeness, enabling more robust aftershock modeling and statistical analysis. AutoBETA is implemented in Python and is available as open-source software on GitHub.

Neural point processes (NPPs) have recently been applied to seismicity modeling, but their theoretical connections to classical point processes models remain elusive. Moreover, two fundamental questions remain unresolved: (a) how much historical information is sufficient for NPPs to effectively model seismicity, and (b) what is the differential impact between inter‐event times and magnitudes on the model predictive performance? To answer these questions, we reinterpret a class of NPPs within the framework of neural modulated renewal processes (NMRPs), which generalize conventional modulated renewal processes by integrating deep learning architectures. We develop and analyze four variants: the unmodulated neural renewal process (NRP), the inter‐event times modulated NMRP (I‐NMRP), the magnitude modulated NMRP (M‐NMRP), and the jointly modulated NMRP (J‐NMRP). Their performance is systematically evaluated against the epidemic‐type aftershock sequence (ETAS) model using the EarthquakeNPP benchmark. Results demonstrate that I‐NMRP and J‐NMRP not only match, but in some cases surpass, ETAS in terms of log‐likelihood, while requiring substantially less historical input. Furthermore, the analysis reveals that inter‐event times play a more critical role than magnitudes in enhancing predictive performance. These findings establish NMRP as a flexible and efficient framework for seismicity modeling, with strong potential to incorporate diverse contextual information and to deepen our understanding of earthquake triggering processes.