4.1 Migration of foreshock activity along a plane
The clear hypocenter migration observed for the foreshock sequence suggests that aseismic physical processes controlled this sequence. In fact, the seismicity rate of the foreshock sequence could not be reproduced by the ETAS model, suggesting that the earthquake-to-earthquake interaction cannot explain this sequence. Thus, the foreshock sequence must be understood as temporary increase in the background seismicity rate, similar to that of the earthquake swarm.
In Fig. 10, the distances of the foreshock hypocenters from the mean location of the first three events are plotted against time. The expansion front of the pore pressure diffusion model reported in Shapiro et al. (1997) is also shown, which can be expressed by the following equation including various diffusion coefficients \(D_{h}\):
\begin{equation} \begin{matrix}r=\sqrt{4\pi D_{h}t},\#\left(9\right)\\ \end{matrix}\nonumber \\ \end{equation}
where \(r\) is the distance from the point pressure source and \(t\) is the time. In this study, we set the initiation time to 220 days before the mainshock because the seismicity rate significantly increased at this time (Fig. 1c). We also show the propagation fronts of the linear spread model that has been used for aseismic slip propagation in the past (e.g., Vidale & Shearer, 2006).