Constraints on the size of the smallest triggering earthquake from the epidemic‐type aftershock sequence model, Båth's law, and observed aftershock sequences

Sornette, Didier; Werner, Maximilian J.

doi:10.1029/2004jb003535

Cited by 81 publications

(89 citation statements)

References 68 publications

(143 reference statements)

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“…Depending on the value of the branching ratio, it is possible to separate significantly different cases of model behaviour: a branching ratio of n > 1 leads to escalating seismic sequences; 0 < n < 1 describes a stationary regime; while n = 0 implies that all events are independent and thus represents a Poisson process. Observational evidence indicates a branching ratio in the range 0.5-1.0 (Sornette & Werner 2005). In our simulations, we assume n = 0.8 to set the K-value.…”

Section: Etas Simulationsmentioning

confidence: 99%

Statistical estimation of the duration of aftershock sequences

Hainzl¹,

Christophersen

Rhoades

et al. 2016

Geophys. J. Int.

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S U M M A R YIt is well known that large earthquakes generally trigger aftershock sequences. However, the duration of those sequences is unclear due to the gradual power-law decay with time. The triggering time is assumed to be infinite in the epidemic type aftershock sequence (ETAS) model, a widely used statistical model to describe clustering phenomena in observed earthquake catalogues. This assumption leads to the constraint that the power-law exponent p of the Omori-Utsu decay has to be larger than one to avoid supercritical conditions with accelerating seismic activity on long timescales. In contrast, seismicity models based on rate-and statedependent friction observed in laboratory experiments predict p ≤ 1 and a finite triggering time scaling inversely to the tectonic stressing rate. To investigate this conflict, we analyse an ETAS model with finite triggering times, which allow smaller values of p. We use synthetic earthquake sequences to show that the assumption of infinite triggering times can lead to a significant bias in the maximum likelihood estimates of the ETAS parameters. Furthermore, it is shown that the triggering time can be reasonably estimated using real earthquake catalogue data, although the uncertainties are large. The analysis of real earthquake catalogues indicates mainly finite triggering times in the order of 100 days to 10 years with a weak negative correlation to the background rate, in agreement with expectations of the rate-and state-friction model. The triggering time is not the same as the apparent duration, which is the time period in which aftershocks dominate the seismicity. The apparent duration is shown to be strongly dependent on the mainshock magnitude and the level of background activity. It can be much shorter than the triggering time. Finally, we perform forward simulations to estimate the effective forecasting period, which is the time period following a mainshock, in which ETAS simulations can improve rate estimates after the occurrence of a mainshock. We find that this effective forecasting period is only in the order of 100 days for moderate mainshocks and in the order of a few years for large events, even if the underlying triggering process lasts much longer.

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Section: Etas Simulationsmentioning

confidence: 99%

Statistical estimation of the duration of aftershock sequences

Hainzl¹,

Christophersen

Rhoades

et al. 2016

Geophys. J. Int.

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“…Here, we allow the ETAS (Ogata, 29 1988;Ogata, 1998) model to use all available earthquakes to achieve optimum 30 performance although the Nepal catalog is complete to M≥4.7. To estimate the necessaryparameters, we use equations for estimating the apparent fraction na with respect to the 32 real fraction of triggered events n (Sornette and Werner, 2005). .…”

Section: Data and Resourcesmentioning

confidence: 99%

Prospective Earthquake Forecasts at the Himalayan Front after the 25 April 2015M 7.8 Gorkha Mainshock

Segou

Parsons

2016

Seismological Research Letters

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When a major earthquake strikes, the resulting devastation can be compounded or even exceeded by the subsequent cascade of triggered seismicity. As the Nepalese recover from the 25 April 2015 shock, knowledge of what comes next is essential. We calculate the redistribution of crustal stresses and implied earthquake probabilities for different periods from daily to 30 years into the future. An initial forecast was completed before a M=7.3 earthquake struck on May 12, 2015 that enables a preliminary assessment; post-forecast seismicity has so far occurred within a zone of 5-fold probability gain. Evaluation of the forecast performance, using 2 months of seismic data, reveals that stress-based approaches present improved skill in higher magnitude triggered seismicity. Our results suggest that considering the total stress field, rather than only the co-seismic one, improves the spatial performance of the model based on the estimation of a wide range of potential triggered faults following a mainshock. 2 IntroductionThe Himalayas rise by absorbing 18-22 mm/yr of Indian-Eurasian plate convergence (Ader et al., 2012) (Fig. 1). On the 25 th of April, 2015, a M=7.8 earthquake ruptured the low-angle (10˚) fault contact between the two plates, leading to more than 8000 confirmed fatalities, 18,000 people injured, and a million families affected (Nepal Red Cross Society 1 ). Eight UNESCO World Heritage sites were damaged or destroyed. The 25 April shock struck the eastern edge of a 500-km-wide gap between historic earthquakes along the Himalayan front (Fig. 1). The potential of triggered earthquakes beneath highly populated basins in the central Himalaya could compound this catastrophe akin to tragedies in Turkey , China , and New Zealand . Recent studies, based on retrospective experiments, investigate the predictive power of short-term earthquake forecasts within different distance ranges and periods (Segou et al., 2013;Strader and Jackson, 2015), but prospective forecasts still face challenges such as the quality of real-time data, the availability of credible historical/modern earthquake catalogs ,and very short research windows.In this study, we calculate the expected redistribution of stress in the Himalayan crust and develop a method, especially applicable to frontier regions, to determine the probability of triggered earthquakes in both space and time. We make prospective earthquake forecasts using four methods incorporating physics-based and statistical approaches for varying time horizons, and formally evaluate the shortest-term calculations.The results reveal the efficiency of physics-based forecasts in estimating short-term earthquake probabilities and their critical contribution in modeling off-fault triggered events, highlighted by the M=5.6 Xegar (3 hours after the mainshock) and the M=7.3 Kodari (May 12) earthquakes. Development of Short-Term Earthquake ForecastsShort-term earthquake forecasts can use empirical statistics to anticipate cascades of triggered events, or simulations of stress redistribution fol...

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“…In statistical seismicity models, on the other hand, the triggering effect of small and moderate quakes is considered important and is accounted for [e.g., Kagan and Knopoff, 1987;Ogata, 1988;Kagan, 1991;Felzer et al, 2002;Console et al, 2003;Sornette and Werner, 2005b;Helmstetter et al, 2006;Werner et al, 2011;Woessner et al, 2010].…”

Section: Introductionmentioning

confidence: 99%

A search for evidence of secondary static stress triggering during the 1992 M_w7.3 Landers, California, earthquake sequence

et al. 2014

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Key Points:• Weak but significant evidence for secondary static stress triggering • 27% of aftershocks receive more positive secondary stress than from main shocks • Secondary stress cannot explain most aftershocks in main shock stress shadows Abstract Secondary triggering of aftershocks is widely observed and often ascribed to secondary static stress transfer. However, small to moderate earthquakes are generally disregarded in estimates of Coulomb stress changes (ΔCFS), either because of source parameter uncertainties or a perceived lack of importance. We use recently published high-quality focal mechanisms and hypocenters to reassess the role of small to moderate earthquakes for static stress triggering of aftershocks during the 1992 M w 7.3 Landers, California, earthquake sequence. We compare the ΔCFS imparted by aftershocks (2 ≤ M ≤ 6) onto subsequent aftershocks with the total ΔCFS induced by the M > 6 main shocks. We find that incremental stress changes between aftershock pairs are potentially more often positive than expected over intermediate distances.Cumulative aftershock stress changes are not reliable for receivers with nearby aftershock stress sources because we exclude unrealistic aftershock stress shadows that result from uniform slip models. Nonetheless, 27% of aftershocks receive greater positive stress from aftershocks than from the main shocks. Overall, 85% of aftershocks are encouraged by the main shocks, while adding secondary stress encourages only 79%. We infer that source parameter uncertainties of small aftershocks remain too large to convincingly demonstrate (or rule out) that secondary stress transfer induces aftershocks. An important exception concerns aftershocks in main shock stress shadows: well-resolved secondary stress from detected aftershocks rarely compensates negative main shock stress; these aftershocks require a different triggering mechanism.

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Constraints on the size of the smallest triggering earthquake from the epidemic‐type aftershock sequence model, Båth's law, and observed aftershock sequences

Cited by 81 publications

References 68 publications

Statistical estimation of the duration of aftershock sequences

Statistical estimation of the duration of aftershock sequences

Prospective Earthquake Forecasts at the Himalayan Front after the 25 April 2015M 7.8 Gorkha Mainshock

A search for evidence of secondary static stress triggering during the 1992 M_w7.3 Landers, California, earthquake sequence

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Constraints on the size of the smallest triggering earthquake from the epidemic‐type aftershock sequence model, Båth's law, and observed aftershock sequences

Cited by 81 publications

References 68 publications

Statistical estimation of the duration of aftershock sequences

Statistical estimation of the duration of aftershock sequences

Prospective Earthquake Forecasts at the Himalayan Front after the 25 April 2015M 7.8 Gorkha Mainshock

A search for evidence of secondary static stress triggering during the 1992 Mw7.3 Landers, California, earthquake sequence

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A search for evidence of secondary static stress triggering during the 1992 M_w7.3 Landers, California, earthquake sequence