dorsal/arxiv
View SchemaMultifractal Omori Law for Earthquake Triggering: New Tests on the California, Japan and Worldwide Catalogs
| Authors | G. Ouillon, E. Ribeiro, D. Sornette |
|---|---|
| Categories | |
| ArXiv ID | physics/0609179 |
| URL | https://arxiv.org/abs/physics/0609179 |
Abstract
The Multifractal Stress-Activated (MSA) model is a statistical model of triggered seismicity based on mechanical and thermodynamic principles. It predicts that, above a triggering magnitude cut-off $M_0$, the exponent $p$ of the Omori law for the seismic decay of aftershocks is a linear increasing function $p(M) =a M+b$ of the main shock magnitude $M$. We previously reported empirical support for this prediction, using the Southern California SCEC catalog. Here, we confirm this law using an updated, longer version of the same catalog, as well as new methods to estimate $p$. One of this methods is the newly defined Scaling Function Analysis, adapted from the wavelet transform. This method is able to measure a singularity ($p$-value), erasing the possible regular part of a time series. The Scaling Function Analysis also proves particularly efficient to reveal the coexistence of several types of relaxation laws (typical Omori sequences and short-lived swarms sequences) which can be mixed within the same catalog. The same methods are used on data from the worlwide Harvard CMT and show results compatible with those of Southern California. For the Japanese JMA catalog, we still observe a linear dependence of $p$ on $M$, yet with a smaller slope. The scaling function analysis shows however that results for this catalog may be biased by numerous swarm sequences, despite our efforts to remove them before the analysis.
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"abstract": "The Multifractal Stress-Activated (MSA) model is a statistical model of\ntriggered seismicity based on mechanical and thermodynamic principles. It\npredicts that, above a triggering magnitude cut-off $M_0$, the exponent $p$ of\nthe Omori law for the seismic decay of aftershocks is a linear increasing\nfunction $p(M) =a M+b$ of the main shock magnitude $M$. We previously reported\nempirical support for this prediction, using the Southern California SCEC\ncatalog. Here, we confirm this law using an updated, longer version of the same\ncatalog, as well as new methods to estimate $p$. One of this methods is the\nnewly defined Scaling Function Analysis, adapted from the wavelet transform.\nThis method is able to measure a singularity ($p$-value), erasing the possible\nregular part of a time series. The Scaling Function Analysis also proves\nparticularly efficient to reveal the coexistence of several types of relaxation\nlaws (typical Omori sequences and short-lived swarms sequences) which can be\nmixed within the same catalog. The same methods are used on data from the\nworlwide Harvard CMT and show results compatible with those of Southern\nCalifornia. For the Japanese JMA catalog, we still observe a linear dependence\nof $p$ on $M$, yet with a smaller slope. The scaling function analysis shows\nhowever that results for this catalog may be biased by numerous swarm\nsequences, despite our efforts to remove them before the analysis.",
"arxiv_id": "physics/0609179",
"authors": [
"G. Ouillon",
"E. Ribeiro",
"D. Sornette"
],
"categories": [
"physics.geo-ph"
],
"title": "Multifractal Omori Law for Earthquake Triggering: New Tests on the California, Japan and Worldwide Catalogs",
"url": "https://arxiv.org/abs/physics/0609179"
},
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