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).