## Abstract

We present a fully coupled energy approach to investigate the important problem of ductile faulting within the lithosphere. Our starting setup consists of a 70 km × 106 km segment of a model lithosphere containing a random set of thermal perturbations. This allows the development of multiple sets of interacting ductile faults. The perturbations diffuse through conduction while the model is subject to constant velocity pure shear boundary conditions. The entire lithosphere has two domains, one governed chiefly by the Peierls mechanism (cold top part) and another by power law creep (hot lower part). In the calculations, the primary creep mechanisms are not assigned but activated by their dominance through adding power and Peierls creep strain-rates. The water content is always below solubility, hence brittle fracture is not considered in this model. Extreme localization through thermal-mechanical feedback is observed in interacting ductile faults inverse cascading from short- to long-length scales. Another outstanding effect of interacting faults is the remarkable ability to reduce the time scale leading to finite amplitude-instability. Both Peierls- and power law-domains are affected, but the Peierls-domain exhibits true, ductile, faults while the power law domain develops unstable slipping events akin to brittle shear faults. This affinity to a seismic response is due to the exponential temperature dependence of power law creep leading to short creep-bursts with time scales less than a day. The addition of water can stabilize the brittle like response into a more ductile one through its effect on the activation energy. The main storage of elastic energy lies in the Peierls domain so that shear zones are attracted to an isotherm 875-1100 K, thus marking the transition between both creep regimes in the p-T-strain-rate space. Criteria for stability and accuracy in the presence of thermal feedback are developed. These show that extremely high mesh resolution (∼100-500 m local resolution) is required for accurately assessing the potential for shear localization. The potential for upscaling schemes based on critical Peclet and dissipation numbers is discussed and the critical energy quantity (dissipation number) for spontaneous symmetry breaking is introduced.

Original language | English (US) |
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Pages (from-to) | 113-135 |

Number of pages | 23 |

Journal | Physics of the Earth and Planetary Interiors |

Volume | 142 |

Issue number | 1-2 |

DOIs | |

State | Published - May 12 2004 |

### Bibliographical note

Funding Information:We would like to thank Yehuda Ben-Zion, Yuri Podladchikov, Bruce Hobbs, Saskia Goes as well as the comments of two anonymous reviewers and Bobby Poliakov for stimulating our earlier work. This project has been supported by the geophysics program of the N.S.F., the Swiss Nationalfond 21-61912.00 and the predictive mineral discovery Cooperative Research Center pmd ∗ CRC.

## Keywords

- Effect of water
- Numerical techniques
- Shear zones
- Symmetry breaking
- Thermal feedback