Aftershock Sequence Model Research Articles

A performance‐based framework for adaptive seismic aftershock risk assessment

SUMMARYOperative seismic aftershock risk forecasting can be particularly useful for rapid decision‐making in the presence of an ongoing sequence. In such a context, limit state first‐excursion probabilities (risk) for the forecasting interval (a day) can represent the potential for progressive state of damage in a structure. This work lays out a performance‐based framework for adaptive aftershock risk assessment in the immediate post‐mainshock environment. A time‐dependent structural performance variable is adopted in order to measure the cumulative damage in a structure. A set of event‐dependent fragility curves as a function of the first‐mode spectral acceleration for a prescribed limit state is calculated by employing back‐to‐back nonlinear dynamic analyses. An epidemic‐type aftershock sequence model is employed for estimating the spatio‐temporal evolution of aftershocks. The event‐dependent fragility curves for a given limit state are then integrated together with the probability distribution of aftershock spectral acceleration based on the epidemic‐type aftershock sequence aftershock hazard. The daily probability of limit state first‐excursion is finally calculated as a weighted combination of the sequence of limit state probabilities conditioned on the number of aftershocks. As a numerical example, daily aftershock risk is calculated for the L'Aquila 2009 aftershock sequence (central Italy). A representative three‐story reinforced concrete frame with infill panels, which has cyclic strength and stiffness degradation, is used in order to evaluate the progressive damage. It is observed that the proposed framework leads to a sound forecasting of limit state first‐excursion in the structure for two limit states of significant damage and near collapse. Copyright © 2014 John Wiley & Sons, Ltd.

Statistical Modeling of the 1997-1998 Colfiorito Earthquake Sequence: Locating a Stationary Solution within Parameter Uncertainty

Abstract The Umbria–Marche region of Italy is a seismically active region that experienced a strong sequence of earthquakes during 1997–1998, with a cluster of magnitude M ≥5 events, during which the average event rate increased from the long‐term level by several orders of magnitude. Using maximum‐likelihood (ML) inversion of the epidemic‐type aftershock sequences model to characterize the seismicity of this region over 22 years, we find, in agreement with previous studies, the event rate during the sequence is underpredicted, based on simulations with the large M ≥5 events fixed. However, by sampling the parameter space around the ML solution within the inversion uncertainty and comparing the simulated event rate with that of the real data, we are able to find near‐maximum‐likelihood parameters that provide a reasonable match to both the long‐term average event rate and the rate during the sequence. We use the shape of the interevent time histogram to infer that the events in the sequence are probably mostly aftershocks of the large events, rather than an increased occurrence of background events. We suggest that event rate comparisons can be useful as an additional constraint on the selection of parameters from within the 95% confidence interval of the ML fit. Our results demonstrate the extra constraint can greatly improve the match between a stationary model and finite catalog data and that care is needed before adding further parameters to ascribe nonstationarity to time‐dependent event rate changes.

Adaptive Smoothing of Seismicity in Time, Space, and Magnitude for Time-Dependent Earthquake Forecasts for California

Research Article| February 18, 2014 Adaptive Smoothing of Seismicity in Time, Space, and Magnitude for Time‐Dependent Earthquake Forecasts for California Agnès Helmstetter; Agnès Helmstetter aISTerre, Université de Grenoble 1, CNRS, BP 53, F‐38041 Grenoble, Franceagnes.helmstetter@ujf-grenoble.fr Search for other works by this author on: GSW Google Scholar Maximilian J. Werner Maximilian J. Werner bDepartment of Geosciences, Princeton University, Princeton, New Jersey 08544mwerner@princeton.edu Search for other works by this author on: GSW Google Scholar Bulletin of the Seismological Society of America (2014) 104 (2): 809–822. https://doi.org/10.1785/0120130105 Article history first online: 14 Jul 2017 Cite View This Citation Add to Citation Manager Share Icon Share MailTo Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation Agnès Helmstetter, Maximilian J. Werner; Adaptive Smoothing of Seismicity in Time, Space, and Magnitude for Time‐Dependent Earthquake Forecasts for California. Bulletin of the Seismological Society of America 2014;; 104 (2): 809–822. doi: https://doi.org/10.1785/0120130105 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyBulletin of the Seismological Society of America Search Advanced Search Abstract We present new methods for short‐term earthquake forecasting that employ space, time, and magnitude kernels to smooth seismicity. These methods are purely statistical and rely on very few assumptions about seismicity. In particular, we do not use Omori–Utsu law, and only one of our two new models assumes a Gutenberg–Richter law to model the magnitude distribution; the second model estimates the magnitude distribution nonparametrically with kernels. We employ adaptive kernels of variable bandwidths to estimate seismicity in space, time, and magnitude bins. To project rates over short time scales into the future, we simply assume persistence, that is, a constant rate over short time windows. The resulting forecasts from the two new kernel models are compared with those of the epidemic‐type aftershock sequence (ETAS) model generated by Werner et al. (2011). Although our new methods are simpler and require fewer parameters than ETAS, the obtained probability gains are surprisingly close. Nonetheless, ETAS performs significantly better in most comparisons, and the kernel model with a Gutenberg–Richter law attains larger gains than the kernel model that nonparametrically estimates the magnitude distribution. Finally, we show that combining ETAS and kernel model forecasts, by simply averaging the expected rate in each bin, can provide greater predictive skill than ETAS or the kernel models can achieve individually. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Estimating the ETAS model from an early aftershock sequence

AbstractForecasting aftershock probabilities, as early as possible after a main shock, is required to mitigate seismic risks in the disaster area. In general, aftershock activity can be complex, including secondary aftershocks or even triggering larger earthquakes. However, this early forecasting implementation has been difficult because numerous aftershocks are unobserved immediately after the main shock due to dense overlapping of seismic waves. Here we propose a method for estimating parameters of the epidemic type aftershock sequence (ETAS) model from incompletely observed aftershocks shortly after the main shock by modeling an empirical feature of data deficiency. Such an ETAS model can effectively forecast the following aftershock occurrences. For example, the ETAS model estimated from the first 24 h data after the main shock can well forecast secondary aftershocks after strong aftershocks. This method can be useful in early and unbiased assessment of the aftershock hazard.

Constraints on the dynamics and spatio-temporal evolution of the 2011 Oichalia seismic swarm (SW Peloponnesus, Greece)

Abstract In this paper, we present a detailed study of a shallow seismic swarm which took place in the area of Oichalia (SW Peloponnesus), between August and December 2011. The seismic crisis started on 14/8/2011 with an Mw = 4.8 earthquake and was followed by more than 1600 events, several of which having magnitude over 4.0. The activity was recorded by local temporary and regional permanent seismic stations. Thousands of records were collected and routinely analyzed. P- and S-wave arrival times were manually picked and incorporated in the HYPOINVERSE algorithm together with a new optimum local velocity model. Hypocentral solutions were improved by applying a double-difference method. Focal mechanisms show that the activated fault zone is dominated by dip-slip normal faulting, trending NNW–SSE, with the average T-axes orientation being N70°E, consistent with regional tectonics. We have investigated towards stress triggering and fluid diffusion, by employing Coulomb stress transfer, spatio-temporal and Frequency–Magnitude Distribution (FMD) analyses. The negligible Coulomb stress transfer and seismicity rate changes that were calculated imply for a stress deficit in the broader study area, hence an external triggering mechanism is required to justify the observed pattern. The b-values increase towards the SSE, compatible with the similarly directed migration of seismicity, showed that the Oichalia swarm could possibly be adapted to an Epidemic Type Aftershock Sequence model (ETAS). Fluid diffusion is reflected in the spatio-temporal hypocenter migration. Clustering analysis, combined with the temporal distribution of b-values, has shown that the swarm evolved in three major phases, the first two being initiated by major events, which were probably triggered externally due to fluid injection that brought the seismogenic volume into a critical state, likely followed by afterslip. The last phase signified a relaxation period, with dispersed seismicity throughout the area and the b-values gently diminishing towards unity.

Stability of earthquake clustering models: Criticality and branching ratios

We study the stability conditions of a class of branching processes prominent in the analysis and modeling of seismicity. This class includes the epidemic-type aftershock sequence (ETAS) model as a special case, but more generally comprises models in which the magnitude distribution of direct offspring depends on the magnitude of the progenitor, such as the branching aftershock sequence (BASS) model and another recently proposed branching model based on a dynamic scaling hypothesis. These stability conditions are closely related to the concepts of the criticality parameter and the branching ratio. The criticality parameter summarizes the asymptotic behavior of the population after sufficiently many generations, determined by the maximum eigenvalue of the transition equations. The branching ratio is defined by the proportion of triggered events in all the events. Based on the results for the generalized case, we show that the branching ratio of the ETAS model is identical to its criticality parameter because its magnitude density is separable from the full intensity. More generally, however, these two values differ and thus place separate conditions on model stability. As an illustration of the difference and of the importance of the stability conditions, we employ a version of the BASS model, reformulated to ensure the possibility of stationarity. In addition, we analyze the magnitude distributions of successive generations of the BASS model via analytical and numerical methods, and find that the compound density differs substantially from a Gutenberg-Richter distribution, unless the process is essentially subcritical (branching ratio less than 1) or the magnitude dependence between the parent event and the direct offspring is weak.

Comparative evaluation of physics‐based and statistical forecasts in Northern California

AbstractWe perform a retrospective forecast test using Northern California seismicity for the period between 1980 and 2009. We compare 7 realizations of the short‐term clustering epidemic‐type aftershock sequence (ETAS) model, and 21 models combining Coulomb stress change calculations and Rate/State theory (CRS) to forecast seismicity rates in 10 day time intervals. We employ a common learning phase (1974–1980) for CRS models to ensure consistency, and we evaluate the forecasts with log likelihood statistics to detect any spatial inconsistencies and compare the total numbers of forecasts versus observed events. We find that: (1) ETAS models are better forecasters of the spatial evolution in seismicity in the near‐source region, (2) CRS models can compete with ETAS models away from the mainshock rupture, and for short periods after mainshocks, (3) CRS models with optimally oriented receiver fault planes perform better in the first few days after mainshocks, whereas mapped fault planes should be implemented for longer‐term forecasting, and (4) CRS models based on shear stress change calculations have comparable performance with Coulomb stress change models, with the benefit of lesser parameters involved in stress calculations. We conclude that physics‐based and statistical forecast models are complimentary to each other and that future forecasts should be based on statistical models for near‐source regions, and physical models for longer periods and distances. However, the realization of the CRS models involves a number of critical parameters (reference seismicity rates, regional stress field, and loading rates), which should be retrospectively tested to improve the predictive power of physics‐based models.

Quantitative description of induced seismic activity before and after the 2011 Tohoku‐Oki earthquake by nonstationary ETAS models

The epidemic‐type aftershock sequence (ETAS) model is extended for application to nonstationary seismic activity, including transient swarm activity or seismicity anomalies, in a seismogenic region. The time‐dependent rates of both background seismicity and aftershock productivity in the ETAS model are optimally estimated from hypocenter data. These rates can provide quantitative evidence for abrupt or gradual changes in shear stress and/or fault strength due to aseismic transient causes such as triggering by remote earthquakes, slow slips, or fluid intrusions within the region. This extended model is applied to data sets from several seismic events including swarms that were induced by the M9.0 Tohoku‐Oki earthquake of 2011.

Seismic moment ratio of aftershocks with respect to main shocks

The empirical Båth's law indicates that the earthquake process is self‐similar and provides an opportunity to estimate the magnitude of the largest aftershock subsequent to a main shock. However, the analysis of this relation is limited to a small magnitude range and also depends on the aftershock selection rules. As an alternative, we analyze, in this paper, the cumulative seismic moment of aftershocks relative to the main shock moment, because (i) it is a physical quantity that does not only take the largest aftershock into account; (ii) background activity can be considered and as a result estimations are less affected by selection rules; and (iii) the effects of the catalog cut‐off magnitude can be corrected, what leads to larger magnitude range for the analysis. We analyze the global preliminary determination of epicenters U.S. Geological Society catalog (combined with centroid moment tensor focal mechanisms) and find that the seismic moment release of aftershocks is on average approximately 5% of the main shock seismic moment. We show that the results can be well fitted by simulations of the Epidemic Type Aftershock Sequence model. In particular, we test whether simulations constrained by predictions of the static stress‐triggering model, proposing a break of self‐similarity due to the finite seismogenic width, are in agreement with observations. Our analysis shows that the observed dependency on the main shock magnitude as well as systematic variations with the main shock fault plane solution can be both explained by the constraints based on the static stress triggering.

Modeling Earthquake Rate Changes in Oklahoma and Arkansas: Possible Signatures of Induced Seismicity

The rate of M L≥3 earthquakes in the central and eastern United States increased beginning in 2009, particularly in Oklahoma and central Arkansas, where fluid injection has occurred. We find evidence that suggests these rate increases are man‐made by examining the rate changes in a catalog of M L≥3 earthquakes in Oklahoma, which had a low background seismicity rate before 2009, as well as rate changes in a catalog of M L≥2.2 earthquakes in central Arkansas, which had a history of earthquake swarms prior to the start of injection in 2009. In both cases, stochastic epidemic‐type aftershock sequence models and statistical tests demonstrate that the earthquake rate change is statistically significant, and both the background rate of independent earthquakes and the aftershock productivity must increase in 2009 to explain the observed increase in seismicity. This suggests that a significant change in the underlying triggering process occurred. Both parameters vary, even when comparing natural to potentially induced swarms in Arkansas, which suggests that changes in both the background rate and the aftershock productivity may provide a way to distinguish man‐made from natural earthquake rate changes. In Arkansas we also compare earthquake and injection well locations, finding that earthquakes within 6 km of an active injection well tend to occur closer together than those that occur before, after, or far from active injection. Thus, like a change in productivity, a change in interevent distance distribution may also be an indicator of induced seismicity.

Triggering cascades and statistical properties of aftershocks

Applying a simple general procedure for identifying aftershocks, we investigate their statistical properties for a high‐resolution earthquake catalog covering Southern California. We compare our results with those obtained by using other methods in order to show which features truly characterize aftershock sequences and which depend on the definition of aftershocks. Features robust across methods include thepvalue in the Omori‐Utsu law for large main shocks, Båth's law, and the productivity law with an exponent smaller than thebvalue in the Gutenberg‐Richter law. The identification of a typical aftershock distance with the rupture length is a feature we confirm as well as a power law decay in the spatial distribution of aftershocks with an exponent less than 2. Other results we obtain, but not common to all other works including Marsan and Lengliné (2008), Hainzl and Marsan (2008), and Zhuang et al. (2008), are (a)pvalues that do not increase with the main shock magnitude; (b) the duration of bare aftershock sequences that scales with the main shock magnitude; (c) an additional power law in the temporal variation, at intermediate times, in the rate of aftershocks for main shocks of small and intermediate magnitude; and (d) abvalue for the Gutenberg‐Richter law of background events that is sensibly larger than that of aftershocks. Tests on synthetic catalogs generated by the epidemic‐type aftershock sequence model corroborate the validity of our approach.

Earthquake clusters in southern California I: Identification and stability

AbstractWe use recent results on statistical analysis of seismicity to present a robust method for comprehensive detection and analysis of earthquake clusters. The method is based on nearest‐neighbor distances of events in space‐time‐energy domain. The method is applied to a 1981–2011 relocated seismicity catalog of southern California having 111,981 events with magnitudes m ≥ 2 and corresponding synthetic catalogs produced by the Epidemic Type Aftershock Sequence (ETAS) model. Analysis of the ETAS model demonstrates that the cluster detection results are accurate and stable with respect to (1) three numerical parameters of the method, (2) variations of the minimal reported magnitude, (3) catalog incompleteness, and (4) location errors. Application of the method to the observed catalog separates the 111,981 examined earthquakes into 41,393 statistically significant clusters comprised of foreshocks, mainshocks, and aftershocks. The results reproduce the essential known statistical properties of earthquake clusters, which provide overall support for the proposed technique. In addition, systematic analysis with our method allows us to detect several new features of seismicity that include (1) existence of a significant population of single‐event clusters, (2) existence of foreshock activity in natural seismicity that exceeds expectation based on the ETAS model, and (3) dependence of all cluster properties, except area, on the magnitude difference of events from mainshocks but not on their absolute values. The classification of detected clusters into several major types, generally corresponding to singles, burst‐like and swarm‐like sequences, and correlations between different cluster types and geographic locations is addressed in a companion paper.

Impact of Aseismic Transients on the Estimation of Aftershock Productivity Parameters

Abstract The epidemic‐type aftershock sequence (ETAS) model has been shown to describe successfully the statistical seismicity properties, if earthquake triggering is related to tectonic forcing and earthquake‐induced stress changes. However, seismicity is locally often dominated by stress changes related to transient aseismic processes. To avoid erroneous parameter estimations leading to biased forecasts, it is important to account for those transients. We apply a recently developed iterative algorithm based on the ETAS model to identify the time‐dependent background and ETAS parameters simultaneously. We find that this procedure works well for synthetic data sets if catalog errors are appropriately considered. However, ignoring the time dependence leads to significantly biased parameter estimations. In particular, the α ‐value describing the magnitude dependence of the triggering kernel can be strongly underestimated if transients are ignored. Low α ‐values have been previously found for swarm activity, for which transient aseismic processes are expected to play a major role. These observed anomalously low α ‐values might thus indicate the importance of transient forcing, rather than being due to differences in the earthquake–earthquake trigger mechanism. To explore this, we apply the procedure systematically to earthquake clusters detected in southern California and to earthquake swarm activity in Vogtland/Western Bohemia. While low α ‐values are mostly shown to be a consequence of catalog errors and time‐dependent forcing but not related to different earthquake–earthquake interaction mechanisms, some significant low values are observed in high heat‐flow areas in California, confirming the existence of thermal control on earthquake triggering.

Earthquake clusters in southern California II: Classification and relation to physical properties of the crust

AbstractThis is a second paper in a study of statistical identification and classification of earthquake clusters using a relocated catalog of 1981–2011 seismicity in southern California and synthetic catalogs produced by the Epidemic Type Aftershock Sequence model. Here we focus on classification of event families—statistically significant clusters composed of foreshocks, mainshocks, and aftershocks—that are detected with the methodology discussed in part I of the study. The families are analyzed using their representation as time oriented tree graphs. The results (1) demonstrate that the clustering associated with the largest earthquakes, m > 7, is statistically different from that of small‐to‐medium earthquakes; (2) establish the existence of two dominant types of small‐to‐medium magnitude earthquake families—burst‐like and swarm‐like sequences—and a variety of intermediate cluster forms obtained as a mixture of the two dominant types; (3) suggest a simple new quantitative measure for identifying the cluster type based on its topological structure; (4) demonstrate systematic spatial variability of the cluster characteristics on a scale of tens of kilometers in relation to heat flow and other properties governing the effective viscosity of a region; and (5) establish correlation between the family topological structure and a dozen of metric properties traditionally considered in the literature (number of aftershocks, duration, spatial properties, b‐value, parameters of Omori‐Utsu and Båth law, etc.). The burst‐like clusters likely reflect highly brittle failures in relatively cold regions, while the swarm‐like clusters are likely associated with mixed brittle‐ductile failures in regions with relatively high temperature and/or fluid content. The results of this and paper I may be used to develop improved region‐specific hazard estimates and earthquake forecasts.

Precursory change in seismicity revealed by the Epidemic-Type Aftershock-Sequences model: A case study of the 1999 Chi-Chi, Taiwan earthquake

For gaining insight into the preparatory process of the 1999 Chi-Chi, Taiwan earthquake and its related statistical feature, the Epidemic-Type Aftershock-Sequences model (ETAS model) was applied to the earthquake data in Taiwan region. By means of the ETAS analysis for Taiwanese earthquakes larger than a magnitude of 2.4, we found seismic quiescence over broader regions of Taiwan. It was also found that inland areas near the epicenter of the Chi-Chi earthquake showed seismic activation in the period from Jan. 1, 1998 to Sep. 20, 1999, which is just before the occurrence of the Chi-Chi earthquake. The assumption that this is due to precursory slip (stress drop) on the fault plane of the Chi-Chi earthquake is supported by previous researches such as a numerical simulation using rate- and state-dependent friction laws and the observation of abnormal change in crustal displacement for a station of Taiwan GPS network near southern edge of the source area of the Chi-Chi earthquake.

A non‐stationary epidemic type aftershock sequence model for seismicity prior to the December 26, 2004 M 9.1 Sumatra‐Andaman Islands mega‐earthquake

We study temporal changes in seismicity in Sumatra‐Andaman Islands region before the M 9.1 earthquake of December 26, 2004. We applied the epidemic type aftershock sequence (ETAS) models to the seismicity. The two‐stage non‐stationary ETAS model with a single change‐point provides a better statistical fit to the seismicity data than the stationary ETAS model throughout the whole period. We made further change‐point analysis of data sets by dividing into two sub‐regions. The best fitted models suggest that the seismic activation relative to the ETAS rates started in the middle of July 2000 (about 4.5 years before the M 9.1 earthquake). This includes an increase in the background seismicity rates, particularly in the southern part of the seismogenic zone near the epicenter. A space‐time ETAS model also suggests that the background seismicity throughout the entire Sumatra‐Andaman Islands area had increased after the change‐point time.

Facilitated Estimation of ETAS

Abstract An approximation technique is introduced that greatly facilitates the estimation of the epidemic‐type aftershock sequence (ETAS) model introduced by Ogata (1988), which is widely used to describe earthquake catalogs. The proposed approximation greatly simplifies the integral term in the log‐likelihood, the computation of which is by far the greatest hurdle in maximum likelihood estimation. The approximation is close, provided the observed region contains most of the aftershock activity caused by earthquakes within the observation region. Through simulations and an example involving earthquakes in Hector Mine, California, the proposed method is shown to produce stable and accurate results, with rapid convergence.

Scaling behavior of the earthquake intertime distribution: Influence of large shocks and time scales in the Omori law

We present a study of the earthquake intertime distribution D(Δt) for a California catalog in temporal periods of short duration T. We compare experimental results with theoretical predictions and analytical approximate solutions. For the majority of intervals, rescaling intertimes by the average rate leads to collapse of the distributions D(Δt) on a universal curve, whose functional form is well fitted by a Gamma distribution. The remaining intervals, exhibiting a more complex D(Δt), are all characterized by the presence of large shocks. These results can be understood in terms of the relevance of the ratio between the characteristic time c in the Omori law and T: Intervals with Gamma-like behavior are indeed characterized by a vanishing c/T. The above features are also investigated by means of numerical simulations of the Epidemic Type Aftershock Sequence (ETAS) model. This study shows that collapse of D(Δt) is also observed in numerical catalogs; however, the fit with a Gamma distribution is possible only assuming that c depends on the main-shock magnitude m. This result confirms that the dependence of c on m, previously observed for m>6 main shocks, extends also to small m>2.

Evolution of the vigorous 2006 swarm in Zakynthos (Greece) and probabilities for strong aftershocks occurrence

A multiplet of moderate-magnitude earthquakes (5.1 ≤ M ≤ 5.6) took place in Zakynthos Island and offshore area (central Ionian Islands, Greece) in April 2006. The activity in the first month occupied an area of almost 35 km long, striking roughly NNW–SSE, whereas aftershocks continued for several months, decaying with time but persisting at the same place. The properties of the activated structure were investigated with accurate relocated data and the available fault plane solutions of some of the stronger events. Both the distribution of seismicity and fault plane solutions show that thrusting with strike-slip motions are both present in high-angle fault segments. The segmentation of the activated structure could be attributed to the faulting complexity inherited from the regional compressive tectonics. Investigation of the spatial and temporal behavior of seismicity revealed possible triggering of adjacent fault segments that may fail individually, thus preventing coalescence in a large main rupture. In an attempt to forecast occurrence probabilities of six of the strong events (Mw ≥ 5.0), estimations were performed following the restricted epidemic-type aftershock sequence model, applied to data samples before each one of these strong events. Stochastic modeling was also used to identify “quiescence” periods before the examined aftershocks. In two out of the six cases, real aftershock rate did decrease before the next strong shock compared to the modeled one. The latter results reveal that rate decrease is not a clear precursor of strong shocks in the swarm and no quantitative information, suitable to supply probability gain, could be extracted from the data.

Virtual California Earthquake Simulator

The model that would eventually become Virtual California started as a limited simulation model developed by Rundle (1988) for the distributed seismicity on the San Andreas and adjacent faults in southern California. This model included stress accumulation and release as well as stress interactions between faults. An updated version of this model was developed (Rundle et al. 2001, 2002, 2004), including the major strike‐slip faults in California, and was called Virtual California. Details of the model were given in Rundle et al. (2006a,b). Yakovlev et al. (2006) utilized Virtual California simulations to examine the recurrence time statistics on faults in California. They concluded that the distribution of return times on a fault is well approximated by a Weibull distribution. Yikilmaz et al. (2010) used Virtual California to simulate earthquakes on the Nankai trough, Japan, and found an excellent agreement with the historical sequence of 13 great earthquakes. Yikilmaz et al. (2011) gave a composite simulation of seismicity in northern California utilizing Virtual California for earthquakes on mapped faults, a random background of smaller earthquakes, and a branching aftershock sequence (BASS) model simulation of aftershocks. In its current incarnation, Virtual California is a sophisticated tool for simulating earthquakes on a wide variety of fault geometries in a high‐performance computing environment and is part of a larger effort by the Southern California Earthquake Center to unify the results from several different earthquake simulators. A description of this effort and a comparison of the results can be found in Tullis et al. (2012a) and Tullis et al. (2012b), respectively. There are three major components that make up Virtual California: a fault model, a set of quasi‐static interactions (Green’s …