A sandpile model of earthquake occurrences
A sandpile model of earthquake occurrences
FEATURED PUBLICATION:
R.C. Batac, Clustering regimes in a sandpile with targeted triggering, EPL (Europhysics Letters) 135, 19003, https://doi.org/10.1209/0295-5075/135/19003 (2021).
R.C. Batac, A.A. Paguirigan Jr., A.B. Tarun, and A.G. Longjas, Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes, Nonlinear Processes in Geophysics 24(2), 179-187, https://doi.org/10.5194/npg-24-179-2017 (2017).
The theory of self-organized criticality (SOC), in which a system drives itself towards a critical behavior without a need for fine-tuning of external parameters, is one of the mechanisms to explain the occurrence of earthquakes. Earthquakes are generated when the crust stores energy driven via the very slow mechanism of tectonic motion, and release the energy in rapid succession through a sequence of correlated events. Despite the differences in the rates and mechanisms of crustal motion, all earthquake occurrences follow the Gutenberg-Richter law, a power-law distribution of energy released. This nearly universal energy distribution is deemed to be a consequence of SOC.
Incidentally, SOC was first introduced through a discrete mathematical model of the sandpile. Imagine a flat surface where sand is added grain by grain; eventually, the pile reaches a critical state where a single grain can trigger anything from a tiny slip to a massive landslide. The sandpile model also leads to power-law distributions of avalanches generated from the grid, whose exponents are found to be robust even upon changing the details of the model.
As such, is it reasonable to assume that a simple sandpile can be used to model earthquakes? It turns out, it is not very straightforward; traditional sandpile models release energy in a "single-shot" avalanche, failing to capture the way real earthquakes produce clustered bursts in time and space, often as aftershock sequences.
By introducing targeted triggering mechanisms in the sandpile, the model simultaneously recovers (A) the Gutenberg-Richter (GR) law of seismicity and (B) the spatio-temporal regimes of clustering (of correlated events) and separation (of independent events). (C) The model parameters can be tuned to recover the signatures of regional seismicity (here, for Philippine earthquakes), without losing the SOC characteristics.
In a pivotal 2017 study published in Nonlinear Processes in Geophysics, researcher Rene C. Batac and his team introduced a simple yet transformative modification to the sandpile. Instead of dropping grains at random locations, they introduced a "targeted triggering" mechanism. By occasionally directing the next grain to the most "stressed" or susceptible site in the system—essentially giving the model a form of "memory"—the researchers successfully recreated the complex spatiotemporal signatures of real-world seismicity. This single adjustment allowed the model to simulate not just the size of earthquakes, but also the realistic "bimodal" patterns of waiting times and distances between events.
Building on this foundation, Batac’s 2021 work in Europhysics Letters (EPL) took the investigation further by exploring different "clustering regimes." By varying the probability of this targeted triggering, the research demonstrated that a system can transition between different states of organization. When triggering is highly targeted, the sandpile mimics "bursty" seismic activity where events are tightly packed together. This refined understanding helps explain why certain fault lines seem to go dormant for years before erupting in a flurry of activity, providing a mathematical lens through which we can view the Earth’s long-term "memory" of stress.
The research highlights that the timing and location of the next quake are not entirely random; rather, they are dictated by a delicate balance between random tectonic loading and the specific, localized history of the fault system. More importantly, the work illustrates that by introducing a simple rule in the sandpile model, the SOC mechanism is preserved, while allowing for the recovery of earthquake signatures in space, time, and energy scales simultaneously.◼