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 law and Omori's law), but explaining and forecasting the spatial distribution of aftershocks is more difficult. Coulomb failure stress change is perhaps the most widely used criterion to explain the spatial distributions of aftershocks, but its applicability has been disputed. 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.

[1] Geodetic observations of interseismic deformation across the Tibetan plateau contain information about both tectonic and earthquake cycle processes. Time-variations in surface velocities between large earthquakes are sensitive to the rheological structure of the subseismogenic crust, and, in particular, the viscosity of the middle and lower crust. Here we develop a semianalytic solution for time-dependent interseismic velocities resulting from viscoelastic stress relaxation in a localized midcrustal layer in response to forcing by a sequence of periodic earthquakes. Earthquake cycle models with a weak midcrustal layer exhibit substantially more near-fault preseismic strain localization than do classic two-layer models at short (<100 yr) Maxwell times. We apply both this three-layer model and the classic two-layer model to geodetic observations before and after the 1997 M W = 7.6 Manyi and 2001 M W = 7.8 Kokoxili strike-slip earthquakes in Tibet to estimate the viscosity of the crust below a 20 km thick seismogenic layer. For these events, interseismic stress relaxation in a weak (viscosity ≤10 18.5 PaÁs) and thin (height ≤20 km) midcrustal layer explains observations of both preseismic near-fault strain localization and rapid (>50 mm/yr) postseismic velocities in the years following the coseismic ruptures. We suggest that earthquake cycle models with a localized midcrustal layer can simultaneously explain both preseismic and postseismic geodetic observations with a single Maxwell viscosity, while the classic two-layer model requires a rheology with multiple relaxation time scales.Citation: DeVries, P. M. R., and B. J. Meade (2013), Earthquake cycle deformation in the Tibetan plateau with a weak mid-crustal layer,

One of the most significant challenges involved in efforts to understand the effects of repeated earthquake cycle activity is the computational costs of large‐scale viscoelastic earthquake cycle models. Computationally intensive viscoelastic codes must be evaluated at thousands of times and locations, and as a result, studies tend to adopt a few fixed rheological structures and model geometries and examine the predicted time‐dependent deformation over short (<10 years) time periods at a given depth after a large earthquake. Training a deep neural network to learn a computationally efficient representation of viscoelastic solutions, at any time, location, and for a large range of rheological structures, allows these calculations to be done quickly and reliably, with high spatial and temporal resolutions. We demonstrate that this machine learning approach accelerates viscoelastic calculations by more than 50,000%. This magnitude of acceleration will enable the modeling of geometrically complex faults over thousands of earthquake cycles across wider ranges of model parameters and at larger spatial and temporal scales than have been previously possible.