Maximum magnitudes in aftershock sequences in Taiwan

In this work, Båth’s Law, the b-value in Gutenberg–Richter Law (G–R Law) in the form of the 1/β relationship, and both the a- and b-values in the G–R Law were introduced in order to estimate maximum aftershock magnitudes of earthquake sequences in the Taiwan region. The averaged difference of magnitude between the mainshock and the maximum aftershock is 1.20, and is consistent with Båth’s Law, however, with a large uncertainty. The large uncertainty implies that the difference may result from a variable controlled by other factors, such as the aftershocks number of an earthquake sequence and magnitude threshold for mainshock. With 1/β, since 86% of the earthquake sequences with a M ⩾ 6.0 mainshock follow this relationship, the upper bound of the maximum magnitude can be estimated for an earthquake sequence with a large mainshock. The a- and b-values in the G–R Law was also considered by evaluating maximum aftershock magnitudes. As there are low residuals between the model and the observations, the results suggest that the G–R Law is a good index for maximum aftershock magnitude determinations. In order to evaluate the temporal decays of maximum aftershock magnitudes, modified Omori’s Law was introduced. Using the approaches mentioned above, the maximum magnitudes and the temporal evolution of an earthquake sequence could be modeled. Among them, the model of the G–R Law has the best fit with observations for most of earthquake sequences. It shows its feasibility. The results of this work may benefit seismic hazards mitigation in the form of rapid re-evaluations for short-term seismic hazards immediately following devastating earthquakes.