Statistical relations between the parameters of aftershocks in time, space, and magnitude

Guo, Zhenqi; Ogata, Yosihiko

doi:10.1029/96jb02946

Cited by 167 publications

(131 citation statements)

References 33 publications

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“…This signals the impact of large earthquake energies, suggesting the relevance of the upper bound E max (t) in (3). This case is actually observed in real seismicity by [27] who obtained a > µ for some aftershock sequences in Greece, and by [23] who found a > µ for 13 out of 34 aftershock sequences in Japan. This case a > µ also characterizes the seismic activity preceding the 1984 M = 6.8 Nagano Prefecture earthquake [22].…”

mentioning

confidence: 81%

Occurrence of Finite-Time Singularities in Epidemic Models of Rupture, Earthquakes, and Starquakes

Sornette

Helmstetter

2002

Phys. Rev. Lett.

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We present a new kind of critical stochastic finite-time-singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock (ETAS) model for aftershocks, based solely on the most solidly documented stylized facts of seismicity (clustering in space and in time and power law Gutenberg-Richter distribution of earthquake energies). This theory accounts for the main observations (power law acceleration and discrete scale invariant structure) of critical rupture of heterogeneous materials, of the largest sequence of starquakes ever attributed to a neutron star as well as of earthquake sequences.A large portion of the current work on rupture and earthquake prediction is based on the search for precursors to large events in the seismicity itself. Observations of the acceleration of seismic moment leading up to large events and "stress shadows" following them have been interpreted as evidence that seismic cycles represent the approach to and retreat from a critical state of a fault network [1]. This "critical state" concept is fundamentally different from the long-time view of the crust as evolving spontaneously in a statistically stationary critical state, called self-organized criticality (SOC) [2]. In the SOC view, all events belong to the same global population and participate in shaping the self-organized critical state. Large earthquakes are inherently unpredictable because a big earthquake is simply a small earthquake that did not stop. By contrast, in the critical point view, a great earthquake plays a special role and signals the end of a cycle on its fault network. The dynamical organization is not statistically stationary but evolves as the great earthquake becomes more probable. Predictability might then become possible by monitoring the approach of the fault network towards the critical state. This hypothesis first proposed in [1] is the theoretical induction of a series of observations of accelerated seismicity [3,4] which has been later strengthened by several other observations [5,6,7,8]. Theoretical support has also come from simple computer models of critical rupture [9] and experiments of material rupture [10], cellular automata, with [11] and without [12] long-range interaction, and from granular simulators [13]. Models of regional seismicity with more faithful fault geometry have been developed that also show accelerating seismicity before large model events [14,15,16].There are at least five different mechanisms that are known to lead to critical accelerated seismicity of the formending at the critical time t c , where N (t) is the seismicity rate (or acoustic emission rate for material rupture). Such finite-time-singularities are quite common and have been found in many well-established models of natural systems, either at special points in space such as in the Euler equations of inviscid fluids, in vortex collapse of systems of point vortices, in the equations of General Relativity coupled to a mass field leading to...

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confidence: 81%

Occurrence of Finite-Time Singularities in Epidemic Models of Rupture, Earthquakes, and Starquakes

Sornette

Helmstetter

2002

Phys. Rev. Lett.

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“…This is nothing but the quiescence of the background activity relative to the stationary Poisson process. It has been shown that ordinary seismicity and even a single sequence of aftershocks is generally well represented by the ETAS model [e.g., Ogata, 1988;Guo and Ogata, 1997]. Therefore the relative quiescence should be more sensitive than the conventional quiescence in the sense that quiescence can be more clearly seen by using a better model of normal aftershock activity or general seismicity.…”

Section: Discussionmentioning

confidence: 99%

Detection of anomalous seismicity as a stress change sensor

Ogata

2005

J. Geophys. Res.

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[1] Anomalous seismicity such as quiescence and activation is defined by a systematic deviation of seismic activity from the predicted rate by the epidemic-type aftershock sequence (ETAS) model that represents the normal occurrence rate of earthquakes in a region indicating the empirical triggering effect by the previous events. The model is fitted to a data set of origin times and magnitudes of earthquakes or aftershocks during MayAugust 2003 in and around northern Japan. The detected quiescence and activation relative to the predicted seismicity rate are consistent with the coseismic changes of Coulomb failure stress (CFS) in the corresponding regions, transferred from certain strong earthquakes. Few results in this paper agree with the claim that there should be a threshold value of DCFS capable of affecting seismic changes. Thus we expect that significant deviation of actual activity from the predicted rates is sensitive enough to detect a slight stress change. Furthermore, I offer a similar interpretation of the detected seismicity lowering relative to the modeled rates preceding the strong earthquakes, assuming some aseismic slips.Citation: Ogata, Y. (2005), Detection of anomalous seismicity as a stress change sensor,

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“…The constructed aftershock rates were modeled using the modified Omori law. The parameters of the model were computed using the maximum likelihood estimate (Utsu et al 1995;Guo & Ogata 1997 The Canterbury aftershock sequence can be also modelled by the combination of the three rates reflecting the occurrence of two large earthquakes which generated their own aftershock sequences: rð! m c ; tÞ ¼ 1…”

Section: Aftershock Decay Ratesmentioning

confidence: 99%

Statistical analysis of the 2010M_W7.1 Darfield Earthquake aftershock sequence

Shcherbakov

Nguyen

Quigley

2012

New Zealand Journal of Geology and Geophysics

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Statistical relations between the parameters of aftershocks in time, space, and magnitude

Cited by 167 publications

References 33 publications

Occurrence of Finite-Time Singularities in Epidemic Models of Rupture, Earthquakes, and Starquakes

Occurrence of Finite-Time Singularities in Epidemic Models of Rupture, Earthquakes, and Starquakes

Detection of anomalous seismicity as a stress change sensor

Statistical analysis of the 2010M_W7.1 Darfield Earthquake aftershock sequence

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Statistical relations between the parameters of aftershocks in time, space, and magnitude

Cited by 167 publications

References 33 publications

Occurrence of Finite-Time Singularities in Epidemic Models of Rupture, Earthquakes, and Starquakes

Occurrence of Finite-Time Singularities in Epidemic Models of Rupture, Earthquakes, and Starquakes

Detection of anomalous seismicity as a stress change sensor

Statistical analysis of the 2010MW7.1 Darfield Earthquake aftershock sequence

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Product

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Statistical analysis of the 2010M_W7.1 Darfield Earthquake aftershock sequence