An energy-based perspective on the correlation between stress drop and rupture speed

Stress drop \Delta \tau and rupture speed V_\textr are two important earthquake source parameters that control the characteristics of rupture process and the associated ground motion. However, how the two parameters correlate with one another is currently still under debate. Here I use an energy-based approach from fracture mechanics to understand the correlation between \Delta \tau and V_\textr . This approach is built on the balance between fracture energy G_\textc and dynamic energy release rate G_\textd (which itself is a function of \Delta \tau and V_\textr ). By synthesizing various observations within a unified fracture-energy ( G_\textc ) framework, I show that near constant G_\textc can yield a positive correlation between \Delta \tau and V_\textr , whereas variable G_\textc dependent on space, time or off-fault damage may cause a negative correlation between \Delta \tau and V_\textr . These results reconcile the debate on the correlation between \Delta \tau and V_\textr and suggest a need to examine the condition of other factors (such as G_\textc ). Additional factors may complicate the evaluation of the correlation between \Delta \tau and V_\textr when rupture process is inferred from far-field observations, accompanied by strong spatiotemporal variation, or followed by additional phases, which should be investigated by future studies.