R. F. Smalley*, D. L. Turcotte, Sara A. Solla

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

140 Scopus citations


A fault is treated as an array of asperities with a prescribed statistical distribution of strengths. When an asperity fails, the stress on the failed asperity is transferred to one or more adjacent asperities. For a linear array the stress is transferred to a single adjacent asperity and for a two-dimensional array to three adjacent asperities. Using a renormalization group (RG) method, the properties of a scale invariant hierarchical model are investigated for the stochastic growth of fault breaks through induced failure by stress transfer. An extrapolation to arbitrarily large scales shows the existence of a critical applied stress at which the solutions bifurcate. At stresses less than the critical stress, virtually no asperities fail on a large scale, and the fault is locked. Above the critical stress, asperity failure cascades away from the nucleus of failure; this catastrophic failure is interpreted as an earthquake and it corresponds to the transition from stick to slip behavior on the fault.

Original languageEnglish (US)
Pages (from-to)1894-1900
Number of pages7
JournalJournal of Geophysical Research
Issue numberB2
StatePublished - 1985

ASJC Scopus subject areas

  • Geophysics
  • Forestry
  • Oceanography
  • Aquatic Science
  • Ecology
  • Water Science and Technology
  • Soil Science
  • Geochemistry and Petrology
  • Earth-Surface Processes
  • Atmospheric Science
  • Earth and Planetary Sciences (miscellaneous)
  • Space and Planetary Science
  • Palaeontology


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