Complex Temporal Patterns of Large Earthquakes: Devil’s Staircases

Abstract

Periodic or quasiperiodic earthquake recurrence on individual faults, as predicted by the elastic rebound model, is not common in nature. Instead, most earthquake sequences are complex and variable, and often show clusters of events separated by long but irregular intervals of quiescence. Such temporal patterns are especially common for large earthquakes in complex fault zones or regional and global fault networks. 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. We found that the lengths of the quiescent intervals between clusters are inversely related to tectonic-loading rates, whereas earthquake clustering can be attributed to many factors, including earthquake-induced viscoelastic relaxation and fault interaction. Whereas the underlying causes of the characteristics of earthquake sequences are not fully known, we attempted to statistically characterize these sequences. We found that most earthquake sequences are burstier than the Poisson model commonly used in probabilistic seismic hazard analysis, implying a higher probability of repeating events soon after a large earthquake.

Periodicity and Clustering in the Long‐Term Earthquake Record

“…Both COV and B ignore the order in which events occur; for example, these measures do not indicate whether shorter interevent times tend to occur consecutively in clusters or separated by longer interevent times (Figures 1a–1c; Chen et al, 2020). For determination of clustering, correlation between consecutive interevent times is important, whereby the conditional probability of a short interevent time following a preceding short interevent time should be greater than the unconditional probability of observing a short interevent time (Livina et al, 2005; Salditch et al, 2020).…”

“…In these sequences, successive interevent times are correlated such that short interevent times typically follow previous short interevent times and long follow long ("memory"; Goh & Barabási, 2008;Livina et al, 2005). This has led to statements like "quasiperiodic earthquake recurrence on individual faults, as predicted by the elastic rebound model, is not common in nature" (Chen et al, 2020). Some long-term geological records also suggest more complex patterns of earthquake recurrence.…”

Aftershocks and Background Seismicity in Tangshan and the Rest of North China

“…Previous studies have noticed that seismic activity in North China seems to fluctuate between highs and lows over periods of a few decades (Xu & Deng, 1996). In general, seismic activity tends to cluster in relatively short periods, separated by long and relatively quiescent periods (Chen et al, 2020 The seismicity rate of all M ≥ 3 earthquakes in North China (Figure 7) shows strong temporal variations due to large earthquakes and their aftershocks. Before January 1976 (Figure 7a), the regions of high seismicity rate are mainly near the epicenters of the 1966 M s 7.2 Xingtai earthquake, the 1969 M b 7.4 Bohai earthquake, and the 1975 M s 7.3 Haicheng earthquake.…”

NDSHA - The New Paradigm for RSHA - An Updated Review

“…Since nothing provided in the Cornell "return period" risk model has ever been both successfully tried and experimentally verified (e.g., Chen et al, 2020); we must therefore agree that this unsupported concept of aseismic design belief and convenience -per Cornell 1968, that: "Owing to the uncertainty in the number, sizes, and locations of future earthquakes it is appropriate that engineers express seismic risk, as design winds or floods are, in terms of return periods [cited references 1952-1967]" -is too simple and simplistic to survive the limitations of its own probabilistic presumptive assumptions! Bummer!…”