# Nucleation Mechanism and Rupture Dynamics of Laboratory Earthquakes at Different Loading Rates
## 4 Conclusions  
In this work, we studied the characteristics of earthquake nucleation and rupture dynamics at different loading rates. Our findings unveiled several key relationships:  
1. Recurrence intervals: As the loading rate increases, the recurrence intervals decrease. This suggests that at higher loading rates, faults require less time to accumulate the stress necessary for an earthquake, resulting in more frequent seismic events.
2. Frictional dynamics: The peak friction coefficient, the change in the friction coefficient, and the change rate of the friction coefficient decrease with the increasing loading  
Figure 14: Summary of relative velocity as a function of loading rate. Two dotted lines refer to the top (\(V_{S}\)) and bottom (\(V_{R}\)) limitations of the so-called “forbidden zone”.  
Figure 13: Nucleation (**a**) velocity and (**b**) time as functions of loading rate. The light color symbols represent the actual values. The highlight color symbols are the mean values with a 95% confidence interval.  
rate. This could imply limited interactions between the fault surfaces at higher rates, potentially undermining the fault's locking mechanisms.
3. Shear stress and energy release: The shear stress drop (or the relative shear stress drop) decreases with the loading rate, which indicates that seismic events at slower loading rates release a more significant portion of accumulated energy. A lower loading rate means a larger recurrence interval and thus longer holding time of the two contact surfaces. This may favor the strengthening of the fault.
4. Critical nucleation length: The critical nucleation length decreases with the loading rate. In simpler terms, higher tectonic activities can trigger earthquakes even in shorter fault segments. We propose a theoretical model to explain the loading rate dependence on the critical nucleation length.
5. Aseismic slip: Our findings revealed that during the initial stages of the nucleation phase, aseismic or stable slip is the only activity. As the process evolves, this slip shifts towards a cascading process. This observation aligns with the results from other studies [16]. However, a long-lasting question is whether the primary seismic event, or the mainshock, is genuinely initiated by this cascade-like sequence. Essentially, it is debated whether the mainshock is merely an amplified foreshock resulting from the rupture of a sufficiently large or weak segment which then propagates across the entire fault plane. Recent seismic data point to a similarity between small and large earthquakes [45], suggesting that this might indeed be the scenario.  
To conclude, we demystified the effects of loading rates on key fault friction parameters, such as the static friction coefficient (\(\mu_{s}\)), the dynamic friction coefficient (\(\mu_{d}\)), and the critical slip distance (\(d_{c}\)). These insights are invaluable for a comprehensive understanding of earthquake processes.  
Conceptualization, C.W. and X.L.; methodology, C.W.; software, K.Z.; validation, C.W. and G.W.; formal analysis, G.W.; investigation, G.W.; resources, X.L.; data curation, G.W.; writing--original draft preparation, G.W.; writing--review and editing, C.W.; visualization, K.Z.; supervision, C.W.; project administration, C.W. and X.L.; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by CNPC Innovation Fund (#2022 DQ02-0610).  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to restrictions from the State Key Laboratory.  
This work was supported by the China Scholarship Council. We also extend our gratitude to [PERSON] of Richmond Hill High School, Ontario, Canada, for his assistance in conducting the experiments and analyzing the data.  
The authors declare no conflict of interest.