skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Dynamical Scaling in Branching Models for Seismicity

Abstract

We propose a branching process based on a dynamical scaling hypothesis relating time and mass. In the context of earthquake occurrence, we show that experimental power laws in size and time distribution naturally originate solely from this scaling hypothesis. We present a numerical protocol able to generate a synthetic catalog with an arbitrary large number of events. The numerical data reproduce the hierarchical organization in time and magnitude of experimental interevent time distribution.

Authors:
 [1];  [2];  [3]
  1. Department of Physical Sciences, University of Naples 'Federico II', 80125 Naples (Italy)
  2. Department of Environmental Sciences and CNISM, Second University of Naples, 81100 Caserta (Italy)
  3. Department of Information Engineering and CNISM, Second University of Naples, 81031 Aversa (CE) (Italy)
Publication Date:
OSTI Identifier:
20957710
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevLett.98.098501; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BRANCHING RATIO; CATALOGS; EARTHQUAKES; MATHEMATICAL MODELS; NUMERICAL DATA; SEISMICITY

Citation Formats

Lippiello, Eugenio, Godano, Cataldo, and De Arcangelis, Lucilla. Dynamical Scaling in Branching Models for Seismicity. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.098501.
Lippiello, Eugenio, Godano, Cataldo, & De Arcangelis, Lucilla. Dynamical Scaling in Branching Models for Seismicity. United States. doi:10.1103/PHYSREVLETT.98.098501.
Lippiello, Eugenio, Godano, Cataldo, and De Arcangelis, Lucilla. Fri . "Dynamical Scaling in Branching Models for Seismicity". United States. doi:10.1103/PHYSREVLETT.98.098501.
@article{osti_20957710,
title = {Dynamical Scaling in Branching Models for Seismicity},
author = {Lippiello, Eugenio and Godano, Cataldo and De Arcangelis, Lucilla},
abstractNote = {We propose a branching process based on a dynamical scaling hypothesis relating time and mass. In the context of earthquake occurrence, we show that experimental power laws in size and time distribution naturally originate solely from this scaling hypothesis. We present a numerical protocol able to generate a synthetic catalog with an arbitrary large number of events. The numerical data reproduce the hierarchical organization in time and magnitude of experimental interevent time distribution.},
doi = {10.1103/PHYSREVLETT.98.098501},
journal = {Physical Review Letters},
number = 9,
volume = 98,
place = {United States},
year = {Fri Mar 02 00:00:00 EST 2007},
month = {Fri Mar 02 00:00:00 EST 2007}
}
  • We analyze the experimental seismic catalog of Southern California and we show the existence of correlations between earthquake magnitudes. We propose a dynamical scaling hypothesis relating time and magnitude as the physical mechanism responsible of the observed magnitude correlations. We show that experimental distributions in size and time naturally originate solely from this scaling hypothesis. Furthermore we generate a synthetic catalog reproducing the organization in time and magnitude of experimental data.
  • Using the epidemic-type aftershock sequence (ETAS) branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all generations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Baath's law. Our theory shows that Baath's law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars {+-}0.1 for Baath's constant value around 1.2, our exact analytical treatmentmore » of Baath's law provides new constraints on the productivity exponent {alpha} and the branching ratio n: 0.9 < or approx. {alpha}{<=}1 and 0.8 < or approx. n{<=}1. We propose a method for measuring {alpha} based on the predicted renormalization of the Gutenberg-Richter distribution of the magnitudes of the largest aftershock. We also introduce the 'second Baath law for foreshocks': the probability that a main earthquake turns out to be the foreshock does not depend on its magnitude {rho}.« less
  • Cited by 5
  • To investigate source-scaling relations for small earthquakes (M{sub w} -1.8 to 1.2) we have determined source parameters for numerous events ({approx}1500) from the 1400-m-deep Pyhasalmi ore mine in Finland. In addition to a spectral integration approach, we have fitted Brune, Boatwright, and Haskell spectral-shape models to the observed spectra and investigated attenuation influences. Of three different constant Q models (200, 350, and 800), a Q of 350 in combination with the Brune spectral model satisfied the data best. We have also investigated the frequency dependence of Q using the spectral decay method and found that Q increases with frequency. Formore » selected events from two distinct clusters, we compared source parameters derived from constant Q models with source parameters using the multiple empirical Green's function (MEGF) approach. By using constant Q models, the apparent stress seems to increase with magnitude, whereas results based on the MEGF approach indicate constant apparent stress with magnitude. In comparison with results from other studies that cover a larger-magnitude scale, we find apparent stresses that are about 1 to 2 orders of magnitude smaller than most of those. A modified M{sub 0} {approx} fc{sup -(3 + {epsilon})} scaling relation allows for increasing apparent stress with magnitude and can hence combine this study's results with apparent stresses found for large earthquakes. However, within the limited-magnitude range of our data, apparent stresses seem constant.« less
  • The phenomenon of Koba-Nielsen-Olesen scaling up to about 100 GeV in c.m. energy in pp collision is described in a branching model supplemented by impact-parameter smearing with geometrical scaling as an essential input. A high-accuracy fit of all data points from CERN ISR is achieved by use of only one parameter, which relates the particle productivity to hadron opacity at each impact parameter. It is deduced that the average number of initial clusters is between 4 and 5, depending upon the energy.