A new paradigm for simulating pulse-like ruptures: The pulse energy equation

Ahmed E. Elbanna, Thomas H. Heaton

Research output: Contribution to journalArticlepeer-review


We investigate the chaotic behaviour of slip pulses that propagate in a spring block slider model with velocity weakening friction by numerically solving a computationally intensive set of n coupled non-linear equations, where n is the number of blocks. We observe that the system evolves into a spatially heterogeneous pre-stress after the occurrence of a sufficient number of events. We observe that, although the spatiotemporal evolution of the amplitude of a slip pulse in a single event is surprisingly complex, the geometric description of the pulses is simple and self-similar with respect to the size of the pulse. This observation allows us to write an energy balance equation that describes the evolution of the pulse as it propagates through the known pre-stress. The equation predicts the evolution of individual ruptures and reduces the computational time dramatically. The long-time solution of the equation reveals its multiscale nature and its potential to match many of the long-time statistics of the original system, but with a much shorter computational time.

Original languageEnglish (US)
Pages (from-to)1797-1806
Number of pages10
JournalGeophysical Journal International
Issue number3
StatePublished - Jun 2012
Externally publishedYes


  • Earthquake dynamics
  • Fractals and multi-fractals
  • Friction
  • Non-linear differential equations
  • Self-organization

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


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