Multifractal analysis of earthquake catalogues

Godano, C.; Caruso, Vincenzo

doi:10.1111/j.1365-246x.1995.tb05719.x

Cited by 59 publications

(41 citation statements)

References 20 publications

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“…[44]). The multifractal structure of earthquake time series is evident in various earthquake catalogues [45][46][47] and multifractal analysis is used as a second-order approximation to enlighten the correlations of seismicity and the local clustering effects [44,48].…”

Section: (A) Phenomenology Of Fault and Earthquake Populations (I) Scmentioning

confidence: 99%

Generalized statistical mechanics approaches to earthquakes and tectonics

2016

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Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, simple empirical scaling relations apply to the collective properties of earthquakes and faults in a variety of tectonic environments and scales. The physical characterization of those properties and the scaling relations that describe them attract a wide scientific interest and are incorporated in the probabilistic forecasting of seismicity in local, regional and planetary scales. Considerable progress has been made in the analysis of the statistical mechanics of earthquakes, which, based on the principle of entropy, can provide a physical rationale to the macroscopic properties frequently observed. The scale-invariant properties, the (multi) fractal structures and the long-range interactions that have been found to characterize fault and earthquake populations have recently led to the consideration of non-extensive statistical mechanics (NESM) as a consistent statistical mechanics framework for the description of seismicity. The consistency between NESM and observations has been demonstrated in a series of publications on seismicity, faulting, rock physics and other fields of geosciences. The aim of this review is to present in a concise manner the fundamental macroscopic properties of earthquakes and faulting and how these can be derived by using the notions of statistical mechanics and NESM, providing further insights into earthquake physics and fault growth processes.

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Section: (A) Phenomenology Of Fault and Earthquake Populations (I) Scmentioning

confidence: 99%

Generalized statistical mechanics approaches to earthquakes and tectonics

2016

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“…However, a clear evidence in support of these geophysical indications has not yet been provided. This is probably the reason why one of the models adopted to describe the time distribution of earthquakes is still the Generalized Poisson (GP) model [5,6,7,8,9]. Basically the GP model assumes that the earthquakes are grouped into temporal clusters of events and these clusters are uncorrelated: in fact the clusters are distributed at random in time and therefore the time intervals between one cluster and the next one follow a Poisson distribution.…”

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confidence: 99%

Power-Law Time Distribution of Large Earthquakes

et al. 2003

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We study the statistical properties of time distribution of seimicity in California by means of a new method of analysis, the Diffusion Entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent µ = 2.06 ± 0.01. We propose the Long-Range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes. The search for correlation in the space-time distribution of earthquakes is a major goal in geophysics. At the short-time and the short-space scale the existence of correlation is well established. Recent geophysical observations indicate that main fracture episodes can trigger long-range as well as short-range seismic effects [1,2,3,4]. However, a clear evidence in support of these geophysical indications has not yet been provided. This is probably the reason why one of the models adopted to describe the time distribution of earthquakes is still the Generalized Poisson (GP) model [5,6,7,8,9]. Basically the GP model assumes that the earthquakes are grouped into temporal clusters of events and these clusters are uncorrelated: in fact the clusters are distributed at random in time and therefore the time intervals between one cluster and the next one follow a Poisson distribution. On the other hand, the intra-cluster earthquakes are correlated in time as it is expressed by the Omori's law [10,11], an empirical law stating that the main shock, i.e. the highest magnitude earthquake of the cluster, occurring at time t 0 is followed by a swarm of correlated earthquakes (after shocks) whose number (or frequency) n(t) decays in time as a power law, n(t) ∝ (t − t 0 ) −p , with the exponent p being very close to 1. The Omori's law implies [12] that the distribution of the time intervals between one earthquake and the next, denoted by τ , is a power law ψ(τ ) ∝ τ −p . This property has been recently studied by the authors of Ref.[12] by means of a unified scaling law for ψ L,M (τ ), the probability of having a time interval τ between two seismic events with a magnitude * Corresponding author: vito.latora@ct.infn.it larger than M and occurring within a spatial distance L. This has the effect of taking into account also space and extending the correlation within a finite time range τ * , beyond which the authors of Ref.[12] recover Poisson statistics.In this letter, we provide evidence of inter-clusters correlation by studing a catalog of seismic events in California with a new technique of analysis called Diffusion Entropy (DE) [13,14]. This technique, scarcely sensitive to predictable events such as the Omori cascade of aftershocks, is instead very sensitive when the deviation from Poisson statistics generates Lévy diffusion [14,15]. This deviation, on the other hand, implies that the geophysical process generating clusters ha...

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“…Evidence of such a complicated dynamics of earthquakes (characterized by the self-organized criticality) stipulates the idea of application of multifractal analysis used by an author previously for characterization of stochastic fracture processes (Silberschmidt 1993(Silberschmidt , 1994. We should also mention the recent data on multifractality of the inter-arrival time between earthquakes, obtained by Godano and Caruso (1995).…”

Section: Multifractal Analysismentioning

confidence: 99%

Fractal approach in modelling of earthquakes

Silberschmidt

1996

Geol Rundsch

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A model for an earthquake simulation is proposed with the use of a fractal approach. Multiple generation and coalescence of shear faults in stochastic brittle media (modelled as a 2d lattice) are considered to be a source of seismicity. Dynamics of local failure events are governed by accumulation of shear defects, described in terms of continuum damage mechanics. Fractal tree structure is used as an analogue for a stress redistribution process. Energy release, caused by the non-uniform failure, is studied for a non-conservative case. Effect of various types of rocks' properties stochasticity on energy release dynamics is analysed with a utilization of multifractal formalism. The latter is shown to be an additional method for seismicity characterization.

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Multifractal analysis of earthquake catalogues

Cited by 59 publications

References 20 publications

Generalized statistical mechanics approaches to earthquakes and tectonics

Generalized statistical mechanics approaches to earthquakes and tectonics

Power-Law Time Distribution of Large Earthquakes

Fractal approach in modelling of earthquakes

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