Dynamical scaling and generalized Omori law

Lippiello, Eugenio; Bottiglieri, M.; Godano, C.; Arcangelis, L. de

doi:10.1029/2007gl030963

Cited by 35 publications

(43 citation statements)

References 17 publications

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“…Since t c is typically larger than c 0 , the fit of equation for the incomplete instrumental data set provides a measured value c meas = t c > c 0 . This is confirmed by several studies (Davidsen & Baiesi, ; de Arcangelis et al, ; Lippiello, Bottiglieri, et al, ; Lippiello, Godano, & de Arcangelis, ) showing that the measured value c meas follows equation . As a consequence, the incompleteness at short times hides the true value of c 0 and introduces a strong bias in the routines for short‐term aftershock forecasting (Lippiello et al, ; Omi et al, , ; Zhuang et al, ).…”

Section: Introductionsupporting

confidence: 77%

The Overlap of Aftershock Coda Waves and Short‐Term Postseismic Forecasting

2018

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The elaboration of reliable forecasting in the first hours after large shocks, very useful for the postseismic management, is strongly affected by the huge incompleteness of seismic catalogs. The deficit of observed events, in the first part of aftershock sequences, can be naturally attributed to different mechanisms such as the inefficiency of the seismic network as well as the overlap of seismic records. In this study we show that short‐term aftershock incompleteness can be explained only in terms of the second mechanism whereas it is only weakly affected by the quality of the instrumental coverage. Indeed, we show that larger deviations from the Gutenberg‐Richter law and the Omori‐Utsu law can be found in regions with a higher seismic network efficiency. We use these results to develop an incomplete Epidemic‐Type Aftershock Sequence model able to reproduce statistical features in time and magnitude of recorded aftershocks.

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Section: Introductionsupporting

confidence: 77%

The Overlap of Aftershock Coda Waves and Short‐Term Postseismic Forecasting

2018

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“…The productivity law [18] indicates that a i is exponentially related to the mainshock magnitude a i ¼ A10 m i . The ETAS model assumes c i ¼ c whereas recent studies on experimental catalogs have obtained c i ¼ c10 m i which leads to the so-called generalized Omori law [5,19,20].…”

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confidence: 99%

Multiple-Time Scaling and Universal Behavior of the Earthquake Interevent Time Distribution

Bottiglieri

Arcangelis²,

Godano³

et al. 2010

Phys. Rev. Lett.

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The interevent time distribution characterizes the temporal occurrence in seismic catalogs. Universal scaling properties of this distribution have been evidenced for entire catalogs and seismic sequences. Recently, these universal features have been questioned and some criticisms have been raised. We investigate the existence of universal scaling properties by analyzing a Californian catalog and by means of numerical simulations of an epidemic-type model. We show that the interevent time distribution exhibits a universal behavior over the entire temporal range if four characteristic times are taken into account. The above analysis allows us to identify the scaling form leading to universal behavior and explains the observed deviations. Furthermore, it provides a tool to identify the dependence on the mainshock magnitude of the c parameter that fixes the onset of the power law decay in the Omori law.

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“…They measure the average number of aftershocks ( t − t m ) obtained by summing the contribution of all the analyzed sequences, and they find ( t − t m ) ∼ ( t − t m ) −q with q = 0.58 for t < 900 sec to be compared with the Omori behavior ( t − t m ) ∼ ( t − t m ) − p with p = 0.92 observed for t > 900 sec. Lippiello et al [2007b] showed that the result of Peng et al [2007], which excludes an Omori law extending to very small times, can be well fitted by the DS model.…”

Section: Origin Of the Magnitude Correlationsmentioning

confidence: 91%

“… Lippiello et al [2007a] proposed that the magnitude difference between two events introduces a characteristic time scale over which the two events are correlated. This leads to a dynamical scaling relationship between magnitude difference and temporal distance [ Lippiello et al , 2007a, 2007b, 2008, 2009], expressed as follows: where H ( x ) is a normalizable function. Within this approach, many statistical features of seismic occurrence can be recovered for different functional forms of H ( x ).…”

Section: Introductionmentioning

confidence: 99%

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Comparison of branching models for seismicity and likelihood maximization through simulated annealing

et al. 2011

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[1] Stochastic branching models provide a good description of some aspects of the temporal organization in seismicity. Generally, they assume that magnitudes are independent of history, as in the widely used Epidemic Type Aftershock Sequence (ETAS) model. Here, we consider a recent epidemic-like model where time-magnitude and magnitude-magnitude correlations are introduced via a dynamical scaling (DS) hypothesis, namely, the magnitude difference between earthquakes fixes the time scale for correlations. We also consider a variation of the ETAS model where the c parameter of the Omori law is not fixed but depends on the parent magnitude. We develop a novel procedure to maximize the log likelihood of the different models. This method is based on a Monte Carlo sampling in the parameter space with a variable step size during the evolution to converge to the given accuracy. The log likelihood indicates that the DS model provides the best fit for the major California sequences and the whole catalog, setting as lower magnitude thresholds M c ≥ 3.5. For M c = 3, the best fit is obtained by a model with c depending on both the parent magnitude and goes into M c as in the generalized Omori law. The better performance of the DS model with respect to the ETAS model is attributed to correlations in magnitudes.Citation: Bottiglieri, M., E. Lippiello, C. Godano, and L. de Arcangelis (2011), Comparison of branching models for seismicity and likelihood maximization through simulated annealing,

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Dynamical scaling and generalized Omori law

Cited by 35 publications

References 17 publications

The Overlap of Aftershock Coda Waves and Short‐Term Postseismic Forecasting

The Overlap of Aftershock Coda Waves and Short‐Term Postseismic Forecasting

Multiple-Time Scaling and Universal Behavior of the Earthquake Interevent Time Distribution

Comparison of branching models for seismicity and likelihood maximization through simulated annealing

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