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 µ(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 µ(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 µ(x,y) by performing pseudoprospective forecasting tests. The noncriticality of seismicity has major implications for the prediction of large events.

Condensation of earthquake location distributions: Optimal spatial information encoding and application to multifractal analysis of south Californian seismicity.

We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDFs) of event locations to improve the spatial information content of seismic catalogs. As its name indicates, the condensation method reduces the size of seismic catalogs while improving the access to the spatial information content of seismic catalogs. The PDFs of events are first ranked by decreasing location errors and then successively condensed onto better located and lower variance event PDFs. The obtained condensed catalog differs from the initial catalog by attributing different weights to each event, the set of weights providing an optimal spatial representation with respect to the spatially varying location capability of the seismic network. Synthetic tests on fractal distributions perturbed with realistic location errors show that condensation improves spatial information content of the original catalog, which is quantified by the likelihood gain per event. Applied to Southern California seismicity, the new condensed catalog highlights major mapped fault traces and reveals possible additional structures while reducing the catalog length by ∼25%. The condensation method allows us to account for location error information within a point based spatial analysis. We demonstrate this by comparing the multifractal properties of the condensed catalog locations with those of the original catalog. We evidence different spatial scaling regimes characterized by distinct multifractal spectra and separated by transition scales. We interpret the upper scale as to agree with the thickness of the brittle crust, while the lower scale (2.5 km) might depend on the relocation procedure. Accounting for these new results, the epidemic type aftershock model formulation suggests that, contrary to previous studies, large earthquakes dominate the earthquake triggering process. This implies that the limited capability of detecting small magnitude events cannot be used to argue that earthquakes are unpredictable in general.