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

Elbanna, Ahmed E. and Heaton, Thomas H. (2012) A new paradigm for simulating pulse-like ruptures: the pulse energy equation. Geophysical Journal International, 189 (3). pp. 1797-1806. ISSN 0956-540X.

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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.

Item Type:Article
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Heaton, Thomas H.0000-0003-3363-2197
Additional Information:© 2012 The Authors. Geophysical Journal International © 2012 RAS. Issue published online: 10 May 2012; Article first published online: 23 Apr 2012; Accepted 2012 March 19; Received 2012 March 14; in original form 2011 September 14. We thank Nadia Lapusta, Jean-Paul Ampuero and Deborah Smith for their comments and we acknowledge the collaboration with Jerrold Marsden. This research was supported by the National Science Foundation, the Southern California Research Center, and the Gordon and Betty Moore Foundation (the Caltech Tectonics Observatory).
Group:Caltech Tectonics Observatory
Funding AgencyGrant Number
Southern California Research CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Subject Keywords:Fractals and multi-fractals; Non-linear differential equations; Self-organization; Friction; Earthquake dynamics
Issue or Number:3
Record Number:CaltechAUTHORS:20120608-092954406
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Official Citation:Elbanna, A. E. and Heaton, T. H. (2012), A new paradigm for simulating pulse-like ruptures: the pulse energy equation. Geophysical Journal International, 189: 1797–1806. doi: 10.1111/j.1365-246X.2012.05464.x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31848
Deposited By: Aucoeur Ngo
Deposited On:08 Jun 2012 22:11
Last Modified:03 Oct 2019 03:55

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