dorsal/arxiv
View SchemaDeviations of the distributions of seismic energies from the Gutenberg-Richter law
| Authors | V. Pisarenko, D. Sornette, M. Rodkin |
|---|---|
| Categories | |
| ArXiv ID | physics/0312020 |
| URL | https://arxiv.org/abs/physics/0312020 |
| Journal | Computational Seismology 35, 138-159 (2004) |
Abstract
A new non-parametric statistic is introduced for the characterization of deviations from power laws. It is tested on the distribution of seismic energies given by the Gutenberg-Richter law. Based on the two first statistical log-moments, it evaluates quantitatively the deviations of the distribution of scalar seismic moments from a power-like (Pareto) law. This statistic is close to zero for the Pareto law with arbitrary power index, and deviates from zero for any non-Pareto distribution. A version of this statistic for discrete distribution of quantified magnitudes is also given. A methodology based on this statistics consisting in scanning the lower threshold for earthquake energies provides an explicit visualization of deviations from the Pareto law, surpassing in sensitivity the standard Hill estimator or other known techniques. This new statistical technique has been applied to shallow earthquakes (h < 70 km) both in subduction zones and in mid-ocean ridge zones (using the Harvard catalog of seismic moments, 1977-2000), and to several regional catalogs of magnitudes (California, Japan, Italy, Greece). We discover evidence for log-periodicity and thus for a discrete hierarchy of scales for low-angle dipping, low-strain subduction zones with a preferred scaling ratio g=7+-1 for seismic moments, compatible with a preferred scaling ratio of 2 for linear rupture sizes, and consistent with previous reports. We propose a possible mechanism in terms of cascades of fault competitions.
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"abstract": "A new non-parametric statistic is introduced for the characterization of\ndeviations from power laws. It is tested on the distribution of seismic\nenergies given by the Gutenberg-Richter law. Based on the two first statistical\nlog-moments, it evaluates quantitatively the deviations of the distribution of\nscalar seismic moments from a power-like (Pareto) law. This statistic is close\nto zero for the Pareto law with arbitrary power index, and deviates from zero\nfor any non-Pareto distribution. A version of this statistic for discrete\ndistribution of quantified magnitudes is also given. A methodology based on\nthis statistics consisting in scanning the lower threshold for earthquake\nenergies provides an explicit visualization of deviations from the Pareto law,\nsurpassing in sensitivity the standard Hill estimator or other known\ntechniques. This new statistical technique has been applied to shallow\nearthquakes (h \u003c 70 km) both in subduction zones and in mid-ocean ridge zones\n(using the Harvard catalog of seismic moments, 1977-2000), and to several\nregional catalogs of magnitudes (California, Japan, Italy, Greece). We discover\nevidence for log-periodicity and thus for a discrete hierarchy of scales for\nlow-angle dipping, low-strain subduction zones with a preferred scaling ratio\ng=7+-1 for seismic moments, compatible with a preferred scaling ratio of 2 for\nlinear rupture sizes, and consistent with previous reports. We propose a\npossible mechanism in terms of cascades of fault competitions.",
"arxiv_id": "physics/0312020",
"authors": [
"V. Pisarenko",
"D. Sornette",
"M. Rodkin"
],
"categories": [
"physics.data-an",
"physics.geo-ph"
],
"journal_ref": "Computational Seismology 35, 138-159 (2004)",
"title": "Deviations of the distributions of seismic energies from the Gutenberg-Richter law",
"url": "https://arxiv.org/abs/physics/0312020"
},
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