dorsal/arxiv
View SchemaNew Approach to the Characterization of Mmax and of the Tail of the Distribution of Earthquake Magnitudes
| Authors | V. F. Pisarenko, A. Sornette, D. Sornette, M. V. Rodkin |
|---|---|
| Categories | |
| ArXiv ID | physics/0703010 |
| URL | https://arxiv.org/abs/physics/0703010 |
| DOI | 10.1007/s00024-008-0341-9 |
Abstract
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.
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"abstract": "We develop a new method for the statistical esitmation of the tail of the\ndistribution of earthquake sizes recorded in the Worldwide Harvard catalog of\nseismic moments converted to mW-magnitudes (1977-2004 and 1977-2006). We show\nthat using the set of maximum magnitudes (the set of T-maxima) in windows of\nduration T days provides a significant improvement over existing methods, in\nparticular (i) by minimizing the negative impact of time-clustering of\nforeshock / main shock /aftershock sequences in the estimation of the tail of\nthe magnitude distribution, and (ii) by providing via a simulation method\nreliable estimates of the biases in the Moment estimation procedure (which\nturns out to be more efficient than the Maximum Likelihood estimation). Using a\nsimulation method, we have determined the optimal window size of the T-maxima\nto be T=500 days. We have estimated the following quantiles of the distribution\nof T-maxima of earthquake magnitudes for the whole period 1977-2006:\nQ_{0.16}(Mmax)=9.3, Q_{0.5}(Mmax)=9.7 and Q_{0.84}(Mmax)=10.3. Finally, we\nsuggest two more stable statistical characterristics of the tail of the\ndistribution of earthquake magnitudes: the quantile QT(q) of a high probability\nlevel q for the T-maxima, and the probability of exceedence for a high\nthreshold magnitude. We obtained the following sample estimates for the global\nHarvard catalog: QT(q=0.98)=8.6 +- 0.2 and a probability for the T-maxima to\nexceed magnitude 8 equal to 0.13-0.20. The comparison between our estimates for\nthe two periods 1977-2004 and 1977-2006, where the later period includes the\ngreat Sumatra earthquake, 24.12.2004, mW=9.0, confirms the instability of the\nestimation of the parameter Mmax and the stability of the two other estimates.",
"arxiv_id": "physics/0703010",
"authors": [
"V. F. Pisarenko",
"A. Sornette",
"D. Sornette",
"M. V. Rodkin"
],
"categories": [
"physics.geo-ph",
"physics.data-an"
],
"doi": "10.1007/s00024-008-0341-9",
"title": "New Approach to the Characterization of Mmax and of the Tail of the Distribution of Earthquake Magnitudes",
"url": "https://arxiv.org/abs/physics/0703010"
},
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