S13E-01
Including foreshocks and aftershocks in time-independent probabilistic seismic hazard analyses
Traditional or time-independent probabilistic seismic hazard analysis (PSHA) treats each source as being temporally and spatially independent; hence foreshocks and aftershocks, which are both spatially and temporally dependent on the mainshock, are removed from earthquake catalogs. Yet, intuitively, these earthquakes should be considered part of the seismic hazard, capable of producing damaging ground motions. In this study, we consider the mainshock and its dependents as a time-independent cluster, having a recurrence time of the mainshock, such that each earthquake in the cluster can contribute to seismic ground motions and hazard. We produce PSHA maps and compare ground motions resulting from the clustered model to a traditional analysis. The concept of clustering in PSHA was outlined by Silva and Toro for the New Madrid series or cluster of earthquakes, in which they suggest that every 500 years, the probability of exceeding a specified ground motion at a given location could be achieved by any of the three segments in the cluster: the southern segment, the central segment, or the northern segment. They considered this mathematically as a union. Therefore, the probability that the New Madrid cluster, pc, will exceed a specified ground motion is expressed by the equation pc=1-(1- p1)(1-p2)(1-p3) where p1, p2, and p3 are the individual ground motion exceedance probabilities of the earthquakes making up the cluster. Generalizing this for n foreshocks and aftershocks, this equation can be written pc=1-\prod{1-pn}. There are several interesting properties of this equation. If any one of the exceedance probabilities is equal to one, the exceedance probability for the cluster is one. As the individual probabilities decrease, as happens for very large and infrequent ground motions or great distances from the fault, the individual exceedance probabilities tend to add. Take, for example, hazard curves for a New Madrid earthquake cluster. At return periods on the order of the cluster recurrence interval, 500 years, only a single earthquake appears to contribute to the hazard. But at longer return periods, say 2500 years, all earthquakes in the cluster appear to contribute fully to the hazard. Because of this behavior, including foreshocks and aftershocks will never increase the hazard by more than the ratio of a catalog containing all shocks to one having the dependent earthquakes removed. Typically, seismic hazard based on earthquake catalogs considers a range of magnitude between 5 and 7. Over this range, we find that for the Central and Eastern US, the rate of all earthquakes is about a factor of 2.5 greater than the rate of independent earthquakes, where the declustered earthquake catalog is obtained with a Gardner and Knopoff declustering algorithm. In the Western US, this ratio is closer to 2. These ratios imply a potentially significant increase in time-independent estimates of seismic hazard at long return periods relative to the recurrence interval of the mainshocks.
S13E-02
The Influence of Declustering on Seismicity Rate Change Estimations
Analyzing seismicity rate changes (SRC) is widely used in statistical seismology because transients in activity can be related to changes in physical properties in the Earth's crust (e.g., changes in static/dynamic stress, fluid migration, precursory signal). However, how to best estimate the significance of SRC in the presence of earthquake clustering remains a challenge. Declustering is commonly applied to separate dependent events (fore- and aftershocks, swarms) from independent events (background) that may contain imprints of changes in physical processes. Because declustering is a non-unique process, it potentially has a large impact on the estimated SRC and, consequently, the interpretation of an observed transient. We present a new approach for estimating the significance of SRC based on extensive Monte Carlo simulations over the entire parameter space of common declustering algorithms. We also include uncertainties of the hypocenter parameters, variations in sampling volumes, duration of rate changes, and bin sizes. To be able to compare the significance of the SRC values across different parameter spaces and different SRC estimators (e.g., z- and β-values) , we translate the values of different estimators into parameter-independent probabilities. We have performed a sensitivity analysis to quantify the impact of declustering algorithms and parameters settings on seismicity analysis. As an example application, we investigate the influence on estimating the significance of precursory seismic quiescence (PSQ). The PSQ hypothesis states that some main shocks are preceded by a significant decrease in the seismicity rate of micro-earthquakes, in the years to months prior, and including parts or all of the subsequent ruptured volume. Detecting PSQ requires careful measurements of background SRC. For the sensitivity analysis, we use a variety of data sets. Preliminary results on simple stochastic simulated catalogs indicate that declustering may have a significant influence on SRC. We will present results using successively increased complexity in the simulated catalogs by combining Poissonian background activity with a PSQ, and/or by including Epidemic Type Aftershock Sequences. Finally, we investigate these effects on real catalog data, using the ANSS catalog for southern California.
S13E-03
The Effect of Clustering Algorithms on Aftershock Productivity and Foreshock Rates
The properties of earthquake clusters are important for the modeling of short-term hazard. In particular the forecasting of larger events is of societal importance. We apply common declustering algorithms, including Reasenberg, Gardner-Knophoff, and the model independent method by Marsan to the Southern California earthquake data to define earthquake clusters. We model the aftershock productivity as a function of mainshock magnitude M for the different clustering algorithms by Nave = 10α(M-M1), where α is the growth parameter and M1 corresponds to the magnitude that on average has one aftershock above the completeness magnitude. The number of aftershocks, hereafter called abundance, depends on the area and time in which to count aftershocks as well as the completeness magnitude. Spatial and temporal extent of aftershock sequences can vary significantly with clustering algorithm. By combining the abundance model with the Gutenberg-Richter equation for the distribution of earthquake magnitude, we can predict foreshock rates and compare them to observations. Depending on the clustering algorithm, foreshock rates can vary up to a factor of two. For some clustering algorithms, the foreshock rate is magnitude dependent, while for other algorithms it is not. However, we find that the foreshock rates predicted from aftershock abundance agree well with the observation for any consistent way of defining fore-and aftershocks. This confirms the common assumption that foreshocks trigger mainshocks in the same manner that mainshocks trigger aftershocks. Our results show that properties of earthquake sequences vary with clustering algorithm. Thus interpretations of fore-or aftershock characteristics need to give careful consideration to the clustering algorithm and data selection.
S13E-04 INVITED
Stochastic declustering: visualizing of the family trees in earthquake catalogs with uncertainty
This presentation is concerned with objectively producing declustered catalogs from the original catalog that includes numerous clustered events in space and time. The method is based a space-time branching process model (the ETAS model), which is used for describing how each event generates offspring events. It is shown that the whole space-time process can split into two subprocesses, the background events and the clustered events stochastically. The proposed algorithm combines a parametric maximum likelihood estimate for the clustering structures using the space-time ETAS model and a nonparametric estimate of the background seismicity that we call a variable weighted kernel estimate. To demonstrate the present methods, we estimate the background seismic activities in the central region of New Zealand and in the central and western regions of Japan, then use these estimates to produce catalogs of background events. The key points of this method are the probabilities of one event being triggered by another previous event and being a background event. Making use of these probabilities, we can reconstruct the functions associated with the characteristics of earthquake clusters to test a number of important hypotheses about the earthquake clustering phenomena, such as: (1) The functions for each component in the formulation of the space-time ETAS model are good enough as a first-order approximation for describing earthquake clusters; (2) a background event triggers less offspring in expectation than a triggered event of the same magnitude; (3) the magnitude distribution of the triggered event depends on the magnitude of its direct ancestor; (4) the diffusion of the aftershock sequence is mainly caused by cascades of individual triggering processes, while no evidence shows that each individual triggering process is diffusive; and (5) the scale of the triggering region is still an exponential law, as formulated in the model but not the same one for the expected number of offspring. Another important application of the stochastic declustering methods is in evaluating the probability that an earthquake is a foreshock. The proportion of events that have 1 or more larger descendants in total events is found to be as high as about 15% from the ETAS model theory and the real catalog, which the proportion of foreshocks in background events is only 8%. Such a difference can be explained by the differences between background events and triggered event in the behavior of triggering children, which can be tested by using the stochastic declustering methods.
S13E-05 INVITED
Model-Independent Stochastic Declustering
Earthquakes, whatever their size, can trigger other earthquakes. For example, large mainshocks are followed by aftershocks, which then in turn activate their own local aftershock sequences, and so on. This results in a cascade of triggering, so that the event initiating this chain can indirectly be the cause of many more earthquake occurrences than what it directly triggered, hence extending its reach through multiple triggering. A long-lasting difficulty is to determine, from earthquake data, which events are directly, indirectly, or not at all, connected together. Here we demonstrate that this can be done in a probabilistic way, with no a priori model nor arbitrary parameterization. It is found that even large regional earthquakes (the 1992, Mw7.3 Landers and 1999, Mw7.1 Hector Mine earthquakes in California) have a surprisingly short direct triggering influence (of the order of 10 days for M3+ aftershocks), which is then very substantially extended (by a factor of ~ 100) in duration through multiple triggering. These results show that cascade triggering is a key component in earthquake interactions, and must therefore be accounted for in probabilistic earthquake prediction and seismic hazard assessment.
S13E-06
Use of dependence probabilities to detect near-fault bias in earthquake triggering
Models of triggered seismicty, such as ETAS, do a good job of predicting observed earthquake patterns in time and space, excepting the largest events. However, these models are typically spatially isotropic and so far do not incorporate the fault structure that controls earthquake distribution. We have demonstrated that the average rate of small earthquakes decays with distance from strike-slip faults in California according to a power law of the form R~(x2+d2)- γ/2, where x is distance from a fault, γ is the decay rate of seismicity, and d is a near-fault inner scale. To determine if aftershock statistics reflect the observed scaling, we decluster our data set using traditional methods (e.g. Reasenberg[1984]) and find that γ is higher for triggered events, indicating a near-fault bias. We also select aftershocks of small to moderate earthquakes, using short time and distance windows, and observe a bias of events towards and along strike-slip faults. These results suggest a more appropriate ETAS spatial kernel would have the form φ~x0<em> -γr<em> -β where x0 is distance from a fault, γ is the fault-seismicity parameter, r is distance from a mainshock, and β controls the radially symmetric decay of aftershocks away from a mainshock. To distinguish such a model from the null hypothesis that there is no fault bias in earthquake triggering, we require a better, probability based (non-binary) means of separating triggered from independent events. Because our data is derived from small regions around strike-slip fault segments, we simplify the process by ignoring events whose triggering intensity function gradient is sufficiently low across the region of interest (i.e. all events of interest are affected equally). Furthermore, because only the spatial component of the intensity function controls the gradient, the intensity function can be reduced to I=Δr β/r where Δr is the distance across the region of interest, and r and β are defined as above. Results will be presented for different sets of California faults, illustrating interesting regional variations.
S13E-07 INVITED
Scaling of clustered space-time-magnitude structure of seismicity
The spatiotemporal properties of seismicity as a function of magnitude are investigated for worldwide earthquake catalogs and for local catalogs in the stationary case (constant rate of occurrence), showing a nearly universal scaling behavior. Distributions of distances between consecutive earthquakes (which we call jumps) are magnitude independent and show two power-law regimes, separated by jump values about 200 km in the worldwide case and a smaller value in the local case. The power law corresponding to long jumps reflects the spatial fractal geometry of epicenters, whereas the short-jump power law is of dynamical origin, characteristic of the triggering process. Measuring distributions of times between consecutive events conditioned to the value of jumps shows two regimes as well: a Poisson time occurrence for distant events and a sharp decreasing power-law distribution for close events, the difference between distant and close events given by the crossover value of the jump distribution (200 km in the worldwide case). Moreover, both variables (times and jumps) are uncorrelated in each regime. Finally, diffusion profiles, showing the jump distribution not for consecutive events but for a fixed time separation, are found to be similar to the jump distributions, and independent on the magnitude, contrary to what the waiting-time distributions suggest. These results indicate a complex random-walk-like picture with the existence of Levy flights and other scale-invariant properties. References A. Corral, Universal Earthquake-Occurrence Jumps, Correlations with Time, and Anomalous Diffusion. Phys. Rev. Lett. 97, 178501 (2006). A. Corral, Structure of earthquake occurrence in space, time, and magnitude. Terra Nova (in press). http://einstein.uab.es/acorralc
S13E-08 INVITED
Estimations of mainshock rates based on interevent-time statistics
The statistics of time delays between successive earthquakes has recently been shown to provide useful information about the properties of earthquake clustering, in particular, about the percentage of mainshocks in the catalog (background fraction) [Hainzl et al., BSSA, 2006]. The shape of the interevent-time distribution can be approximated by the gamma distribution where the background fraction is simply determined by the variance and mean value. Although detailed analytical analysis of Saichev & Sornette [JGR, 2007] shows that the distribution for the ETAS-type mainshock-aftershock activity is more complicated, the simple approximation seems to work for a large parameter range. This is verified with synthetic simulations where the underlying frequency-magnitude distribution of the background activity is successfully reconstructed by this method. Here, I will compare the method with "classical" declustering algorithms like the Reasenberg algorithm and the statistical declustering based on the explicit estimation of the ETAS parameters and will discuss its advantages and shortcomings.