Hierarchical Bayesian Calibration of the Epicentral Distance Estimation Model for Earthquake Early Warning System

Abstract Onsite earthquake early warning (EEW) systems rely on predictive models that relate the early portion of recorded seismic waves to seismicity parameters or ground-shaking characteristics, which serve as key decision variables in triggering alerts. However, because such models must operate in real time—often within the first few seconds after P-wave arrival—the limited available information introduces considerable uncertainty into the prediction process. To improve calibration, datasets from multiple seismic stations in a region are typically combined. Although this increases data volume, it also introduces additional variability due to local site effects and regional wave propagation differences, which can compromise model generalizability. This study introduces a hierarchical Bayesian calibration framework that addresses this trade-off by allowing station-specific model (first level) calibration while enabling information sharing through common hyperparameters across stations (second level). The approach focuses on epicentral distance estimation using the B−Δ method, for which waveform features are extracted from early acceleration signals. Conjugate priors are employed to enhance computational efficiency, and posterior sampling is performed using a Metropolis-within-Gibbs algorithm. A case study using seismic data from the 2008 Wenchuan and 2013 Lushan earthquakes in the Sichuan region of China demonstrates the effectiveness of the proposed method. Results show that the hierarchical model improves robustness and accuracy, particularly for stations with limited data, by enabling statistical information sharing across stations through common hyperparameters. In comparative analysis, the hierarchical model significantly outperformed both complete-pooling and no-pooling approaches in terms of reducing regression error and improving the reliability of epicentral distance estimates. The approach is particularly beneficial in data-scarce environments, where it yields more stable predictions without sacrificing station-specific sensitivity. This approach offers a flexible and scalable solution for improving EEW model performance under uncertainty.