Figure 9. (a ) M–T diagram. (b ) Observed cumulative number of aftershocks with \(M_{L}\ \geq 1.0\) (red solid line) and predicted number based on the estimated ETAS parameters (blue solid line). Each curve represents the cumulative numbers starting 0.1 days after the mainshock. (c ) Results of the residual analysis, where the blue solid line shows the observed events with respect to the transformed time on the horizontal axis and cumulative number of observed \(M_{L}\ \geq 1.0\) earthquakes on the vertical axis. The black dotted line represents the transformed time at which the assumed model fully matches the observation. The red solid and red broken lines indicate the two-sided 95% and 99% error bounds of the Kolmogorov–Smirnov statistic, respectively. The gray zone in (c ) shows the range of the transformed time corresponding to the period of 20–44 days after the mainshock highlighted in gray in (b ).
The large discrepancy between the predicted and observed seismicity rates 20–40 days (~1.000–1.500 in Fig. 9c) after the mainshock can be explained by a temporary increase in the background seismicity, which was assumed to be constant over the entire period of this analysis in the model. The transient increase in the background seismicity rate suggests that the Kagoshima Bay earthquake sequence may have been affected by physical processes other than earthquake-to-earthquake interactions, especially during this period (20–40 days) and that an aseismic process may have led to the largest aftershock (ML 4.4) that occurred 44 days after the mainshock. Contrarily, most aftershocks can be explained as general mainshock–aftershock seismic activity, suggesting that stress changes caused by the mainshock resulted in numerous aftershocks.