Spatiotemporal correlations of aftershock sequences

Peixoto, Tiago P.; Doblhoff-Dier, Katharina; Davidsen, Jörn

doi:10.1029/2010jb007626

Cited by 11 publications

(14 citation statements)

References 52 publications

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“…Figure also shows that the spatial distribution of aftershocks for different main shock magnitude ranges collapse over a wide range of scales only excluding the tail of the distribution. The latter fact is already incompatible with the functional form reported in some studies [ Marsan and Lengliné , ; Lippiello et al , ]

P_{m} (r) = \frac{qr}{L_{m}^{2} {((), \frac{r^{2}}{L_{m}^{2}} + 1)}^{1 + q / 2}},

which is frequently used in statistical models of seismicity such as the ETAS model [ Helmstetter et al , ; Peixoto et al , ; Gu et al , ; Console et al , ; Zhuang et al , ]. Note that often the corresponding areal density instead of the linear density is given.…”

Section: Spatial Distribution Of Aftershocks In Southern Californiamentioning

confidence: 95%

“…

ζ_{m_{i}} (\overset{r}{true})

in equation is the normalized spatial distribution of aftershocks with distance

\overset{r}{true}

from the main shock. The direction of this distance vector is typically chosen at random [ Gu et al , ; Peixoto et al , ; Helmstetter and Sornette , ], a procedure we follow here. Its length is chosen according to the functional form of the spatial distribution of aftershocks as captured by equation with L m = L R /2, i.e.,

P_{m} (r) = \int_{0}^{2 π} ζ_{m} (\vec{r}) dφ .

This framework allows us to consider isotropic and anisotropic spatial distributions in the epicenter distances.…”

Section: Comparison With Surrogate Catalogsmentioning

confidence: 99%

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Nontrivial decay of aftershock density with distance in Southern California

2014

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The decay of the aftershock density with distance plays an important role in the discussion of the dominant underlying cause of earthquake triggering. Here, we provide evidence that its form is more complicated than typically assumed and that in particular a transition in the power law decay occurs at length scales comparable to the thickness of the crust. This is supported by an analysis of a very recent high-resolution catalog for Southern California (SC) and surrogate catalogs generated by the Epidemic-Type Aftershock Sequence (ETAS) model, which take into account inhomogeneous background activity, short-term aftershock incompleteness, anisotropic triggering, and variations in the observational magnitude threshold. Our findings indicate specifically that the asymptotic decay in the aftershock density with distance is characterized by an exponent larger than 2, which is much bigger than the observed exponent of approximately 1.35 observed for shorter distances ranging from the main shock rupture length up to a length scale comparable to the thickness of the crust. This has also important consequences for time-dependent seismic hazard assessment based on the ETAS model.

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P_{m} (r) = \frac{qr}{L_{m}^{2} {((), \frac{r^{2}}{L_{m}^{2}} + 1)}^{1 + q / 2}},

Section: Spatial Distribution Of Aftershocks In Southern Californiamentioning

confidence: 95%

“…

ζ_{m_{i}} (\overset{r}{true})

in equation is the normalized spatial distribution of aftershocks with distance

\overset{r}{true}

P_{m} (r) = \int_{0}^{2 π} ζ_{m} (\vec{r}) dφ .

This framework allows us to consider isotropic and anisotropic spatial distributions in the epicenter distances.…”

Section: Comparison With Surrogate Catalogsmentioning

confidence: 99%

Nontrivial decay of aftershock density with distance in Southern California

2014

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“…Following recent empirical studies [ Felzer and Brodsky , ], triggered events are assumed to be distributed in space according to a probability density function

{normalΦ}_{m_{i}} (\overset{r}{true} - \overset{r_{i}}{true})

that is isotropic and reduces to

ϕ_{m_{i}} (| \overset{r}{true} - \overset{r_{i}}{true} |) = \frac{μ | \overset{r}{true} - \overset{r_{i}}{true} |}{l {(m_{i})}^{2} {((), \frac{| \overset{r}{true} - \overset{r_{i}}{true} |^{2}}{l {(m_{i})}^{2}} + 1)}^{1 + μ / 2}}

for the distribution of distances

| \overset{r}{true} - \overset{r_{i}}{true} |

. Here l ( m i ) is the rupture length of the trigger given by

l (m_{i}) = l_{0} 1 0^{0.45 \cdot m_{i}}

[ Peixoto et al , ], and μ is another constant. To minimize the effect of catalog incompleteness due to missing aftershocks triggered by events that occurred before the simulation period, we remove all data in the time interval [0, t c ] from the catalog.…”

Section: Synthetic Etas Catalogsmentioning

confidence: 99%

Triggering cascades and statistical properties of aftershocks

et al. 2013

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[1] 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 the p value in the Omori-Utsu law for large main shocks, Båth's law, and the productivity law with an exponent smaller than the b value 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), Zhuang et al. (2008), are (a) p values 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) a b value 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.

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“…This approach has proved helpful in characterizing the spatiotemporal clustering of earthquakes in southern California and to establish non-trivial features by direct comparison with stochastic null models Peixoto and Davidsen, 2008;Peixoto et al, 2010). Most importantly, the latter approach has led to a new and independent estimate of the rupture length and its scaling with magnitude.…”

Section: Introductionmentioning

confidence: 99%

Intraplate seismicity in Canada: a graph theoretic approach to data analysis and interpretation

Vasudevan

Eaton

Davidsen

2010

Nonlin. Processes Geophys.

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Abstract. Intraplate seismicity occurs in central and northern Canada, but the underlying origin and dynamics remain poorly understood. Here, we apply a graph theoretic approach to characterize the statistical structure of spatiotemporal clustering exhibited by intraplate seismicity, a direct consequence of the underlying nonlinear dynamics. Using a recently proposed definition of "recurrences" based on record breaking processes (Davidsen et al., 2006 , with attributes drawn from the location, origin time and the magnitude of the events. Based on comparisons with a null model derived from Poisson distribution or Monte Carlo shuffling of the catalogue data, our results provide strong evidence in support of spatiotemporal correlations of seismicity in all three regions considered. Similar evidence for spatiotemporal clustering has been documented using seismicity catalogues for southern California, suggesting possible similarities in underlying earthquake dynamics of both regions despite huge differences in the variability of seismic activity.

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Spatiotemporal correlations of aftershock sequences

Cited by 11 publications

References 52 publications

Nontrivial decay of aftershock density with distance in Southern California

Nontrivial decay of aftershock density with distance in Southern California

Triggering cascades and statistical properties of aftershocks

Intraplate seismicity in Canada: a graph theoretic approach to data analysis and interpretation

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