### Abstract

We obtain quasi-static, two-dimensional solutions for earthquake nucleation on faults obeying Dieterich's "aging" version of the rate and state friction equations. Two distinct nucleation regimes are found, separated by roughly a/b ∼ 0.5, where a and b are the constitutive parameters relating changes in slip rate V and state χ to frictional strength. When fault healing is unimportant (Vχ/D_{c} ≫ 1, where D_{c} is the characteristic slip distance for the evolution of χ), the nucleation zone spontaneously evolves toward a state of accelerating slip on a patch of fixed half length L_{v} ≈ 1.3774(μ′D_{c} /bσ), where μ′ is the intrinsic stiffness of the medium and σ is the normal stress. This is the fixed length solution for which the stress intensity factor K = 0. Although this solution does not depend upon a/b explicitly, only for a/b < 0.3781 does healing remain unimportant as instability is approached. For a/b ≳ 0.5 and a wide range of slow loading conditions, Vχ/D_{c} ultimately approaches a quasi-constant value near 1, and the nucleation zone takes on the appearance of an expanding slip-weakening crack. A fracture energy balance indicates that in this regime the nucleation length asymptotically approaches π^{-1}[b/(b - a)]^{2}(μ′D_{c}/bσ), a result that is consistent with the numerical simulations despite considerable complexity as a approaches b. This suggests that nucleation lengths can sometimes be much larger than those found by Dieterich (e.g., by a factor of 100 for a/b = 0.95). For surfaces this close to velocity neutral, nucleation might produce signals detectable by surface seismometers for values of D_{c} at the upper end of the lab range (100 μm). However, the attributes of the aging law that give rise to such large nucleation lengths may be nonphysical; additional laboratory experiments are needed to address this issue.

Original language | English (US) |
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Article number | B11312 |

Pages (from-to) | 1-24 |

Number of pages | 24 |

Journal | Journal of Geophysical Research: Solid Earth |

Volume | 110 |

Issue number | 11 |

DOIs | |

State | Published - Nov 4 2005 |

### All Science Journal Classification (ASJC) codes

- Geophysics
- Geochemistry and Petrology
- Earth and Planetary Sciences (miscellaneous)
- Space and Planetary Science

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## Cite this

*Journal of Geophysical Research: Solid Earth*,

*110*(11), 1-24. [B11312]. https://doi.org/10.1029/2005JB003686