Natural disasters like forest fires and earthquakes have more than just havoc-reeking, destructive natures in common, according to scientist Eduardo Jagla of the National Atomic Energy Commission in Argentina. In a paper to appear in the APS journal, Physical Review Letters, Jagla found that a statistical model describing the behavior of forest fires could be used to characterize the decay rate of earthquakes.
The number of earthquakes that can occur in a given region over a period of time follows a surprisingly simple logarithmic scale expressed by the Gutenberg-Richter Law. The law takes into account the magnitude of an earthquake, the seismicity rate of the region in question and a constant, called the b-value. Although the b-value hovers around one (give or take 0.5) for most regions, scientists do not fully understand why one is the magic number.
The b-value satisfies observational experiments that follow the GR law, but its origin remains unknown. Jagla proposed that aftershocks are, in part, the reason behind the b-value. This conclusion emerged when Jagla discovered that he could obtain the appropriate b-value by applying the GR model to a scenario of a forest fire spreading from tree to tree.
|Credit: Eduardo Jagla who describes: "The attached figure can be interpreted in two different ways: each black pixel can represent a tree in a forest, or intensity of gray can represent the local stress of a tectonic fault."|
Grabbing from the Drossel-Schwable (DS) model that describes the spread of forest fires, Jagla designed a computational simulation of a forest fire. He started with a clump of trees where he then struck one of the trees with lightning that initiated a fire – analogous to how an earthquake might spontaneously occur in a given location.
In the original DS model, trees that catch fire propagate the fire instantaneously to all of their neighbors. Jagla introduced a different flavor of trees to the sample, however, that spread fire to their neighbors only after some random time period. Jagla analogized these trees to aftershocks, because aftershocks can occur hours after the initial quake.
The size distribution of the burning trees/aftershocks, in Jagla’s modified DS model followed a similar pattern to the distribution of earthquakes in Southern California over a 20-year time period. In particular, the slope describing the decay rate of both distributions took on a sharp dive as more trees burned or the number of aftershocks grew.
“I have considered an analogy between a forest fire model and the stress in a single planar fault,” Jagla stated in his paper. “The inclusion of a second tree species that delays propagation of fire, was shown to be analogous to include the possibility of aftershocks in the seismic counterpart.”
Right now, the model describes a single fault whereas in reality seismic active regions can be comprised of many individual faults. Therefore, the model still has a ways to go before it can apply to reality, Jagla said, however, the ingredients are there.