Three‐dimensional analyses are reported of slip on a long vertical strike‐slip fault between steadily driven elastic crustal blocks. A rate‐ and state‐dependent friction law governs motion on the fault; the law includes a characteristic slip distance L for evolution of surface state and slip weakening. Because temperature and normal stress vary with depth, frictional constitutive properties (velocity weakening/strengthening) do also. Those properties are taken either as uniform along‐strike at every depth or as perturbed modestly from uniformity. The governing equations of quasi‐static elasticity and frictional slip are solved on a computational grid of cells as a discrete numerical system, and a viscous radiation damping term is included to approximately represent inertial control of slip rates during earthquake‐like instabilities. The numerical results show richly complex slip, with a spectrum of event sizes, when solved for a grid with oversized cells, that is, with cell size h that is too large to validly represent the underlying continuous system of equations. However, in every case for which it has been feasible to do the computations (moderately large L only), that spatio‐temporally complex slip disappears in favor of simple limit cycles of periodically repeated large earthquakes with reduction of cell size h . Further study will be necessary to determine whether a similar transition occurs when the elastodynamics of rupture propagation is treated more exactly, rather than in the radiation damping approximation. The transition from complex to ordered fault response occurs as h is reduced below a theoretically derived nucleation size h * which scales with L but is 2 × 10 4 to 10 5 larger in cases considered. Cells larger than h * can fail independently of one another, whereas those much smaller than h * cannot slip unstably alone and can do so only as part of a cooperating group of cells. The results contradict an emergent view that spatio‐temporal complexity is a generic feature of mechanical fault models. Such generic complexity does apparently result from models which are inherently discrete in the sense of having no well‐defined continuum limit as h diminishes. Those models form a different class of dynamical systems from models like the present one that do have a continuum limit. Strongly oversized cells cause the model developed here to mimic an inherently discrete system. It is suggested that oversized cells, capable of failing independently of one another, may crudely represent geometrically disordered fault zones, with quasi‐independent fault segments that join one another at kinks or jogs. Such geometric disorder, at scales larger than h * , may force a system with a well‐defined continuum limit to mimic an inherently discrete system and show spatio‐temporally complex slip at those larger scales.
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ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTLong-Range Proton Spin—Spin Coupling in Dimethyl Sulfone1aGeorge M. Whitesides and John D. RobertsCite this: J. Phys. Chem. 1964, 68, 6, 1583–1584Publication Date (Print):June 1, 1964Publication History Published online1 May 2002Published inissue 1 June 1964https://pubs.acs.org/doi/10.1021/j100788a512https://doi.org/10.1021/j100788a512research-articleACS PublicationsRequest reuse permissionsArticle Views44Altmetric-Citations6LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts
