dorsal/arxiv
View SchemaRelation between stress heterogeneity and aftershock rate in the rate-and-state model
| Authors | Agnes Helmstetter, Bruce E. Shaw |
|---|---|
| Categories | |
| ArXiv ID | physics/0509252 |
| URL | https://arxiv.org/abs/physics/0509252 |
| DOI | 10.1029/2005JB004077 |
| Journal | J. Geophys. Res., 111, B07304, doi:10.1029/2005JB004077 (2006) |
Abstract
We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich [1994].We show that an exponential stress distribution Pt(au) ~exp(-tautau_0) gives an Omori law decay of aftershocks with time ~1/t^p, with an exponent p=1-A sigma_n/tau_0, where A is a parameter of the rate-and-state friction law, and \sigma_n the normal stress. Omori exponent p thus decreases if the stress "heterogeneity" tau_0 decreases. We also invert the stress distribution P(tau) from the seismicity rate R(t), assuming that the stress does not change with time. We apply this method to a synthetic stress map, using the (modified) scale invariant "k^2" slip model [Herrero and Bernard, 1994]. We generate synthetic aftershock catalogs from this stress change.The seismicity rate on the rupture area shows a huge increase at short times, even if the stress decreases on average. Aftershocks are clustered in the regions of low slip, but the spatial distribution is more diffuse than for a simple slip dislocation. Because the stress field is very heterogeneous, there are many patches of positive stress changes everywhere on the fault.This stochastic slip model gives a Gaussian stress distribution, but nevertheless produces an aftershock rate which is very close to Omori's law, with an effective p<=1, which increases slowly with time. We obtain a good estimation of the stress distribution for realistic catalogs, when we constrain the shape of the distribution. However, there are probably other factors which also affect the temporal decay of aftershocks with time. In particular, heterogeneity of A\sigma_n can also modify the parameters p and c of Omori's law. Finally, we show that stress shadows are very difficult to observe in a heterogeneous stress context.
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"abstract": "We estimate the rate of aftershocks triggered by a heterogeneous stress\nchange, using the rate-and-state model of Dieterich [1994].We show that an\nexponential stress distribution Pt(au) ~exp(-tautau_0) gives an Omori law decay\nof aftershocks with time ~1/t^p, with an exponent p=1-A sigma_n/tau_0, where A\nis a parameter of the rate-and-state friction law, and \\sigma_n the normal\nstress. Omori exponent p thus decreases if the stress \"heterogeneity\" tau_0\ndecreases. We also invert the stress distribution P(tau) from the seismicity\nrate R(t), assuming that the stress does not change with time. We apply this\nmethod to a synthetic stress map, using the (modified) scale invariant \"k^2\"\nslip model [Herrero and Bernard, 1994]. We generate synthetic aftershock\ncatalogs from this stress change.The seismicity rate on the rupture area shows\na huge increase at short times, even if the stress decreases on average.\nAftershocks are clustered in the regions of low slip, but the spatial\ndistribution is more diffuse than for a simple slip dislocation. Because the\nstress field is very heterogeneous, there are many patches of positive stress\nchanges everywhere on the fault.This stochastic slip model gives a Gaussian\nstress distribution, but nevertheless produces an aftershock rate which is very\nclose to Omori\u0027s law, with an effective p\u003c=1, which increases slowly with time.\nWe obtain a good estimation of the stress distribution for realistic catalogs,\nwhen we constrain the shape of the distribution. However, there are probably\nother factors which also affect the temporal decay of aftershocks with time. In\nparticular, heterogeneity of A\\sigma_n can also modify the parameters p and c\nof Omori\u0027s law. Finally, we show that stress shadows are very difficult to\nobserve in a heterogeneous stress context.",
"arxiv_id": "physics/0509252",
"authors": [
"Agnes Helmstetter",
"Bruce E. Shaw"
],
"categories": [
"physics.geo-ph"
],
"doi": "10.1029/2005JB004077",
"journal_ref": "J. Geophys. Res., 111, B07304, doi:10.1029/2005JB004077 (2006)",
"title": "Relation between stress heterogeneity and aftershock rate in the rate-and-state model",
"url": "https://arxiv.org/abs/physics/0509252"
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