RESUMO
Aftershocks are a response to changes in stress generated by large earthquakes and represent the most common observations of the triggering of earthquakes. The maximum magnitude of aftershocks and their temporal decay are well described by empirical laws (such as Bath's law1 and Omori's law2), but explaining and forecasting the spatial distribution of aftershocks is more difficult. Coulomb failure stress change3 is perhaps the most widely used criterion to explain the spatial distributions of aftershocks4-8, but its applicability has been disputed9-11. Here we use a deep-learning approach to identify a static-stress-based criterion that forecasts aftershock locations without prior assumptions about fault orientation. We show that a neural network trained on more than 131,000 mainshock-aftershock pairs can predict the locations of aftershocks in an independent test dataset of more than 30,000 mainshock-aftershock pairs more accurately (area under curve of 0.849) than can classic Coulomb failure stress change (area under curve of 0.583). We find that the learned aftershock pattern is physically interpretable: the maximum change in shear stress, the von Mises yield criterion (a scaled version of the second invariant of the deviatoric stress-change tensor) and the sum of the absolute values of the independent components of the stress-change tensor each explain more than 98 per cent of the variance in the neural-network prediction. This machine-learning-driven insight provides improved forecasts of aftershock locations and identifies physical quantities that may control earthquake triggering during the most active part of the seismic cycle.
RESUMO
Earthquakes at seismogenic plate boundaries are a response to the differential motions of tectonic blocks embedded within a geometrically complex network of branching and coalescing faults. Elastic strain is accumulated at a slow strain rate on the order of 10^{-15} s^{-1}, and released intermittently at intervals >100 yr, in the form of rapid (seconds to minutes) coseismic ruptures. The development of macroscopic models of quasistatic planar tectonic dynamics at these plate boundaries has remained challenging due to uncertainty with regard to the spatial and kinematic complexity of fault system behaviors. The characteristic length scale of kinematically distinct tectonic structures is particularly poorly constrained. Here, we analyze fluctuations in Global Positioning System observations of interseismic motion from the southern California plate boundary, identifying heavy-tailed scaling behavior. Namely, we show that, consistent with findings for slowly sheared granular media, the distribution of velocity fluctuations deviates from a Gaussian, exhibiting broad tails, and the correlation function decays as a stretched exponential. This suggests that the plate boundary can be understood as a densely packed granular medium, predicting a characteristic tectonic length scale of 91±20 km, here representing the characteristic size of tectonic blocks in the southern California fault network, and relating the characteristic duration and recurrence interval of earthquakes, with the observed sheared strain rate, and the nanosecond value for the crack tip evolution time scale. Within a granular description, fault and blocks systems may rapidly rearrange the distribution of forces within them, driving a mixture of transient and intermittent fault slip behaviors over tectonic time scales.
