2.4 Detection of aseismic processes from seismicity
The Epidemic Type Aftershock Sequence (ETAS) model (Ogata, 1988), which is based on the superposition of the modified Omori law (Ustu, 1961), can be used to explain mainshock–aftershock seismicity. The ETAS model assumes that the seismicity rate is the sum of the background rate of independent events, \(\lambda_{0}\), and aftershocks triggered by each event, \(\lambda_{i}(t)\):
\(\lambda\left(t\right)=\lambda_{0}+\sum_{i:t_{i}<t}{\lambda_{i}\left(t\right).}\)(6)
Based on the modified Omori law, each earthquake can trigger its own aftershock sequence (Utsu et al., 1995):
\(\Lambda_{i}\left(t\right)=\frac{K_{0}}{\left(c+t-t_{i}\right)^{p}}e^{\alpha\left(M_{i}-M_{\min}\right)},\)(7)
where \(t_{i}\) is the occurrence time; \(M_{i}\) is the magnitude of each event, \(i\), that occurred prior to time \(t\); \(M_{\min}\) is the magnitude of completeness of the earthquake catalogue; \(K_{0}\),\(c\), and \(p\) are constants; and \(t\) is the time that has elapsed since the main event.
We applied the ETAS model to the seismicity observed after the mainshock in Kagoshima Bay and investigated the difference between the simulated and observed seismicity. The results show that the foreshock activity cannot be explained by the ETAS model, likely because aseismic processes mainly controlled the foreshock activity. We used the timings and magnitudes of the earthquakes listed in the JMA catalogue. The lower limit of the magnitude, MC, was set to 1.0. Figure S4 shows the magnitude–frequency distribution. The distribution follows the Gutenberg–Richter law (Gutenberg & Richter, 1944) when MJMA ≥ 1.0. The SASeis2006 algorithm by Ogata (2006) was used to estimate the model parameters and calculate the residuals of the ETAS model.