Summary Earthquake hazard assessment is the first step towards implementing prevention, preparedness, and response or faster recovery actions to reduce the risk of seismic disasters. In this paper, we present a comprehensive study on present-day seismicity in terms of the estimated waiting time and conditional probability in Africa by 2022 – 2072 using four competing distribution models (Brownian passage time (BPT), gamma, lognormal, and Weibull). We also investigate how much Coulomb stress change ($\Delta CFF$) induced by previous earthquakes that occurred in neighboring active sources should revise the probability of occurrence at the location of the next events. We analyze large earthquakes with moment magnitude, ${M}_w \ge 6.0$, collating data from the Global Centroid Moment Tensor and from several published literature that list fault plane solutions of large African earthquakes since 1900. We assume that the dataset is stationary and consists of independent events. First, the model's parameters are estimated and the results of the statistical analysis of the interevent times show clear evidence of quasi-periodic recurrence behavior for large earthquakes ${M}_w \ge $ 6.0 in different seismotectonic regions in Africa. Next, a comparison among the distribution models is performed with the aim of selecting the most suitable one. The results in terms of the maximum likelihood criterion and its extension (Akaike Information Criterion) indicate that, in general, the BPT and Weibull models had similar fits to each other, and performed slightly better than gamma and lognormal models. Then, we use Gaussian random distributions to treat parameter uncertainties (e.g., aperiodicity, maximum expected magnitude, slip rate, and mean recurrence time) of the distribution models associated with each seismotectonic region. From repeated Monte Carlo draws, we assess uncertainties of the 50-year conditional probability values for the next earthquake obtained from two distribution models (BPT and BPT + $\Delta CFF$) related to the 50th percentile. The results of the BPT distribution indicate very high chances of future earthquakes in the study region where the conditional probability of a large earthquake reaches 99.5%, 95.6%, 83.1%, and 82.2% for the western branch of the East African Rift System (EARS), northwest Africa, the Afar region, and the eastern branch of EARS, respectively. Taking into account the effect of stress change from interacting sources (BPT + $\Delta CFF$), these probabilities are slightly modified to 99.8%, 98.4%, 89.9%, and 87.3% for the western branch of EARS, northwest Africa, the Afar region, and the eastern branch of EARS, respectively. These marginal increases suggest that the estimated effect of the earthquake interaction introduced by the coseismic slip of previous earthquakes on neighboring active sources is minor if compared with the uncertainties affecting the renewal models used for the basic time-dependent conditional probability assessment.

Investigation of the characteristic behavior of successive earthquakes that closely occur in space and time is important to understand the generation mechanism of earthquakes and useful to assess a triggered earthquake, especially around the area, where a first large earthquake took place. Here, we analyzed the Global Centroid Moment Tensor catalog from 1976 to 2016 for shallow earthquakes with a moment magnitude, $${M}_{w}$$ M w , of at least 5.5, and the F-net catalog, Japan, for $$4\le {M}_{w}<5.5$$ 4 ≤ M w < 5.5 , to clarify the spatio-temporal characteristics of the successive earthquakes. We first sorted all of the earthquakes in time and removed the aftershocks that occurred in and around the faults of earthquakes with $${M}_{w}$$ M w larger than the target magnitude range we investigated. Then, we selected source events from the beginning and searched for earthquakes that occurred within a horizontal distance (D) and a lapsed time ($${T}_{a}$$ T a ) from the source event to group them in clusters. Then, the source event was selected from the catalog in order, and the same procedure was repeated. We counted the number of clusters, each of which consisted of successive earthquakes, for different D and $${T}_{a}.$$ T a . To examine whether successive earthquakes were explained by random occurrences, we compared the results with simulations in which earthquakes occurred randomly in time but at the same locations matching the centroids in the real data. The comparison showed that the number of clusters for the simulation rapidly increased with D and merged with that for real data at a short distance, which is defined here as the triggering distance. We find that triggering distance is proportional to about 1/5 to 1/4 of the seismic moment $${(M}_{0})$$ ( M 0 ) of the source event, and exponentially decreases with increasing $${T}_{a}$$ T a . Relating the derived empirical scaling relations between $${M}_{0}$$ M 0 and triggering distance from the equations in the ETAS model, we show that the observed exponents of 1/5 to 1/4 were well predicted from the estimated ETAS parameters in various regions around the world. These consistencies first show that successive occurrence of earthquakes is well explained by the ETAS model. Graphical abstract

Spatio-temporal clustering of seismicity features is an interesting phenomenon that is relevant for earthquake generation process and operational earthquake forecasting. We analyze successive earthquakes that closely occur in space and time in order to clarify how large earthquakes successively occur. We use the Global Centroid Moment Tensor catalog for the period from 1976 to 2016. Shallow earthquakes with a moment magnitude, Mw , of larger than or equal to 5.0 are analyzed. We first sort all of the earthquakes in time to select a master event from the beginning. Then, we group the earthquakes that occur within a horizontal distance ( D ) and a lapse time ( Ta ) from the master event into a cluster. Next master event is selected from the catalog in order, and the same procedure is repeated. We count the number of the clusters, which represent the successive earthquakes, for different D and Ta To examine whether or not successive earthquakes randomly occur, we compare the results with simulations in which earthquakes are set to occur randomly in time but at the locations same with the estimated centroid. The results show that the cumulative numbers of clusters for the simulation more rapidly increase with the horizontal distance than those for real data at short distance ranges, and the formers approach to the latter at long distance range. The triggering distance, at which the cumulative numbers of real and simulation data merge, increases with increasing the magnitude of master event. The triggering distance becomes smaller as the lapse time increases, which implies that the seismic activity turns to become the normal condition in which the occurrence time intervals of large earthquakes obey a Poisson distribution. The triggering distance increases with being almost proportional to the 1/3 of the seismic moment of master earthquake, and the number of earthquakes occurring in the region with positive Coulomb stress change (ΔCFF) are more than 60-80% of the total number of the successive earthquakes. These results suggest that static stress change introduced by a master event is one of the triggering mechanism of successive earthquakes.

The modeling of statistical distribution of the eruptive frequency provides basic information to quantitatively assess the volcanic hazard and constrain the physics of the eruptive process. Here, we discuss the statistics of the time series of lateral eruptions of the Nyiragongo volcano in the Virunga Volcanic Province, western branch of the East African Rift System. We examine eruption data with a volcanic explosivity index of at least 1 listed in the Global Volcanism Network Bulletins. After investigating the completeness, stationarity, and independence of the eruption time series, we employ five distribution models (Brownian passage time, gamma, log-logistic, lognormal, and Weibull) to fit the repose time. First, we identify a clear tendency for events to cluster in time. We hypothesize two clusters, the ‘pre-1927’ cluster related to the intracraterial and volcanic activity of the lava lake, and the ‘post-1977’ cluster mainly related to lateral eruptions (i.e. those potentially generating lava flows). Using the maximum likelihood estimations, we evaluate the model parameters with a 95% confidence interval. Next, we use the Akaike Information Criterion to determine the most suitable distribution and we perform the Bayesian Model Averaging approach to assess uncertainty issues in model selection process. The results suggest that the BPT distribution provides the best fit for data of lateral eruptions (post-1977). Then we estimate the time-dependent probability of the occurrence of a lateral eruption for the 50-year period between 2022 and 2072. The estimates reach 50.79%, 88.61%, 97.59%, 99.50%, and 99.89% for 2032, 2042, 2052, 2062, and 2072 years, respectively.