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Yan Y Kagan - One of the best experts on this subject based on the ideXlab platform.

  • statistical Distributions of earthquake numbers consequence of branching process
    Geophysical Journal International, 2010
    Co-Authors: Yan Y Kagan
    Abstract:

    We discuss various statistical Distributions of earthquake numbers. Previously we derived several discrete Distributions to describe earthquake numbers for the branching model of earthquake occurrence: these Distributions are the Poisson, geometric, logarithmic, and the negative binomial (NBD). The theoretical model is the `birth and immigration' population process. The first three Distributions above can be considered special cases of the NBD. In particular, a point branching process along the magnitude (or log seismic moment) axis with independent events (immigrants) explains the magnitude/moment-frequency relation and the NBD of earthquake counts in large time/space windows, as well as the dependence of the NBD parameters on the magnitude threshold (magnitude of an earthquake catalogue completeness). We discuss applying these Distributions, especially the NBD, to approximate event numbers in earthquake catalogues. There are many different representations of the NBD. Most can be traced either to the Pascal Distribution or to the mixture of the Poisson Distribution with the gamma law. We discuss advantages and drawbacks of both representations for statistical analysis of earthquake catalogues. We also consider applying the NBD to earthquake forecasts and describe the limits of the application for the given equations. In contrast to the one-parameter Poisson Distribution so widely used to describe earthquake occurrence, the NBD has two parameters. The second parameter can be used to characterize clustering or over-dispersion of a process. We determine the parameter values and their uncertainties for several local and global catalogues, and their subdivisions in various time intervals, magnitude thresholds, spatial windows, and tectonic categories. The theoretical model of how the clustering parameter depends on the corner (maximum) magnitude can be used to predict future earthquake number Distribution in regions where very large earthquakes have not yet occurred.

  • statistical Distributions of earthquake numbers consequence of branching process
    arXiv: Geophysics, 2009
    Co-Authors: Yan Y Kagan
    Abstract:

    We discuss various statistical Distributions of earthquake numbers. Previously we derived several discrete Distributions to describe earthquake numbers for the branching model of earthquake occurrence: these Distributions are the Poisson, geometric, logarithmic, and the negative binomial (NBD). The theoretical model is the `birth and immigration' population process. The first three Distributions above can be considered special cases of the NBD. In particular, a point branching process along the magnitude (or log seismic moment) axis with independent events (immigrants) explains the magnitude/moment-frequency relation and the NBD of earthquake counts in large time/space windows, as well as the dependence of the NBD parameters on the magnitude threshold (magnitude of an earthquake catalog completeness). We discuss applying these Distributions, especially the NBD, to approximate event numbers in earthquake catalogs. There are many different representations of the NBD. Most can be traced either to the Pascal Distribution or to the mixture of the Poisson Distribution with the gamma law. We discuss advantages and drawbacks of both representations for statistical analysis of earthquake catalogs. We also consider applying the NBD to earthquake forecasts and describe the limits of the application for the given equations. In contrast to the one-parameter Poisson Distribution so widely used to describe earthquake occurrence, the NBD has two parameters. The second parameter can be used to characterize clustering or over-dispersion of a process. We determine the parameter values and their uncertainties for several local and global catalogs, and their subdivisions in various time intervals, magnitude thresholds, spatial windows, and tectonic categories.

G A Papadopoulos - One of the best experts on this subject based on the ideXlab platform.

  • poissonian and negative binomial modelling of earthquake time series in the aegean area
    Physics of the Earth and Planetary Interiors, 1992
    Co-Authors: Demetrios D Dionysiou, G A Papadopoulos
    Abstract:

    Abstract The time Distribution of mainshocks listed in 25 data sets, covering several magnitude classes, time intervals and seismotectonic segments of the Aegean area, has been tested against the Poisson and negative binomial (Pascal) theoretical models. In each χ2 test we make the null hypothesis of fit by a Poisson or Pascal Distribution at the 5% and 1% significance levels. In each test the counting interval is non-arbitrarily selected as equal to the mean return period, Tm, of earthquakes of magnitude equal to or larger than the minimum magnitude in the earthquake sample. Values of Tm have been calculated from magnitude-frequency relationships determined by linear regression analysis. Twenty-two earthquake data sets are successfully modelled by the Poisson process at both the 5% and 1% levels. In contrast, only six sets are successfully modelled by the Pascal Distribution. The results clearly indicate that the occurrence of earthquake mainshocks in the Aegean is stationary and random with respect to time regardless of the segment, time interval and magnitude class considered. A short review of earlier similar studies shows that contradictory results were obtained, which may be the result of several methodological problems. The most important problem seems to be the arbitrary selection of counting intervals when tests are performed. The degree of crustal heterogeneity, which varies from place to place, may provide a physical basis for explanation of earthquake time modelling and for the contradictions in earlier results.

Guo Dawei - One of the best experts on this subject based on the ideXlab platform.

Demetrios D Dionysiou - One of the best experts on this subject based on the ideXlab platform.

  • poissonian and negative binomial modelling of earthquake time series in the aegean area
    Physics of the Earth and Planetary Interiors, 1992
    Co-Authors: Demetrios D Dionysiou, G A Papadopoulos
    Abstract:

    Abstract The time Distribution of mainshocks listed in 25 data sets, covering several magnitude classes, time intervals and seismotectonic segments of the Aegean area, has been tested against the Poisson and negative binomial (Pascal) theoretical models. In each χ2 test we make the null hypothesis of fit by a Poisson or Pascal Distribution at the 5% and 1% significance levels. In each test the counting interval is non-arbitrarily selected as equal to the mean return period, Tm, of earthquakes of magnitude equal to or larger than the minimum magnitude in the earthquake sample. Values of Tm have been calculated from magnitude-frequency relationships determined by linear regression analysis. Twenty-two earthquake data sets are successfully modelled by the Poisson process at both the 5% and 1% levels. In contrast, only six sets are successfully modelled by the Pascal Distribution. The results clearly indicate that the occurrence of earthquake mainshocks in the Aegean is stationary and random with respect to time regardless of the segment, time interval and magnitude class considered. A short review of earlier similar studies shows that contradictory results were obtained, which may be the result of several methodological problems. The most important problem seems to be the arbitrary selection of counting intervals when tests are performed. The degree of crustal heterogeneity, which varies from place to place, may provide a physical basis for explanation of earthquake time modelling and for the contradictions in earlier results.

Murugusundaramoorthy G. - One of the best experts on this subject based on the ideXlab platform.