Neural-Network-Based Sequential Estimation of b Values Using ETAS Simulations

Abstract The b value of the Gutenberg–Richter law is a fundamental parameter characterizing seismicity, and its temporal variation is often interpreted as reflecting changes in subsurface stress conditions. Sequential estimation of the b value is important for monitoring earthquake and volcanic activity, yet the conventional moving-window-based maximum-likelihood estimation (MLE) approach involves an inherent trade-off between temporal stability and adaptability, controlled by a single parameter, the window length. Here, we propose a neural-network-based framework for sequential estimation of time-dependent b values. Because the true b value is never known for real earthquake catalogs, we train the model using synthetic catalogs generated by epidemic-type aftershock sequence simulations, in which realistic temporal clustering is reproduced while the true b value is explicitly prescribed. Our model, based on bidirectional long short-term memory, directly maps a sequence of earthquake magnitudes to the corresponding sequence of b values. The model is trained on piecewise-linear b value variations with instantaneous jumps. For this primary test setting, the proposed model achieves lower root-mean-square errors compared with the moving-window-based MLE. Additional tests with constant and sinusoidally varying b values demonstrate that the model suppresses spurious short-timescale fluctuations while reconstructing reasonably well beyond the training setting. Application to the 2011 Tohoku earthquake sequence confirms a gradual premainshock decrease in b value, consistent with earlier studies, while providing smoother sequential estimates. Although the bidirectional architecture yields retrospective estimates, the framework can be applied in a quasi-real-time manner by updating the analysis as the catalog grows. Comparison with causal estimators further reveals a trade-off between lag and leakage around abrupt changes. The main advantage of the proposed method is a better balance between temporal stability and adaptability without manually specifying a window length.