13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- found to be larger than 2Lν. Seeking for a characteristic patch length with the revised RSF, we then compare it with another length scale Lb−a ≡ μ*L (b−a) σ , (6) where Lb-a is a characteristic nucleation length based on long-tem stick-slip instability [6]. 2Lb-a is plotted for reference by thick dashed line in Fig. 5. It seems to show a better agreement than 2Lν and may be a possible reference length at the moment. It is a tentative scale as a matter of course and future analytic work will be absolutely necessary to quantify the nucleation patch length explicitly including c parameter [17]. 4. Conclusion Nucleation on frictional faults was reexamined by using the revised RSF which seems to be free from previously known flaws. Our simulation results with systematic changes in the frictional parameter sets (a/b,c) comprehensively disclosed two major differences. 1) For weakly velocity-weakening range of 0.85<a/b<1, nucleation had characteristics of both unidirectional slip-pulse regime found in the slip law case and crack-like expansion regime in the aging law case. 2) Fixed-length patch regime occurred over a wider condition of a/b up to 0.85 in contrast with the previously reported range of a/b<0.5 implying strongly velocity-weakening faults, and its patch length was larger than that predicted by the aging law. Acknowledgements N. Kato provided his numerical code. N.K. was supported by MEXT Grant-in-Aid for Scientific Research on Innovative Areas Number 21107007. This study was also supported by MEXT, under its Observation and Research Program for Prediction of Earthquakes and Volcanic Eruptions. References [1] K. Nagata, M. Nakatani, S. Yoshida, A revised rate- and state-dependent friction law obtained by constraining constitutive and evolution laws separately with laboratory data, J Geophys Res, 117 (2012) B02314 doi:10.1029/2011JB008818. [2] J.H. Dieterich, Modeling of rock friction 1. experimental results and constitutive equations, J Geophys Res, 84 (1979) 2161-2168. [3] S.T. Tse, J.R. Rice, Crustal earthquake instability in relation to the depth variation of frictional slip properties, J Geophys Res, 91 (1986) 9452-9472. [4] J.H. Dieterich, A constitutive law for rate of earthquake production and its application to earthquake clustering, J Geophys Res, 99 (1994) 2601-2618. [5] J.H. Dieterich, Earthquake nucleation on faults with rate- and state-dependent strength, Tectonophysics, 211 (1992) 115-134. [6] A.M. Rubin, J.-P. Ampuero, Earthquake nucleation on (aging) rate and state faults, J Geophys Res, 110 (2005) B11312 doi:10.1029/2005JB003686. [7] J.-P. Ampuero, A.M. Rubin, Earthquake nucleation on rate and state faults - Aging and slip laws, J Geophys Res, 113 (2008) B01302 doi:10.1029/2007JB005082. [8] M. Nakatani, Conceptual and physical clarification of rate and state friction: Frictional sliding as a thermally activated rheology, J Geophys Res, 106 (2001) 13347-13380. [9] J.H. Dieterich, B.D. Kilgore, Imaging surface contacts: power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic, Tectonophysics, 256 (1996) 219-239.
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