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Hal
Article . 1992
Data sources: Hal
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Journal de Physique I
Article . 1992 . Peer-reviewed
Data sources: Crossref
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Mean-field solution of a block-spring model of earthquakes

Authors: Sornette, Didier;

Mean-field solution of a block-spring model of earthquakes

Abstract

A mean field version of the Burridge-Knopoff block-spring stick-slip model of earthquake faults is mapped onto a cycled generalization of the democratic fiber bundle model (DFM). This provides an exactly soluble model which describes the set of earthquakes preceding a major earthquake. We find the coexistence of 1) a differential Gutenberg-Richter distribution d(Δ)∼Δ-3/2 of bursts of size Δ, with a cut-off Δmax ∼(σr-σ)-1 as the stress σ↦σr and 2) a run away occurring at a well-defined stress threshold σr. The total number of bursts of size Δ up to the run away scales as D(Δ)∼Δ-5/2. The exponent 5/2 reflects the occurrence of larger and larger events when approaching the run away instability (Omori's law for foreshocks). The Gutenberg-Richter and Omori power laws are not associated with a stationary criticality but to fluctuations accompanying the nucleation of the run away. Introducing long range correlations in the model lead to a continuous dependence of the above exponents as a function of the correlation exponent.

Country
France
Keywords

[PHYS.HIST]Physics [physics]/Physics archives, [ PHYS.HIST ] Physics [physics]/Physics archives, [PHYS.HIST] Physics/Physics archives, [PHYS.HIST] Physics [physics]/Physics archives

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    Top 10%
    influence
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
56
Top 10%
Top 10%
Average
Green