The timing of large, shallow earthquakes across the globe follows a mathematical pattern known as the devil's staircase, according to a new study of seismic sequences.

Previously, scientists and their models have theorized that earthquake sequences happen periodically or quasi-periodically, following cycles of growing tension and release. Researchers call it the elastic rebound model. In reality, periodic earthquake sequences are surprisingly rare.

Instead, scientists found global earthquake sequences tend to occur in clusters -- outbursts of seismic events separated by long but irregular intervals of silence.

The findings, published this week in the journal Bulletin of the Seismological Society of America, suggest large earthquakes increase the probability of subsequent seismic events.

Previous models failed to account for the interconnected nature of global fault systems. Seismic event don't occur in isolation. Each major quake alters the dynamics of other fault systems.

While the research suggests large quake sequences are "burstier" than previously thought, they remain as unpredictable as ever. The gaps between bursts are irregular, making it exceedingly difficult to anticipate the next cluster.

"Mathematically described as the devil's staircase, such temporal patterns are a fractal property of nonlinear complex systems, in which a change of any part -- e.g., rupture of a fault or fault segment -- could affect the behavior of the whole system," scientists wrote in their paper.

The devil's staircase pattern is also evidence in Earth's sedimentation sequences and reversals of the planet's magnetic field, as well as crustal uplift and erosion rates.

In addition to ignoring the interconnected nature of fault systems, most previous earthquake pattern models focused on too few earthquakes across time frames that were too short and regions that were too small. As a result, earlier models failed to pick up on the staircase pattern.

When models fail to take a wide-angle view of earthquake sequences -- instead, looking at seismic patterns over short periods of time -- it becomes impossible to tell whether a series of seismic events occurred within a single cluster or spanned two clusters and an interval of silence.

"For this same reason, we need to be cautious when assessing an event is 'overdue' just because the time measured from the previous event has passed some 'mean recurrence time' based an incomplete catalog," researchers wrote in their paper.

While scientists still aren't sure of the mechanisms that dictate the irregularity of the gaps between earthquake clusters, they hope that by studying the influence of major earthquakes on other fault systems via stress transfer, they can better predict how outbursts of large, shallow earthquakes will play out -- knowledge that could offer advanced warnings to vulnerable populations.

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