eprintid: 1382 rev_number: 16 eprint_status: archive userid: 2 dir: disk0/00/00/13/82 datestamp: 2015-02-23 14:46:56 lastmod: 2017-02-08 12:21:35 status_changed: 2015-04-27 12:10:48 type: article metadata_visibility: show creators_name: Helmstetter, Agnes creators_name: Shaw, Bruce E. creators_id: agnes@ldeo.columbia.edu creators_id: corp_creators: Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York, USA. corp_creators: Laboratoire de Ge´ophysique Interne et Tectonophysique, Universite´ Joseph Fourier, Grenoble, France title: Relation between stress heterogeneity and aftershock rate in the rate-and-state model ispublished: pub subjects: MP5 divisions: EPOS-P full_text_status: none abstract: We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich. We show that an exponential stress distribution P t (t) exp(t/t 0 ) gives an Omori law decay of aftershocks with time 1/t p, with an exponent p = 1 As n /t 0 , where A is a parameter of the rate-and-state friction law and s n is the normal stress. Omori exponent p thus decreases if the stress ‘‘heterogeneity’’ t 0 decreases. We also invert the stress distribution P t (t) 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 ‘‘k2’’ slip model (Herrero and Bernard). 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 As 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. date: 2006-07-21 date_type: published publication: Journal of Geophysical Research volume: 111 number: B7 publisher: American Geophysical Union pagerange: 1-12 id_number: doi:10.1029/2005JB004077 refereed: TRUE issn: 0148-0227 official_url: http://dx.doi.org/10.1029/2005JB004077 access_IS-EPOS: limited owner: Publisher citation: Helmstetter, Agnes and Shaw, Bruce E. (2006) Relation between stress heterogeneity and aftershock rate in the rate-and-state model. Journal of Geophysical Research, 111 (B7). pp. 1-12. DOI: https://doi.org/10.1029/2005JB004077