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.