arXiv subjects

M. V. Rodkin

Publications and source records attributed to M. V. Rodkin.

3 recordsLinked to original sources

arXiv2009

Distribution of Maximum Earthquake Magnitudes in Future Time Intervals, Application to the Seismicity of Japan (1923-2007)

We modify the new method for the statistical estimation of the tail distribution of earthquake seismic moments introduced by Pisarenko et al. [2009] and apply it to the earthquake catalog of Japan (1923-2007). The method is based on the two main limit theorems of the theory of extreme values and on the derived duality between the Generalized Pareto Distribution (GPD) and Generalized Extreme Value distribution (GEV). We obtain the distribution of maximum earthquake magnitudes in future time intervals of arbitrary duration tau. This distribution can be characterized by its quantile Qq(tau) at any desirable statistical level q. The quantile Qq(tau) provides a much more stable and robust characteristic than the traditional absolute maximum magnitude Mmax (Mmax can be obtained as the limit of Qq(tau) as q tends to 1, and tau tends to infinity). The best estimates of the parameters governing the distribution of Qq(tay) for Japan (1923-2007) are the following: Form parameter for GEV = -0.1901 +- 0.0717; position parameter GEV(tau=200)= 6.3387 +- 0.0380; spread parameter for GEV(tau=200)= 0.5995 +- 0.0223; Q_0.90,GEV(tau=10)= 8.34 +- 0.32. We also estimate Qq(tau) for a set of q-values and future time periods in the range for tau between 1 and 50 years from 2007. For comparison, the absolute maximum estimate Mmax from GEV, which is equal to 9.57 +- 0.86, has a scatter more than twice that of the 90 percent quantile Q_{0.90,GEV}(tau=10) of the maximum magnitude over the next 10 years counted from 2007.

physics.geo-ph↗

arXiv2008

Characterization of the tail of the distribution of earthquake magnitudes by combining the GEV and GPD descriptions of Extreme Value Theory

We present a generic and powerful approach to study the statistics of extreme phenomena (meteorology, finance, biology...) that we apply to the statistical estimation of the tail of the distribution of earthquake sizes. The chief innovation is to combine the two main limit theorems of Extreme Value Theory (EVT) that allow us to derive the distribution of T-maxima (maximum magnitude occurring in sequential time intervals of duration T) for arbitrary T. We propose a method for the estimation of the unknown parameters involved in the two limit theorems corresponding to the Generalized Extreme Value distribution (GEV) and to the Generalized Pareto Distribution (GPD). We establish the direct relations between the parameters of these distributions, which permit to evaluate the distribution of the T-maxima for arbitrary T. The duality between the GEV and GPD provides a new way to check the consistency of the estimation of the tail characteristics of the distribution of earthquake magnitudes for earthquake occurring over arbitrary time interval. We develop several procedures and check points to decrease the scatter of the estimates and to verify their consistency. We test our full procedure on the global Harvard catalog (1977-2006) and on the Fennoscandia catalog (1900-2005). For the global catalog, we obtain the following estimates: Mmax = 9.53 +- 0.52; quantile(0.97)==9.21 +- 0.20. For Fennoscandia, we obtain Mmax = 5.76 +- 0.165; quantile(0.97) =5.44 +- 0.073. The estimates of all related parameters for the GEV and GPD, including the most important form parameter, are also provided.

physics.geo-ph↗

arXiv2007

New Approach to the Characterization of Mmax and of the Tail of the Distribution of Earthquake Magnitudes

We develop a new method for the statistical esitmation of the tail of the distribution of earthquake sizes recorded in the Worldwide Harvard catalog of seismic moments converted to mW-magnitudes (1977-2004 and 1977-2006). We show that using the set of maximum magnitudes (the set of T-maxima) in windows of duration T days provides a significant improvement over existing methods, in particular (i) by minimizing the negative impact of time-clustering of foreshock / main shock /aftershock sequences in the estimation of the tail of the magnitude distribution, and (ii) by providing via a simulation method reliable estimates of the biases in the Moment estimation procedure (which turns out to be more efficient than the Maximum Likelihood estimation). Using a simulation method, we have determined the optimal window size of the T-maxima to be T=500 days. We have estimated the following quantiles of the distribution of T-maxima of earthquake magnitudes for the whole period 1977-2006: Q_{0.16}(Mmax)=9.3, Q_{0.5}(Mmax)=9.7 and Q_{0.84}(Mmax)=10.3. Finally, we suggest two more stable statistical characterristics of the tail of the distribution of earthquake magnitudes: the quantile QT(q) of a high probability level q for the T-maxima, and the probability of exceedence for a high threshold magnitude. We obtained the following sample estimates for the global Harvard catalog: QT(q=0.98)=8.6 +- 0.2 and a probability for the T-maxima to exceed magnitude 8 equal to 0.13-0.20. The comparison between our estimates for the two periods 1977-2004 and 1977-2006, where the later period includes the great Sumatra earthquake, 24.12.2004, mW=9.0, confirms the instability of the estimation of the parameter Mmax and the stability of the two other estimates.

physics.geo-ph↗