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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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doi:10.5194/npg-2016-28
© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
02 Jun 2016
Review status
A revision of this discussion paper was accepted for the journal Nonlinear Processes in Geophysics (NPG) and is expected to appear here in due course.
Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes
Rene C. Batac1, Antonino A. Paguirigan Jr.1, Anjali B. Tarun1, and Anthony G. Longjas2 1National Institute of Physics, University of the Philippines Diliman 1101 Quezon City, Philippines
2St. Anthony Falls Laboratory, University of Minnesota, 2 Third Ave. SE, Minneapolis MN 55414, USA
Abstract. We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of self-organized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy (magnitude) distributions closely follow power-law probability density functions (PDFs) with scaling exponent −5/3, consistent with the expectations of the Gutenberg–Richter (GR) law, for a wide range of the targeted-triggering probability values; this suggests that SOC mechanisms are still present in the model despite the introduction of the targeted triggering. Additionally, for targeted triggering probabilities within the range 0.004–0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, without disrupting the SOC properties of the sandpile grid. We believe that the critical targeting probability is a key requirement for SOC in seismicity, as it parametrizes the memory that is inherently present in earthquake-generating regions.

Citation: Batac, R. C., Paguirigan Jr., A. A., Tarun, A. B., and Longjas, A. G.: Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes, Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-28, in review, 2016.
Rene C. Batac et al.
Rene C. Batac et al.

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Short summary
The sandpile-based model is the paradigm model of self-organized criticality (SOC), a mechanism believed to be responsible for the occurrence of scale-free (power-law) distributions in nature. One particular SOC system that is rife with power-law distributions is that of earthquakes, the most widely-known of which is the Gutenberg–Richter (GR) law of earthquake energies. Here, we modify the sandpile to be of use in capturing the energy, space, and time statistics of earthquakes simultaneously.
The sandpile-based model is the paradigm model of self-organized criticality (SOC), a mechanism...
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