The timing of large earthquakes follows the mathematical pattern

On a regional level and around the world, the occurrence of large shallow earthquakes appears to follow a mathematical pattern called the Devil’s Staircase, in which seismic event groups are separated by long but irregular periods of seismic calm.

The results published in the Bulletin of the American Seismic Society differ from the pattern predicted by classical seismic modeling that indicates the occurrence of periodic or semi-periodic earthquakes based on cycles of accumulation and release of tectonic stress. In fact, Yuxuan Chen of the University of Missouri, Colombia, and his colleagues say that periodic large earthquake sequences are relatively rare.

Researchers note that their results can have implications for seismic risk assessment. For example, they found that large seismic sequences (those with events of 6.0 or greater) are “more impulsive” than expected, which means that timely seismology leads to a higher probability of a repeat of seismic events shortly after a major earthquake. The irregular gap between the bursts of events makes it difficult to predict the average recurrence time between large earthquakes.

The seismologists ’catalogs of large earthquakes in the region may include very few earthquakes within a very short period of time to capture the entire staircase pattern, making it difficult to“ see if a few events in the catalog occurred within the seismic group or spanned both clusters and quiet periods ”, Chen and colleagues noted.

They added, “For the same reason, we must be careful when the event evaluation is” overdue “just because the time measured from the previous event has exceeded some” average repeat time “based on an incomplete catalog.

Devil’s Stairway, sometimes called Cantor’s function, is a fractal exhibited by nonlinear dynamic systems, in which a change in any part can affect the behavior of the entire system. In nature, the pattern can be found in the precipitation sequence, changes in elevation rates, erosion, and reflections in the Earth’s magnetic field, among other examples.

Chen’s Doctorate. Chancellor Mian Liu had an unusual introduction to the Devil’s staircase. “I stumbled upon this topic a few years ago when I read about a study by researchers from the University of California, Los Angeles, about the timeline of the infamous serial killer, André Chicatello, who killed at least 52 people from 1979 to 1990 in the former Soviet Union.” explained. “The time pattern for killing him is the ladder of the devil. Researchers have been trying to understand how the criminal’s mind works, and how neurons stimulate each other in the brain. I was intrigued because I realized that earthquakes operate in a similar way, and that rupture rupture can stimulate activity on other errors by transferring Pressure “.

“Theoretically, we also know that many large earthquakes, which involve rupture multiple and variable parts of faults in each rupture, violate the basic assumption of the periodic seismic model, which relies on frequent accumulation and release of energy at a specific error level,” Liu added.

The factors that control grouped events are complex, and could involve pressure that triggers the earthquake, changes in friction properties, and the transfer of stress between malfunctions or malfunction sectors during rupture, among other factors, said Gang Lu of Wuhan University. He indicated that the time periods seem inversely related to the rate of tectonic stress in the background of the region.

Devil’s stair pattern can be found in large earthquakes in the Great Basin of the western United States, in Australia, on the borders of the Africa-Eurasia plate off the coast of West Algeria, along the mistake of diverting the Dead Sea, and perhaps in new earthquakes in Madrid and Liu said the central United States, Noting that the specific details of the pattern differ from one region to another.

Reference: “Complex Time Patterns for Large Earthquakes: Devil Baskets,” by Yushuan Chen, Mian Liu, and Jang Luo, April 14, 2020, Bulletin of the American Seismic Society. DOI: 10.1785 / 0120190148

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