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A Deep Learning Application to Model the Full Distribution of Higher-order Aftershock Numbers in the ETAS Framework

The Epidemic-Type Aftershock Sequence (ETAS) model is the state-of-the-art framework used for operational earthquake forecasting worldwide. It models earthquake occurrence as a stochastic point process, where earthquakes trigger cascades of aftershocks according to a set of empirical laws governing the timing, location, and quantity of direct aftershocks, as well as the magnitude distribution. These laws are described analytically and depend on several region-specific parameters that characterize the triggering relationships between earthquakes and their direct aftershocks. However, due to the stochastic nature of the cascading process, the distribution of indirect aftershocks has traditionally been obtained only through extensive simulations—a process that is both time- and resource-intensive.

In our recent study (Mizrahi and Jozinović, 2024), we demonstrated that the mean number of expected indirect aftershocks, given the parameters governing the direct aftershock distribution, can be accurately estimated using a simple deep-learning model. The main advantage of our approach compared to the simulation-based approach is the significant speed-up of the calculations, with the ML model taking only 813 µs on average, without a loss in accuracy. Here, we extend this approach to estimate not only the mean but the full distribution of higher-order aftershock numbers, modeling it as a negative binomial distribution. While estimating the full distribution is more challenging than estimating the mean, it is a crucial step toward enabling the faster machine-learning-based approach to replace simulations without sacrificing valuable information about forecast uncertainty. We demonstrate that this extended model can infer the full distribution of higher-order aftershock numbers accurately orders of magnitude faster than the classical simulation-based approach.

Session: Improving the State of the Art of Earthquake Forecasting Through Models, Testing and Communication [Poster]

Type: Poster

Room: Exhibit Hall

Date: 4/15/2025

Presentation Time: 08:00 AM (local time)

Presenting Author: Leila Mizrahi

Student Presenter: No

Invited Presentation: 

Poster Number: 133

Additional Authors