Measuring seismicity diversity and anomalies using point process models: case studies before and after the 2016 Kumamoto earthquakes in Kyushu, Japan

Earth, Planets and Space

Table 6 MLEs of the single and two-stage ETAS models for the foreshock sequence

	Target period	\(\mu\)	\(K_{0} \left( { \times \,10^{2} } \right)\)	\(c\left( { \times \,10^{ - 2} } \right)\)	\(\alpha \left( { \times \,10^{ - 1} } \right)\)	\(p\)	\(dAIC\)
M _c = 1.5	S = 0.01, T _end = 1.166	0.000	2.377	3.166	1.478	1.000	− 7.04
	S = 0.01, T _c = 0.16	0.000	4.353	9.055	1.516	1.000
	T _c = 0.16, T _end = 1.166	0.000	1.483	4.492	3.608	1.000
M _c = 2.0	S = 0.01, T _end = 1.166	0.000	1.278	1.878	1.153	1.000	− 7.94
	S = 0.01, T _c = 0.16	0.000	2.406	6.630	0.9659	1.000
	T _c = 0.16, T _end = 1.166	0.000	1.273	0.001	1.683	1.000
M _c = 2.5	S = 0.01, T _end = 1.166	0. 000	0.560	0.906	1.119	1.000	− 1.61
	S = 0.01, T _c = 0.16	0. 000	0.865	0.290	0.913	1.000
	T _c = 0.16, T _end = 1.166	0. 000	0.291	0.073	0.286	1.000

Single ETAS model (1) is fitted to the M6.5 aftershock sequence prior to the M7.3 mainshock. For each threshold magnitude, the first row shows the MLEs for the entire period (S = 0.01 days, T _end = 1.166 days) with AIC = AIC₀, the second row shows those for the pre-change-point period (S = 0.01 days, T _c = 0.16 day) with AIC = AIC₁, and the third row shows those for the post-change-point period (T _c = 0.16 days, T _end = 1.166 days) with AIC = AIC₂. The last column shows ΔAIC = AIC₁ + AIC₂ − AIC₀