dorsal/arxiv
View SchemaTheory of Earthquake Recurrence Times
| Authors | A. Saichev, D. Sornette |
|---|---|
| Categories | |
| ArXiv ID | physics/0606001 |
| URL | https://arxiv.org/abs/physics/0606001 |
| DOI | 10.1029/2006JB004536 |
| Journal | J. Geophys. Res., 112, B04313, (2007) |
Abstract
The statistics of recurrence times in broad areas have been reported to obey universal scaling laws, both for single homogeneous regions (Corral, 2003) and when averaged over multiple regions (Bak et al.,2002). These unified scaling laws are characterized by intermediate power law asymptotics. On the other hand, Molchan (2005) has presented a mathematical proof that, if such a universal law exists, it is necessarily an exponential, in obvious contradiction with the data. First, we generalize Molchan's argument to show that an approximate unified law can be found which is compatible with the empirical observations when incorporating the impact of the Omori law of earthquake triggering. We then develop the full theory of the statistics of inter-event times in the framework of the ETAS model of triggered seismicity and show that the empirical observations can be fully explained. Our theoretical expression fits well the empirical statistics over the whole range of recurrence times, accounting for different regimes by using only the physics of triggering quantified by Omori's law. The description of the statistics of recurrence times over multiple regions requires an additional subtle statistical derivation that maps the fractal geometry of earthquake epicenters onto the distribution of the average seismic rates in multiple regions. This yields a prediction in excellent agreement with the empirical data for reasonable values of the fractal dimension $d \approx 1.8$, the average clustering ratio $n \approx 0.9$, and the productivity exponent $\alpha \approx 0.9$ times the $b$-value of the Gutenberg-Richter law.
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"abstract": "The statistics of recurrence times in broad areas have been reported to obey\nuniversal scaling laws, both for single homogeneous regions (Corral, 2003) and\nwhen averaged over multiple regions (Bak et al.,2002). These unified scaling\nlaws are characterized by intermediate power law asymptotics. On the other\nhand, Molchan (2005) has presented a mathematical proof that, if such a\nuniversal law exists, it is necessarily an exponential, in obvious\ncontradiction with the data. First, we generalize Molchan\u0027s argument to show\nthat an approximate unified law can be found which is compatible with the\nempirical observations when incorporating the impact of the Omori law of\nearthquake triggering. We then develop the full theory of the statistics of\ninter-event times in the framework of the ETAS model of triggered seismicity\nand show that the empirical observations can be fully explained. Our\ntheoretical expression fits well the empirical statistics over the whole range\nof recurrence times, accounting for different regimes by using only the physics\nof triggering quantified by Omori\u0027s law. The description of the statistics of\nrecurrence times over multiple regions requires an additional subtle\nstatistical derivation that maps the fractal geometry of earthquake epicenters\nonto the distribution of the average seismic rates in multiple regions. This\nyields a prediction in excellent agreement with the empirical data for\nreasonable values of the fractal dimension $d \\approx 1.8$, the average\nclustering ratio $n \\approx 0.9$, and the productivity exponent $\\alpha \\approx\n0.9$ times the $b$-value of the Gutenberg-Richter law.",
"arxiv_id": "physics/0606001",
"authors": [
"A. Saichev",
"D. Sornette"
],
"categories": [
"physics.geo-ph",
"physics.gen-ph"
],
"doi": "10.1029/2006JB004536",
"journal_ref": "J. Geophys. Res., 112, B04313, (2007)",
"title": "Theory of Earthquake Recurrence Times",
"url": "https://arxiv.org/abs/physics/0606001"
},
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