Eur. Phys. J. B 15, 193-197 (2000)
https://doi.org/10.1007/s100510051115

Novel mechanism for discrete scale invariance in sandpile models

¹ Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095, USA
² Department of Earth and Space Science, University of California, Los Angeles, California 90095, USA
³ LPMCUMR 6622 du CNRS and Université de Nice-Sophia Antipolis, BP 71, Parc Valrose, 06108 Nice Cedex 2, France

Received: 24 November 1999
Published online: 15 May 2000

Abstract

Numerical simulations and a mean-field analysis of a sandpile model of earthquake aftershocks in 1d, 2d and 3d Euclidean lattices determine that the average stress decays in a punctuated fashion after a main shock, with events occurring at characteristic times increasing as a geometrical series with a well-defined multiplicative factor which is a function of the stress corrosion exponent, the stress drop ratio and the degree of dissipation. These results are independent of the discrete nature of the lattice and stem from the interplay between the threshold dynamics and the power law stress relaxation. This novel mechanism of log-periodicity does not rely on a pre-existing discrete structural hierarchy of faults but is dynamical and reflects the existence of an approximately fixed stress drop together with the scale-free stress corrosion power law acting during inter-seismic phases.