Rupture speed Vr and stress drop Δτ are two key parameters that can characterize earthquake source and the associated potential for ground shaking. Despite their importance, a controversy has emerged in recent years regarding whether there is a positive or negative correlation between Δτ and Vr. Here I attempt to reconcile the controversy by presenting a context-based solution and a physics-based solution. The first solution calls for attention to the specific context under which Vr and Δτ are discussed, as their meanings and estimated values can vary between different studies. It is noted that a negative correlation between Δτ and Vr can result, at least partly, from a tradeoff effect inherent to certain analysis method. For the second solution, it is shown that the specific correlation between Δτ and Vr can depend on the condition of fracture energy Gc. Constant Gc often favors a positive correlation, whereas introducing a variability of Gc can lead to a negative correlation. More efforts are needed to improve the methods for estimating Vr and Δτ, and to explore other mechanisms that may explain the correlation between the two parameters.

We report laboratory experimental results to reveal the factors that control the occurrence and magnitude of foreshocks. We conducted rock friction experiments using an apparatus that can shear 4-meter-long rock specimens. We observed many stick-slip events, as well as very slow (several tens of μm/s) but long-lasting slips between those main events. These long-term slow slips individually initiated from both the leading and trailing edges of the fault, and kept propagating steadily towards each other. Such steady slips did not immediately trigger any seismic events, regardless of the accumulated slip amount. After the coalescence of the two long-term slow slip fronts, a second phase of slow slip with higher slip rate (several hundreds of μm/s) — called precursory slow slip, began at the central area and was accompanied by the occurrence of small seismic events (foreshocks). Subsequently, the main fast rupture eventually developed. We propose that the asperities that hosted foreshocks had similar size to the local critical nucleation length h*; the asperities slipped stably when the local loading rate was low, but could also slip unstably and radiated seismic waves when the local loading rate became high. We further found a clear positive correlation between foreshock magnitude and local slip rate. These results suggest that local loading rate has a significant influence on the occurrence and magnitude of foreshocks. Therefore, its effect should be taken into account during the studies of earthquake nucleation process and other similar phenomena such as Episodic Tremor and Slip (ETS), icequakes, and repeating earthquakes.