June 4, 2001 CHAMPAIGN, Ill. — When Karin Dahmen hears the crackling noise in a bowl of crisped-rice cereal, her thoughts turn to earthquakes.
That’s because both the cereal and an earthquake fault zone have something in common: Each responds to an external force with a power law distribution of events of all sizes, independent of microscopic or macroscopic details. By studying such universal behavior, which depends upon just a few basic properties, scientists may better understand the physics of earthquakes.
Dahmen, a physicist at the University of Illinois, initially studied a similar effect – called Barkhausen noise – in magnets. That work was done in collaboration with her thesis adviser, Jim Sethna at Cornell University. "Magnetic materials respond to an external field by changing their magnetization in a series of bursts, or avalanches," she said. "In highly disordered materials, we find small avalanches. But in clean materials, we find huge avalanches that sweep through the material." What all three systems – a bowl of cereal, a reel of magnetic tape and a fault zone – have in common is a competition between interaction and disorder, Dahmen said. "First, there is a slow driving force – such as a magnetic field in magnets or continental drift in earthquakes – and some interaction that promotes the avalanche. Then, there is some disorder that stops the avalanche. This competition between interaction and disorder creates a very broad distribution of avalanche sizes."
Dahmen and her colleagues – Daniel Fisher at Harvard University, Yehuda Ben-Zion at the University of Southern California, Deniz Ertas at Exxon Research and Engineering, and Sharad Ramanathan at Bell Labs – recently took the tools used to study noise in magnets and applied them to earthquake models. The tools, such as mean-field theory and renormalization group techniques, allowed the researchers to examine the interplay between disorder and dynamical effects in earthquakes.
Fault zones with highly irregular geometry display power law statistics over the entire range of observed magnitudes, Dahmen said. Faults with more regular geometry, however, display such distributions only for small events, which typically occur between much larger events that rupture a large fraction of the fault.
"Our model suggests a competition between the earthquake-promoting effect of seismic waves and the earthquake-stopping effect of heterogeneities in the fault plane," said Dahmen, who was to present the team’s findings at the American Geophysical Union Spring Meeting May 29-June 2 in Boston. "In highly heterogeneous faults, dynamical effects can be neglected, and we expect to see the pure power law distribution. But in highly regular faults, the weakening effects of seismic waves become important." Earthquakes that grow larger than a critical size – which depends on the amount of disorder in the fault plane – become unstoppable in the presence of seismic waves, Dahmen said. "These earthquakes then grow to the characteristic runaway event size, in which a large fraction of the fault zone ruptures."
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