Rapid earthquake magnitude estimation from fuzzy C-means clustering-weighted fusion of seismogeodetic PGD and PGV

Rapid and reliable earthquake magnitude estimation is essential for earthquake early warning and tsunami-impact assessment, particularly for large events for which conventional seismic estimates may saturate. This study develops a seismogeodetic magnitude-estimation framework that combines peak ground displacement (PGD) and peak ground velocity (PGV) derived from near-colocated GNSS and strong-motion observations. Fuzzy C-means clustering is used to construct observation-dependent prior weights, while robust and geometry-aware weighting are introduced to reduce the effects of anomalous observations and uneven station distributions. The method was evaluated using 1,147 paired observations from 19 earthquakes with moment magnitudes ranging from 6.1 to 9.0. In leave-one-earthquake-out validation, the PGD-only and PGV-only solutions yield mean absolute errors of 0.338 and 0.320 Mw, respectively, whereas joint PGD/PGV estimation reduces the error to 0.261 Mw. The full robust geometry-aware solution yields an MAE of 0.259 Mw. A two-event holdout test gives a fused mean absolute error of 0.194 Mw, although fusion does not outperform the better single-parameter estimate for every event. These results demonstrate that combining PGD and PGV provides the main improvement in magnitude estimation, while robust and geometry-aware weighting offer additional event-dependent benefits.