Is Seismicity Operating at a Critical Point?

Seismicity and faulting within the Earth’s crust are characterized by many scaling laws that are usually interpreted as qualifying the existence of underlying physical mechanisms associated with some kind of criticality in the sense of phase transitions. Using an augmented epidemic-type aftershock sequence (ETAS) model that accounts for the spatial variability of the background rates $\mu (x,y)$, we present a direct quantitative test of criticality. We calibrate the model to the ANSS catalog of the entire globe, the region around California, and the Geonet catalog for the region around New Zealand using an extended expectation-maximization (EM) algorithm including the determination of $\mu (x,y)$. We demonstrate that the criticality reported in previous studies is spurious and can be attributed to a systematic upward bias in the calibration of the branching ratio of the ETAS model, when not accounting correctly for spatial variability. We validate the version of the ETAS model that possesses a space varying background rate $\mu (x,y)$ by performing pseudoprospective forecasting tests. The noncriticality of seismicity has major implications for the prediction of large events.

Figure 1

Spatial density of the earthquakes identified as background events by the ${\mathrm{ETAS}}_{\mu }$ and ${\mathrm{ETAS}}_{\mu (x,y)}$ models for the global catalog.

Figure 2

(a),(b) Time series of cumulative information gain of ${\mathrm{ETAS}}_{\mu (x,y)}$ over the ${\mathrm{ETAS}}_{\mu }$ model in 368 pseudoprospective experiments with the global catalog, at nine spatial resolutions (different colors whose meaning is given in the inset) and two magnitude thresholds (different panels) of the testing catalog; (c)–(d) Mean information gain (MIG) of ${\mathrm{ETAS}}_{\mu (x,y)}$ over the ${\mathrm{ETAS}}_{\mu }$ model in 368 pseudo prospective experiments for the global catalog, at nine spatial resolutions and two magnitude thresholds (different panels) of the testing catalog. The error bars indicate the 99% and 95% confidence interval of the mean information gain. The two numbers indicate the $p$ value and $t$ statistic resulting from the student’s $t$ test, in which we test the null hypothesis that the MIG is equal to 0 against the alternative that it is larger than 0. When the $p$ value is smaller than 0.05, the null hypothesis is rejected.