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We estimate high-frequency (4–20 Hz) energy release due to the 2016 Kumamoto, Japan, earthquake sequence, within a time period from April 14 to 26 through envelope inversion analysis applied to the Hi-net continuous seismograms. We especially focus on energy releases after each of the April 14 MJMA6.5 and the April 16 MJMA7.3 earthquakes. The cumulative energy release from aftershocks of the April 14 event reaches 60% of that from the April 14 event itself by the lapse time of 27 h (pre-April 16 period). On the other hand, the cumulative energy release from aftershocks of the April 16 event reaches only 11 and 13% of that from the April 16 event itself by the lapse times of 27 h and 10 days (post-April 16 period), respectively. This discrepancy in the normalized cumulative energy release (NCER) indicates that the April 14 event was followed by much larger relative aftershock productivity than the April 16 event. Thus, NCER would provide information that reflects relative aftershock productivity and ongoing seismicity pattern after a large earthquake. We also find that the temporal decay of the energy release rate obeys the power law. The exponent pE of the power-law decay is estimated to be 1.7–2.1, which is much larger than the typical p value of the Omori–Utsu law: slightly larger than 1. We propose a simple relationship given by pE = βp/b, where p value, b value of the Gutenberg–Richter law, and β value of the magnitude–energy release relationship are combined.Graphical abstracta Cumulative energy releases (4–20 Hz) by the aftershocks occurring in the pre (black)- and the post (red)-April 16 periods. b Similar plot as a except that they are normalized by the energy releases from the April 14 (2.7 × 1012 J) and the April 16 (2.1 × 1013 J) events, respectively

Preliminary estimation of high-frequency (4–20 Hz) energy released from the 2016 Kumamoto, Japan, earthquake sequence