Subject Areas : Nonlinear Dynamics , Geophysics A Viewpoint on : Statistical Similarity between the Compression of a Porous Material and Earthquakes

The 1970s heyday of earthquake research was characterized by a high degree of optimism, as leading scientists expressed hope that some method of predicting earthquakes might be around the corner. This was partly based on the assumption of a close similarity between seismic events and controlled indoor laboratory tests on the fracture of rock samples [1]. Such expectations led to the belief that diagnostic earthquake precursors (such as electromagnetic or acoustic phenomena, radon gas emissions, and the like) may be identified. This early optimism faltered as reliable precursors failed to materialize when subjected to rigorous statistical testing [2], and as results from theories of complexity [3] provided a possible physical explanation for their absence [4]: even fully deterministic systems of interacting elements can exhibit chaotic behavior, associated with an extreme sensitivity to initial conditions that makes accurate prediction impossible. While the deterministic prediction of individual earthquakes with sufficient accuracy to justify an evacuation before an event is still considered to be beyond reach—and may not even be a realistic scientific goal [5]—probabilistic earthquake forecasting (i.e., the quantification of earthquake hazards in a given area and period of time) is instead enabled by the fact that earthquakes are not completely random events: they are localized, predominantly on plate boundaries (see Fig. 1), and tend to cluster in time [6]. Earthquake statistics obey a range of empirical scaling laws that help carry out seismic hazard analysis, set building design codes, or identify periods of elevated risk due to clustering. Such scaling laws may also provide strong constraints on the physics underlying the occurrence of earthquakes. Earthquake models are often built by scaling up constitutive rules derived from fracture and friction experiments in the laboratory, but an accurate statistical comparison between such lab tests and real earthquakes was lacking. Now, writing in Physical Review Letters, Jordi Barò at the University of Barcelona, Spain, and colleagues provide perhaps the most comprehensive statistical comparison to date between seismic events in the laboratory and in nature [7]. Their results show that, within an impressive range of several orders of magnitude, data collected from their laboratory-scale experiments and from earthquake databases collapse on the same distribution curves, revealing very similar scaling laws. Ultimately, the clustering of earthquake probability distributions in space and time is due to a sensitive response to small fluctuations in local stress, consistent with a physical system that is close to criticality (e.g., at a firstor second-order phase transition), in which the failure of an element of the system can trigger that of another element that is close in space or time. This is analogous to the spread of a contagious disease in a population by local transmission of infection between a carrier and a healthy but susceptible individual. Based on this idea, statisticians have developed a purely stochastic earthquake model, called epidemic-type aftershock sequence (ETAS) that combines epidemic-type models for disease transmission with empirical scaling laws observed more or less ubiquitously in earthquake occurrence. Three scaling laws have proven to be of very general validity. First, the Gutenberg-Richter law captures the fact that small earthquakes are more frequent than large earthquakes, providing a relationship between the magnitude and number of earthquakes in a given region. Second, the Omori law describes how the probability of aftershocks decreases with time: it is approximately inversely proportional to the time elapsed from the main shock (the largest in a sequence). Finally, the so-called “aftershock productivity” law relates the rate of aftershocks triggered by a mainshock to its magnitude: largermagnitude earthquakes produce on average more after-