Data replenishment of five moderate earthquake sequences in Japan, with semi-automatic cluster selection

Missing early aftershocks following relatively large or moderate earthquakes can cause significant bias in the analysis of seismic catalogs. In this paper, we systematically address the aftershock missing problem for five earthquake sequences associated with moderate-size events that occurred inland Japan, by using a stochastic replenishing method. The method is based on the notion that if a point process (e.g., earthquake sequence) with time-independent marks (e.g., magnitudes) is completely observed, it can be transformed into a homogeneous Poisson process by a bi-scale empirical transformation. We use the Japan Meteorological Agency (JMA) earthquake catalog to select the aftershock data and replenish the missing early events using the later complete part of each aftershock sequence. The time windows for each sequence span from 6 months before the mainshock to three months after. The semi-automatic spatial selection uses a clustering method for the epicentral selection of earthquakes. The results obtained for the original JMA catalog and replenished datasets are compared to get insight into the biases that the missing early aftershocks may cause on the Omori-Utsu law parameters’ estimation, characterizing the aftershock decay with time from the mainshock. We have also compared the Omori-Utsu law parameter estimates for two datasets following the same mainshock; the first dataset is the replenished sequence, while the second dataset has been obtained by waveform-based analysis to detect early aftershocks that are not recorded in the JMA catalog. Our results demonstrate that the Omori-Utsu law parameters estimated for the replenished datasets are robust with respect to the threshold magnitude used for the analyzed datasets. Even when using aftershock time windows as short as three days, the replenished datasets provide stable Omori-Utsu law parameter estimations. The p-values for all the analyzed sequences are about 1.1 and c-values are significantly smaller compared to those of original datasets. Our findings prove that the replenishment method is a fast, reliable approach to address the missing aftershock problem.