This study investigates the missing data problem in the Japan Meteorological Agency catalog of the Kumamoto aftershock sequence, which occurred since April 15, 2016, in Japan. Based on the assumption that earthquake magnitudes are independent of their occurrence times, we replenish the short-term missing data of small earthquakes by using a bi-scale transformation and study their influence on the maximum likelihood estimate (MLE) of the epidemic-type aftershock sequences (ETAS) parameters by comparing the analysis results from the original and the replenished datasets. The results show that the MLEs of the ETAS parameters vary when this model is fitted to the recorded catalog with different cutoff magnitudes, while those MLEs remain stable for the replenished dataset. Further analysis shows that the seismicity becomes quiescent after the occurrence of the second major shock, which can be regarded as a precursory phenomenon of the occurrence of the subsequent $$M_J7.3$$ mainshock. This relative quiescence is demonstrated more clearly by the analysis of the replenished dataset.

Elastic rebound theory forms the basis of the standard earthquake cycle model and predicts large earthquakes to recur regularly through cycles of strain accumulation and release. Yet few individual earthquake records are sufficiently long to test the theory. Here we characterize the distribution of earthquake interevent times from a global compilation of 80 long‐term records. We find that large earthquakes recur more regularly than a random Poisson process on individual fault segments. The majority of Earth's well‐studied faults shows weakly periodic and uncorrelated large earthquake recurrence, consistent with the expectations of elastic rebound theory. However, many low activity‐rate (annual occurrence rates < 2 × 10⁻⁴) faults show random or clustered earthquake recurrence, which cannot be explained by elastic rebound theory.

Large magnitude explosive eruptions in Japan were compiled for the Large Magnitude Explosive Volcanic Eruptions (LaMEVE) database. Here we use this dataset to investigate the under-recording of Japanese explosive eruptions. We identify under-recording of Volcanic Explosivity Index (VEI) 4–5 eruptions on two timescales. Model fitting and Akaike’s information criterion (AIC and AICc) model selection suggest that these trends can be represented with the double exponential decay model, reflecting geologic processes. The time series of the recording rate of larger eruptions (VEI 6 and 7) show a slowly decreasing trend in comparison to smaller eruptions. These time series can be represented with the single exponential decay model. The percentages of missing eruptions are estimated from the fitted models. Our results show an inverse correlation between VEI and degree of under-reporting suggesting that even larger VEI eruptions are under-recorded in the Quaternary. For example, 89 % of VEI 4 events, 65–66 % of VEI 5 events, 46–49 % of VEI 6 events and 36–39 % of VEI 7 events are missing from the record at 100 ka, 200 ka, 300 ka, and 500 ka, respectively. Comparison of frequencies of Japanese and global eruptions suggests that under-recording of the global database is 7.9–8.7 times larger than in the Japanese dataset. Therefore, under-recording of events must be taken into account in estimating recurrence rates of explosive eruptions using the geologic record.