Seismic moment efficiency reveals the potential for larger earthquakes after M6-class events

Understanding how stress and strength conditions evolve before and after large earthquakes remains a fundamental challenge in seismology. Here, we introduce an observationally grounded metric-the ratio of the summed moment tensor to scalar seismic moment (Mstk/M₀)-to track temporal changes in deformation behavior surrounding earthquake faults. Using high-resolution focal mechanism datasets, we analyze two well-instrumented sequences with M6-class foreshocks followed by M7-class mainshocks: the 2016 Kumamoto and 2019 Ridgecrest events. We find that Mstk/M₀ remains elevated after M6-class foreshocks but decreases sharply after M7-class mainshocks, indicating a transition toward a more heterogeneous deformation state. To evaluate broader applicability, we examined nine inland M6-M7 earthquake sequences in Japan (2000-2020). Among ten events that exhibited high Mstk/M₀ during foreshock activity, five maintained high values after the M6-class event, and three of these were subsequently followed by even larger earthquakes. In contrast, all other sequences not followed by larger events showed clear decreases in Mstk/M₀ after the initial large earthquake. These observations suggest that sustained high Mstk/M₀ after an M6-class earthquake may indicate conditions favorable for continued rupture growth, whereas decreases may reflect reduced likelihood of further large rupture. Relationships between Mstk/M₀ and inelastic strain rate further support a physical interpretation linking deformation consistency with the ambient stress field to the potential for large earthquake occurrence. Monitoring Mstk/M₀ in the immediate aftermath of large earthquakes may therefore provide useful information for assessing whether an even larger event is likely to follow.