Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model

Rene Batac, Anthony Longjas, Christopher Monterola

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S- 1.3 for the first layer to gamma distributions p(S) ≈exp(-SS0) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature.

Original languageEnglish (US)
Pages (from-to)616-624
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Issue number3
StatePublished - Feb 1 2012
Externally publishedYes

Bibliographical note

Funding Information:
The authors would like to thank Prof. B.D. Malamud for the empirical landslide data and Prof. E. Piegari for the synthetic model results. We would also like to thank G.A. Esleta for his contributions in the early part of the work. The work is supported by the OVCRD—University of the Philippines Diliman and the National Research Council of the Philippines . RB and AL acknowledge the DOST-PCASTRD.


  • Cellular automata
  • Inter-sandpile cascade model
  • Landslides


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