Model Of Earthquake Occurrence Research Articles

Probabilistic earthquake-tsunami financial risk evaluation for the District of Tofino, British Columbia, Canada

ABSTRACT Southwestern British Columbia in Canada has a high likelihood of facing significant earthquake threats in the future. It is exposed to significant seismic and tsunami hazards, originating from the Cascadia subduction zone and shallow crustal and deep inslab earthquakes. This study presents a new probabilistic earthquake-tsunami loss model for the Cascadia subduction zone by focusing on the District of Tofino, British Columbia. The earthquake occurrence and rupture models for the Cascadia subduction zone are developed by incorporating the time-dependency of earthquake occurrence and by adopting a stochastic source modelling approach, which allows for consideration of heterogeneous earthquake slip distributions. The results produce single-hazard and multi-hazard exceedance probability loss curves for earthquakes and tsunamis from the Cascadia subduction zone. In addition, earthquake risks due to other seismic sources are integrated with the multi-hazard loss curves due to the Cascadia events. In this way, a complete financial exposure from all major seismic and tsunami sources is evaluated. These loss curves can be used for determining the insurance rates for multi-hazard and multi-source risk coverage. The results are beneficial for providing more risk financing options via insurance against the future Cascadia and other seismic events.

Impact of the Uncertainty in the Parameters of the Earthquake Occurrence Model on Loss Estimates of Urban Building Portfolios

Abstract Understanding the potential socioeconomic losses due to natural hazards, such as earthquakes, is of foremost importance in the field of catastrophe risk management. The construction of a probabilistic seismic risk model is complex and requires the tuning of several parameters essential to represent the seismic hazard of the region, the definition of the exposed inventory characteristics, and its vulnerability to ground motion. Because significant uncertainties could be associated with each model component, the loss estimates are often highly volatile. Nevertheless, to reduce the conceptual complexity and the computational burden, in many real-life applications these uncertainties are either not adequately treated or neglected altogether. The false high fidelity of the ensuing loss estimates can mislead decision-making strategies. Hence, it is useful to assess the influence that the variability in the estimated values of the model input parameters may exert on the final risk results and their relevant contributions. To this purpose, we have performed a sensitivity analysis of the results of an urban seismic risk assessment for Isfahan (Iran). Systematic variations have been applied to the values of the parameters that control the earthquake occurrence in the probabilistic seismic hazard model. Curves of input–output relative variations were built for different risk metrics with the goal of identifying the parameters most sensitive to input uncertainty. Our findings can be useful to support risk managers and practitioners in the process of building seismic hazard and risk models. We found that the Gutenberg–Richter a and b values, the maximum magnitude, and the threshold magnitude are large contributors to the variability of important risk measures, such as the 475 yr and the average annual loss, with the more frequent losses being, in general, most sensitive.

Long-Term Recurrence Pattern and Stress Transfer along the Kefalonia Transform Fault Zone (KTFZ), Greece: Implications in Seismic Hazard Evaluation

An effort is exerted to investigate the recurrence pattern of large earthquakes (Mw ≥ 6.0) in the Kefalonia Transform Fault Zone (KTFZ), Greece, by considering the incorporation of the 74-year (1948–2022) evolving stress field. Four earthquake occurrence models—the Poisson, Poisson with the incorporation of the static stress changes (Poisson + ΔCFF), Brownian passage time (BPT) and Brownian passage time with the incorporation of the static stress changes (BPT + ΔCFF)—have been applied to estimate the occurrence probabilities of nearly characteristic earthquakes for the seven fault segments of the study area. The mean recurrence time, Tr, is estimated using the physics-based seismic moment rate conservation method. The results show large variability depending upon fault parameters. Incorporating the state of stress into Tr results in both advanced and delayed recurrence patterns. The occurrence probability estimates for the next 10, 20 and 30 years indicate that the fault segment most likely to be ruptured is the Paliki North fault segment in all models. Overall, the occurrence probabilities, combined with the state of stress along the fault segments, emphasize the high seismic moment rate of the study area. The application of time-dependent models (BPT, BPT + ΔCFF) resulted in significant increases or decreases in the associated seismic hazard.

First paleoseismic data from the Balkan Range

The normal faults along the Balkan range front integrate great tectonic relief, prominent basin-and-range morphology, historic seismic quiescence, and ongoing dilatation rate varying near zero. The official standards prioritize the instrumental seismicity in a random model of earthquake occurrence, and the region is assessed at low seismic hazard levels. The need of geologic data on earthquake occurrence motivated us to excavate the first paleoseismological trench in the Balkan Range. We trenched the Zlatitsa normal fault, which occupies the westernmost position within a zone of localized strain along the Central Balkan Range. The trench exposure revealed two surface-rupturing earthquakes generated at a long-term slip rate lower than 0.04 mm/yr, probably about 0.02 mm/yr for the past 42 thousand years. A stratigraphic hiatus between the earthquake records, coincident with the Last Glacial Maximum, results in large uncertainties in the estimated inter-event time, yielding 13.2–33.4 kyr (95 % confidence interval). The new data suggest that the strain is released by regionally distributed faulting. The Zlatitsa fault may form spatial clusters with the neighboring faults, analogous to the two M6.8–7.1 earthquake pairs in 1904 and 1928, south the studied location. The time elapsed since the most recent earthquake on the Zlatitsa fault is 1–15 % from the duration of the previous seismic cycle. The geodetic dilatation rate in the fault vicinity most likely exceeds several times the paleoseismic dilatation rate. However, the geodetic rate eastward from the fault is nearly identical to the paleoseismic rate obtained in the trench. Assuming exponentially decreasing fault reloading, the Zlatitsa fault may still undergo rapid stress restoration, whereas the time elapsed since the most recent earthquakes on faults to the east may be longer than the corresponding relaxation time.

Correlation of paleoearthquake records at multiple sites along the southern Yangsan Fault, Korea: Insights into rupture scenarios of intraplate strike-slip earthquakes

The construction of spatiotemporal models of earthquake occurrence for intraplate areas is challenging due to the low deformation rates in these areas. In this study, we conducted paleoseismological investigations along the southern Yangsan Fault (SYF), a typical low-deformation-rate fault, on the Korean Peninsula. The SYF is distinct from the northern Yangsan Fault (NYF), and the boundary between them is located at the junction between the NNE-striking YF and another major structure, the NNW-striking Ulsan Fault (UF), which branches off from the YF. Paleoseismological trenches at four sites along the SYF indicate that this fault section has not ruptured during the Holocene, in contrast to the NYF and UF. In detail, surface ruptures along the studied section of the SYF occurred during three different time periods, as inferred from stratigraphy and radiocarbon dating: 74 to 49 ka at two sites, 39 to 35 ka at another site, and 28,000 cal yr BP (or 30 ka considering the OSL age) to 16 ka at all sites. These results suggest two alternative rupture scenarios for the timing of paleoearthquakes along the studied fault section during the Late Pleistocene: (1) full rupture along the entire studied section during each earthquake event, or (2) multiple partial ruptures along the two structurally distinguishable parts of the studied fault section, that is, the Wolsan–Miho and Inbo north–Inbo sections. We conclude that geometric discontinuities of the long-lived YF system in the Korean Peninsula intraplate region have played an important role in controlling recent spatiotemporal rupture behavior.

Probabilistic tsunami hazard analysis for western Makran coasts, south-east Iran

Makran subduction zone, along the southern coasts of Iran and Pakistan, has a wide potential seismogenic zone and may be capable of generating large magnitude (M ~ 9) tsunamigenic earthquakes. Considering ambiguities exist in tsunamigenic source characterization for subduction megathrusts like Makran, where detailed geologic, seismic, and geodetic data are insufficient, the probabilistic tsunami hazard analysis (PTHA) is the most prevalent approach to handle uncertainties and estimate more reliable tsunami hazard. Here, PTHA is performed for the coastal region of the western Makran, south-eastern Iran. Using the logic tree approach, we have considered the uncertainty of maximum seismic magnitude, earthquake occurrence model, continuity of seismic zone, seismic coupling coefficient, rupture depth, presence or absence of splay faults, fault locations, and fault slip distribution in PTHA calculation for the western Makran region. We have derived uniform tsunami hazard maps for two return periods of 475 and 2475 years for two confidence levels, the mean and the 84th percentile. Ground subsidence effects are also evaluated in a probabilistic manner. According to the PTHA results, Chabahar and Sirik towns are at the highest and lowest tsunami risk, respectively.

Analyzing the Correlations and the Statistical Distribution of Moderate to Large Earthquakes Interevent Times in Greece

Seismic temporal properties constitute a fundamental component in developing probabilistic models for earthquake occurrence in a specific area. Earthquake occurrence is neither periodic nor completely random but often accrues into bursts in both short- and long-term time scales, and involves a complex summation of triggered and independent events (ΔT). This behavior underlines the impact of the correlations on many potential applications such as the stochastic point process for the earthquake interevent times. In this respect, we intend firstly to determine the appropriate magnitude thresholds, Mthr, indicating the temporal crossover between correlated and statistically independent earthquakes in each 1 of the 10 distinctive sub-areas of the Aegean region. The second goal is the investigation of the statistical distribution that optimally fits the interevent times’ data for earthquakes with M≥Mthr after evaluating the Gamma, Weibull, Lognormal and Exponential distributions performance. Results concerning the correlations analysis evidenced that the temporal crossover of the earthquake interevent time data ranges from Mthr≥ 4.7 up to Mthr≥ 5.1 among the 10 sub-areas. The distribution fitting and comparison reveals that the Gamma distribution outperforms the other three distributions for all the data sets. This finding indicates a burst or clustering behavior in the earthquake interevent times, in which each earthquake occurrence depends upon only the occurrence time of the last one and not from the full seismic history.

An Efficient, Analytic Solution Using Order Statistics for Probabilistic Seismic-Hazard Assessment without the Poisson Assumption

ABSTRACT Standard approaches to probabilistic seismic-hazard assessment (PSHA) assume that earthquakes are random, independent events that follow a Poisson distribution of occurrences in a given time period (Cornell, 1968). To overcome the limitations of the Poisson assumption, such as ignoring earthquake clustering, we introduce an analytic method for PSHA that uses order statistics to allow for arbitrary distributions of earthquake occurrence. Cornell (1968) used the Poisson assumption to achieve a computationally efficient method that enables users to explore the impact of parameters used in earthquake occurrence and ground-motion models. We apply our order statistics method to the highly clustered seismicity associated with caldera collapses at Kīlauea and explore the general implications of non-Poisson behavior for PSHA. We find that non-Poisson behavior has the greatest impact for high probabilities of exceedance, low-mean rates of occurrence, and multiple exceedances. Those conditions can be important for applications such as operating standards for buildings and infrastructure engineering, standards for temporary structures and during construction, the insurance industry, the design of earthquake early warning, and to assess hazards due to clustered processes such as aftershock sequences and earthquake swarms. The commonly used rate of exceedance hides the difference between the hazard due to a non-Poisson distribution and a Poisson distribution with the same mean rate of earthquakes. Thus, including non-Poisson behavior in PSHA means that we must plot and discuss PSHA results as the probability and not the rate of exceedance.

Bayesian Parameter Estimation for Space and Time Interacting Earthquake Rupture Model Using Historical and Physics-Based Simulated Earthquake Catalogs

ABSTRACTThis article introduces a framework to supplement short historical catalogs with synthetic catalogs and determine large earthquakes’ recurrence. For this assessment, we developed a parameter estimation technique for a probabilistic earthquake occurrence model that captures time and space interactions between large mainshocks. The technique is based on a two-step Bayesian update that uses a synthetic catalog from physics-based simulations for initial parameter estimation and then the historical catalog for further calibration, fully characterizing parameter uncertainty. The article also provides a formulation to combine multiple synthetic catalogs according to their likelihood of representing empirical earthquake stress drops and Global Positioning System-inferred interseismic coupling. We applied this technique to analyze large-magnitude earthquakes’ recurrence along 650 km of the subduction fault’s interface located offshore Lima, Peru. We built nine 2000 yr long synthetic catalogs using quasi-dynamic earthquake cycle simulations based on the rate-and-state friction law to supplement the 450 yr long historical catalog. When the synthetic catalogs are combined with the historical catalog without propagating their uncertainty, we found average relative reductions larger than 90% in the recurrence parameters’ uncertainty. When we propagated the physics-based simulations’ uncertainty to the posterior, the reductions in uncertainty decreased to 60%–70%. In two Bayesian assessments, we then show that using synthetic catalogs results in higher parameter uncertainty reductions than using only the historical catalog (69% vs. 60% and 83% vs. 80%), demonstrating that synthetic catalogs can be effectively combined with historical data, especially in tectonic regions with short historical catalogs. Finally, we show the implications of these results for time-dependent seismic hazard.

Calculation of landslide occurrence probability in Taiwan region under different ground motion conditions

In this study, Bayesian probability method and machine learning model are used to study the real occurrence probability of earthquake-induced landslide risk in Taiwan region. The analyses were based on the 1999 Taiwan Chi-Chi Earthquake, the largest earthquake in the history in this Region in a hundred years, thus can provide better control on the prediction accuracy of the model. This seismic event has detailed and complete seismic landslide inventories identified by polygons, including 9272 seismic landslide records. Taking into account the real earthquake landslide occurrence area, the difference in landslide area and the non-sliding/sliding sample ratios and other factors, a total of 13,656,000 model training samples were selected. We also considered other seismic landslide influencing factors, including elevation, slope, aspect, topographic wetness index, lithology, distance to fault, peak ground acceleration and rainfall. Bayesian probability method and machine learning model were combined to establish the multi-factor influence of earthquake landslide occurrence model. The model is then applied to the whole Taiwan region using different ground motion peak accelerations (from 0.1 g to 1.0 g with 0.1 g intervals) as a triggering factor to complete the real probability of earthquake landslide map in Taiwan under different peak ground accelerations, and the functional relationship between different Peak Ground Acceleration and their predicted area is obtained.

Time-dependent model for earthquake occurrence and effects of design spectra on structural performance: a case study from the North Anatolian Fault Zone, Turkey

Time-dependent model for earthquake occurrence and effects of design spectra on structural performance: a case study from the North Anatolian Fault Zone, Turkey

Attention-Based Bi-Directional Long-Short Term Memory Network for Earthquake Prediction

An earthquake is a tremor felt on the surface of the earth created by the movement of the major pieces of its outer shell. Till now, many attempts have been made to forecast earthquakes, which saw some success, but these attempted models are specific to a region. In this paper, an earthquake occurrence and location prediction model is proposed. After reviewing the literature, long short-term memory (LSTM) is found to be a good option for building the model because of its memory-keeping ability. Using the Keras tuner, the best model was selected from candidate models, which are composed of combinations of various LSTM architectures and dense layers. This selected model used seismic indicators from the earthquake catalog of Bangladesh as features to predict earthquakes of the following month. Attention mechanism was added to the LSTM architecture to improve the model’s earthquake occurrence prediction accuracy, which was 74.67%. Additionally, a regression model was built using LSTM and dense layers to predict the earthquake epicenter as a distance from a predefined location, which provided a root mean square error of 1.25.

Probabilistic Tsunami Hazard Assessment in South China Sea With Consideration of Uncertain Earthquake Characteristics

AbstractIn this paper, we have conducted a probabilistic tsunami hazard assessment (PTHA) for Hong Kong (China) and Kao Hsiung (Taiwan), considering earthquakes generated in the Manila subduction zone. The new PTHA methodology with the consideration of uncertainties of slip distribution and location of future earthquakes extends the stochastic approach of Sepúlveda et al. (2017). Using sensitivity analyses, we further investigate the uncertainties of probability properties defining the slip distribution, the location, and the occurrence of earthquakes. We demonstrate that Kao Hsiung and Hong Kong would be significantly impacted by tsunamis generated by MW > 8.5 earthquakes in the Manila subduction zone. For instance, a specific MW 9.0 earthquake scenario is capable of producing tsunami amplitudes exceeding 4.0 and 3.5 m in Kao Hsiung and Hong Kong, respectively, with a probability of 50%. Despite the significant tsunami impact, great earthquakes have long mean return periods. As a result, the PTHA shows that Kao Hsiung and Hong Kong are exposed to a relatively small tsunami hazard. For instance, maximum tsunami amplitudes in the assessed locations of Kao Hsiung and Hong Kong exceed 0.32 and 0.18 m, respectively, with a mean return period of 100 years. The inundation hazard in populated areas is small as well, with mean return periods exceeding 1,000 years. Sensitivity analyses demonstrate that the PTHA can be affected by the uncertainties of the probability properties defining the slip distribution, the location, and the occurrence of earthquakes. However, PTHA results are most sensitive to the choice of the earthquake occurrence model.

Structural reliability approach to analysis of probabilistic seismic hazard and its sensitivities

This paper presents a new probabilistic framework for seismic hazard assessment and hazard sensitivity analysis. Hazard in this context means the probability of exceeding a measure of ground shaking intensity, such as peak ground acceleration and spectral acceleration. The main components of the proposed framework include structural reliability methods to estimate exceedance probabilities and their sensitivities, and multiple probabilistic models for earthquake occurrence, magnitude, location, and ground motion. This paper presents two analysis approaches. The first approach utilizes the first- and second-order reliability methods and importance sampling. This approach efficiently yields the hazard exceedance probabilities at a single site. The second approach employs the Monte Carlo sampling reliability method and yields the hazard exceedance probabilities at a multitude of sites in a single analysis, which is suited for large-scale seismic zonation. This paper also presents the probabilistic models that are suited for such analyses with an emphasis on characterization of epistemic uncertainties. Finally, novel sensitivity measures are proposed for hazard sensitivity analysis. These measures provide a framework to identify the most important uncertainties and guide the research to reduce these uncertainties over time. The proposed approach is validated and showcased by an illustrative example. The companion paper presents a comprehensive application to hazard analysis of Iran.

Global strain rates in western to central Himalayas and their implications in seismic hazard assessment

The Himalayas has experienced varying rates of earthquake occurrence in the past in its seismo-tectonically distinguished segments which may be attributed to different physical processes of accumulation of stress and its release, and due diligence is required for its inclusion for working out the seismic hazard. The present paper intends to revisit the various earthquake occurrence models applied to Himalayas and examines it in the light of recent damaging earthquakes in Himalayan belt. Due to discordant seismicity of Himalayas, three types of regions have been considered to estimate larger return period events. The regions selected are (1) the North-West Himalayan Fold and Thrust Belt which is seismically very active, (2) the Garhwal Himalaya which has never experienced large earthquake although sufficient stress exists and (3) the Nepal region which is very seismically active region due to unlocked rupture and frequently experienced large earthquake events. The seismicity parameters have been revisited using two earthquake recurrence models namely constant seismicity and constant moment release. For constant moment release model, the strain rates have been derived from global strain rate model and are converted into seismic moment of earthquake events considering the geometry of the finite source and the rates being consumed fully by the contemporary seismicity. Probability of earthquake occurrence with time has been estimated for each region using both models and compared assuming Poissonian distribution. The results show that seismicity for North-West region is observed to be relatively less when estimated using constant seismicity model which implies that either the occupied accumulated stress is not being unconfined in the form of earthquakes or the compiled earthquake catalogue is insufficient. Similar trend has been observed for seismic gap area but with lesser difference reported from both methods. However, for the Nepal region, the estimated seismicity by the two methods has been found to be relatively less when estimated using constant moment release model which implies that in the Nepal region, accumulated strain is releasing in the form of large earthquake occurrence event. The partial release in second event of May 2015 of similar size shows that the physical process is trying to release the energy with large earthquake event. If it would have been in other regions like that of seismic gap region, the fault may not have released the energy and may be inviting even bigger event in future. It is, therefore, necessary to look into the seismicity from strain rates also for its due interpretation in terms of predicting the seismic hazard in various segments of Himalayas.

Long-range dependence in earthquake-moment release and implications for earthquake occurrence probability

Since the beginning of the 1980s, when Mandelbrot observed that earthquakes occur on ‘fractal’ self-similar sets, many studies have investigated the dynamical mechanisms that lead to self-similarities in the earthquake process. Interpreting seismicity as a self-similar process is undoubtedly convenient to bypass the physical complexities related to the actual process. Self-similar processes are indeed invariant under suitable scaling of space and time. In this study, we show that long-range dependence is an inherent feature of the seismic process, and is universal. Examination of series of cumulative seismic moment both in Italy and worldwide through Hurst’s rescaled range analysis shows that seismicity is a memory process with a Hurst exponent H ≈ 0.87. We observe that H is substantially space- and time-invariant, except in cases of catalog incompleteness. This has implications for earthquake forecasting. Hence, we have developed a probability model for earthquake occurrence that allows for long-range dependence in the seismic process. Unlike the Poisson model, dependent events are allowed. This model can be easily transferred to other disciplines that deal with self-similar processes.

MODEL OF TECTONIC EARTHQUAKE PREPARATION AND OCCURRENCE AND ITS PRECURSORS IN CONDITIONS OF CRUSTAL STRETCHING

In connection with changes in the stress-strain state of the Earth's crust, various physical and mechanical processes, including destruction, take place in the rocks and are accompanied by tectonic earthquakes. Different models have been proposed to describe earthquake preparation and occurrence, depending on the mechanisms and the rates of geodynamic processes. One of the models considers crustal stretching that is characteristic of formation of rift structures. The model uses the data on rock samples that are stretched until destruction in a special laboratory installation. Based on the laboratory modeling, it is established that the samples are destroyed in stages that are interpreted as stages of preparation and occurrence of an earthquake source. The preparation stage of underground tremors is generally manifested by a variety of temporal (long-, medium- and short-term) precursors. The main shortcoming of micro-modeling is that, considering small sizes of the investigated samples, it is impossible to reveal a link between the plastic extension of rocks (taking place in the earthquake hypocenter) and the rock rupture. Plasticity is the ability of certain rocks to change shape and size irreversibly, while the rock continuity is maintained, in response to applied external forces. In order to take into account the effect of plastic deformation of rocks on earthquake preparation and occurrence, we propose not to refer to the diagrams showing stretching of the rock samples, but use a typical diagram of metal stretching, which can be obtained when testing a metal rod for breakage (Fig. 1). The diagram of metal stretching as a function of the relative elongation (to some degree of approximation and taking into account the coefficient of plasticity) can be considered as a model of preparation and occurrence of an earthquake source in case of rifting. The energy released in the period immediately preceding the earthquake contributes to the emergence of its precursors. This article discusses various earthquake precursors with reference to the energy model of tectonic earthquake preparation and occurrence in conditions of crustal stretching.

Probabilistic seismic hazard assessment of southern part of Ghana

This paper presents a seismic hazard map for the southern part of Ghana prepared using the probabilistic approach, and seismic hazard assessment results for six cities. The seismic hazard map was prepared for 10% probability of exceedance for peak ground acceleration in 50 years. The input parameters used for the computations of hazard were obtained using data from a catalogue that was compiled and homogenised to moment magnitude (Mw). The catalogue covered a period of over a century (1615–2009). The hazard assessment is based on the Poisson model for earthquake occurrence, and hence, dependent events were identified and removed from the catalogue. The following attenuation relations were adopted and used in this study—Allen (for south and eastern Australia), Silva et al. (for Central and eastern North America), Campbell and Bozorgnia (for worldwide active-shallow-crust regions) and Chiou and Youngs (for worldwide active-shallow-crust regions). Logic-tree formalism was used to account for possible uncertainties associated with the attenuation relationships. OpenQuake software package was used for the hazard calculation. The highest level of seismic hazard is found in the Accra and Tema seismic zones, with estimated peak ground acceleration close to 0.2 g. The level of the seismic hazard in the southern part of Ghana diminishes with distance away from the Accra/Tema region to a value of 0.05 g at a distance of about 140 km.

Application of hidden semi-Markov models for the seismic hazard assessment of the North and South Aegean Sea, Greece

ABSTRACTThe real stress field in an area associated with earthquake generation cannot be directly observed. For that purpose we apply hidden semi-Markov models (HSMMs) for strong earthquake occurrence in the areas of North and South Aegean Sea considering that the stress field constitutes the hidden process. The advantage of HSMMs compared to hidden Markov models (HMMs) is that they allow any arbitrary distribution for the sojourn times. Poisson, Logarithmic and Negative Binomial distributions as well as different model dimensions are tested. The parameter estimation is achieved via the EM algorithm. For the decoding procedure, a new Viterbi algorithm with a simple form is applied detecting precursory phases (hidden stress variations) and warning for anticipated earthquake occurrences. The optimal HSMM provides an alarm period for 70 out of 88 events. HMMs are also studied presenting poor results compared to these obtained via HSMMs. Bootstrap standard errors and confidence intervals for the parameters are evaluated and the forecasting ability of the Poisson models is examined.

Three Regimes of the Distribution of the Largest Event in the Critical ETAS Model

Abstract This article proves that three regimes of asymptotic behavior exist in the critical case and transit smoothly from one to another according to a single parameter. Our results correct and extend the results of Saichev and Sornette (2005), Zhuang and Ogata (2006), and Vere‐Jones and Zhuang (2008) on the asymptotic behavior of the largest event in the epidemic‐type aftershock sequence model for earthquake occurrence when the process is critical.