Letter | Published:

Deep learning of aftershock patterns following large earthquakes

Naturevolume 560pages632634 (2018) | Download Citation

Abstract

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 aftershocks4,5,6,7,8, but its applicability has been disputed9,10,11. 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.

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Acknowledgements

This work was supported by Harvard University and Google. The computations in this paper were run on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University.

Reviewer information

Nature thanks D. Trugman and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

Affiliations

  1. Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA

    • Phoebe M. R. DeVries
    •  & Brendan J. Meade
  2. Center for Integrative Geosciences and Department of Physics, University of Connecticut, Storrs, CT, USA

    • Phoebe M. R. DeVries
  3. Google, Cambridge, MA, USA

    • Fernanda Viégas
    •  & Martin Wattenberg

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Contributions

All authors conceived the idea for this paper; P.M.R.D. and B.J.M. implemented the analysis and wrote the paper.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Phoebe M. R. DeVries.

Extended data figures and tables

  1. Extended Data Fig. 1 Comparisons of spatial patterns of stress metrics.

    ad, Analogous to Fig. 2e–h, but for an idealized thrust earthquake. The fault plane dips 45° to the north and the red line is the trace of the fault at the surface. Depth shown is 10 km.

  2. Extended Data Fig. 2 Mainshock–aftershock examples.

    ah, Analogous to Fig. 1a–h, using the same sign conventions for Coulomb failure stress change, but with results based on a training dataset (Supplementary Table 1) that excludes grid cells more than 5 km below the maximum depth of each slip distribution.

  3. Extended Data Fig. 3 Comparisons of performance.

    ah, Analogous to Fig. 2a–h, using training and test datasets (Supplementary Table 1) that exclude grid cells more than 5 km below the maximum depth of each slip distribution.

  4. Extended Data Fig. 4 ROC curves associated with realization 6 of the datasets.

    ad, Curves incorporate grid cells down to a depth of 50 km. eh, Curves including grid cells down to 5 km beyond the maximum depth of each slip distribution. Thus, the neural network in d is trained and evaluated on a version of dataset realization 6 (Supplementary Table 2) that incorporates grid cells down to a depth of 50 km, whereas that in h is trained and evaluated on the same realizations of slip distributions, but incorporating only grid cells down to 5 km below each slip distribution.

  5. Extended Data Fig. 5 Forward predictions of the neural networks from each realization of the training dataset, incorporating all grid cells down to 50 km.

    Each panel is analogous to Fig. 2h, but uses one of ten distinct neural networks trained on one of ten different realizations of the training dataset (Supplementary Table 2). See Methods for further discussion.

  6. Extended Data Fig. 6 Forward predictions of the neural networks from each realization of the training dataset, incorporating grid cells down to 5 km beyond the depth of each slip distribution.

    Each panel is analogous to Fig. 2h, but uses one of ten distinct neural networks trained on one of ten different realizations of the training dataset (Supplementary Table 2). See Methods for further discussion.

  7. Extended Data Table 1 Comparison of physical metrics to the neural network for an idealized case
  8. Extended Data Table 2 Summary of results for ten realizations of the training and test datasets

Supplementary information

  1. Supplementary Table 1

    This file contains a list of slip distributions and references randomly assigned to testing and training data sets (from http://equake-rc.info/SRCMOD/references/). Excel spreadsheet.

  2. Supplementary Table 2

    This file contains a list of slip distributions randomly assigned to testing and training data set realizations (listed by the SRCMOD filename identifiers; for complete references please see Supplementary Information Table 1). Excel spreadsheet.

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https://doi.org/10.1038/s41586-018-0438-y

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