Interpretable Gradient-Boosted Poisson Modeling of Aftershock Productivity: Magnitude-Sensitive 7-Day/100-km Forecasts that Outperform RJ89

Abstract

Aim: The aim of this study is to predict the number of aftershocks that may occur within 7 days and a 100-kilometer radius following a mainshock. This prediction is made based on the parameters of the mainshock and early catalog features, including magnitude, focal depth, magnitude type, number of stations, azimuthal gap of the network, minimum distance to the epicenter, root mean square of arrival time residuals, latitude-longitude, and origin time of the earthquake using U.S. Geological Survey Earthquake dataset. The Reasenberg-Jones model was used for comparison, and productivity estimation was provided using XGBoost.

Methods: Using the Gardner-Knopoff declustering method, 3,000 records were separated into mainshocks and aftershocks. Subsequently, aftershocks were predicted using both the RJ89 and XGBoost Poisson models and compared to each other.

Results: From 122 mainshocks identified through Gardner-Knopoff declustering, the target count distribution within 7 days and 100 kilometers was found to be approximately 47% zero-weighted and right-skewed. In general testing, the XGBoost Poisson and RJ89 models yielded similar results. However, in stratified evaluation, the MAE of XGBoost was lower than RJ89 by 5.0% for earthquakes with magnitudes between 5.0–5.5, by 11.8% for magnitudes between 5.5–6.0, and by 14.2% for magnitudes equal to or greater than 6. The graphs indicated that while both models performed poorly for large counts, they exhibited reasonable calibration in small and medium ranges. SHAP interpretations revealed clear interaction effects in variables such as mag×depth and depth×dmin.

Conclusions: For small counts, both models showed similar accuracy; however, XGBoost achieved a significantly higher overall accuracy.