Fig. 8

Estimates of stationary ETAS model, two-stage ETAS model and non-stationary ETAS model. The models were applied to a seismicity of M ≥ 1.5 in the shallow depth range down to 23 km. a The black curve shows the empirical cumulative number of the shallow aftershocks; the red dashed curve shows the theoretical cumulative estimate of the ETAS model. Beneath the empirical cumulative curves, the thick light gray curve indicates the theoretical cumulative curves of the non-stationary ETAS model. The dashed red cumulative curves show those of the reference ETAS model for the entire period. b The two-stage ETAS model is fitted to the periods separated by the change-point at 36 days. The parameter estimates are listed. The dashed red cumulative curves show those of the two-stage ETAS model for respective period. c The non-stationary ETAS model estimate: μ(t) (red) and K₀(t) (blue) with twofold errors. Pale solid and dashed horizontal lines, respectively, indicate background rate (red) and triggering coefficient (blue) of the two-stage ETAS and the reference model. The spiky gray line is the theoretical occurrence rate of the non-stationary ETAS model, and the + signs indicate magnitude vs. time of the shallow aftershocks. See Additional file 1: Table S8 for the fitting configurations and results of model comparisons