Real-time discrimination of earthquake foreshocks and aftershocks


Immediately after a large earthquake, the main question asked by the public and decision-makers is whether it was the mainshock or a foreshock to an even stronger event yet to come. So far, scientists can only offer empirical evidence from statistical compilations of past sequences, arguing that normally the aftershock sequence will decay gradually whereas the occurrence of a forthcoming larger event has a probability of a few per cent. Here we analyse the average size distribution of aftershocks of the recent Amatrice–Norcia and Kumamoto earthquake sequences, and we suggest that in many cases it may be possible to discriminate whether an ongoing sequence represents a decaying aftershock sequence or foreshocks to an upcoming large event. We propose a simple traffic light classification to assess in real time the level of concern about a subsequent larger event and test it against 58 sequences, achieving a classification accuracy of 95 per cent.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Time–space analysis of b values for the Amatrice–Norcia sequence.
Fig. 2: Time–space analysis of b values for the Kumamoto sequence.
Fig. 3: Frequency–magnitude distributions for the Tohoku case study.
Fig. 4: The foreshock traffic light system.
Fig. 5: Performance analysis of the proposed foreshock traffic light system.

Data and code availability

The datasets generated and analysed during the current study, as well as the Matlab codes written for the analysis, are available at


  1. 1.

    Jordan, T. H. et al. Operational earthquake forecasting state of knowledge and guidelines for utilization. Ann. Geophys. 54, 315–391 (2011).

    Google Scholar 

  2. 2.

    Lippiello, E., Giacco, F., Marzocchi, W., Godano, C. & de Arcangelis, L. Statistical features of foreshocks in instrumental and ETAS catalogs. Pure Appl. Geophys. 174, 1679–1697 (2017).

    ADS  Google Scholar 

  3. 3.

    Reasenberg, P. A. & Jones, L. M. California aftershock hazard forecast. Science 247, 345–346 (1990).

    ADS  CAS  Google Scholar 

  4. 4.

    Roeloffs, E. & Goltz, J. The California earthquake advisory plan: a history. Seismol. Res. Lett. 88, 784–797 (2017).

    Google Scholar 

  5. 5.

    Field, E. H. et al. The potential uses of operational earthquake forecasting. Seismol. Res. Lett. 87, 313–322 (2016).

    Google Scholar 

  6. 6.

    Zechar, J. D., Marzocchi, W. & Wiemer, S. Operational earthquake forecasting in Europe: progress, despite challenges. Bull. Earthquake Eng. 14, 2459–2469 (2016).

    Google Scholar 

  7. 7.

    Ogata, Y. Statistical models for earthquake occurrences and residual analysis for point processes. J. Am. Stat. Assoc. 83, 9–27 (1988).

    Google Scholar 

  8. 8.

    Ogata, Y. Space-time point-process models for earthquake occurrences. Ann. Inst. Stat. Math. 50, 379–402 (1998).

    MATH  Google Scholar 

  9. 9.

    Gerstenberger, M. C., Wiemer, S., Jones, L. M. & Reasenberg, P. A. Real-time forecasts of tomorrow’s earthquakes in California. Nature 435, 328–331 (2005).

    ADS  CAS  Google Scholar 

  10. 10.

    Parsons, T. et al. Stress-based aftershock forecasts made within 24 h postmain shock: expected north San Francisco Bay area seismicity changes after the 2014 M = 6.0 West Napa earthquake. Geophys. Res. Lett. 41, 8792–8799 (2014).

    ADS  Google Scholar 

  11. 11.

    Stein, R. Earthquake conversations. Sci. Am. 288, 72–79 (2003).

    ADS  Google Scholar 

  12. 12.

    Woessner, J. et al. A retrospective comparative forecast test on the 1992 Landers sequence. J. Geophys. Res. 116, B05305 (2011).

    ADS  Google Scholar 

  13. 13.

    van Stiphout, T., Wiemer, S. & Marzocchi, W. Are short-term evacuations warranted? Case of the 2009 L’Aquila earthquake. Geophys. Res. Lett. 37, L06306 (2010).

    ADS  Google Scholar 

  14. 14.

    Gulia, L., Tormann, T., Wiemer, S., Herrmann, M. & Seif, S. Short-term probabilistic earthquake risk assessment considering time-dependent b values. Geophys. Res. Lett. 43, 1100–1108 (2016).

    ADS  Google Scholar 

  15. 15.

    Brodsky, E. E. & Lay T. Recognizing foreshocks from the 1 April 2014 Chile earthquake. Science 344, 700–702 (2014).

    ADS  CAS  Google Scholar 

  16. 16.

    Bouchon, M., Durand, V., Marsan, D., Karabulut, H. & Schmittbuhl, J. The long precursory phase of most large interplate earthquakes. Nat. Geosci. 6, 299–302 (2013).

    ADS  CAS  Google Scholar 

  17. 17.

    Ellsworth, W. L. & Bulut, F. Nucleation of the 1999 Izmit earthquake by a triggered cascade of foreshocks. Nat. Geosci. 11, 531–535 (2018).

    ADS  CAS  Google Scholar 

  18. 18.

    Gutenberg, B. & Richter, C. F. Frequency of earthquakes in California. Bull. Seismol. Soc. Am. 34, 185–188 (1944).

    Google Scholar 

  19. 19.

    Ishimoto, M. & Iida, I. Observations of earthquakes registered with the microseismograph constructed recently. Bull. Earthquake Res. Inst. Univ. Tokyo 17, 443–478 (1936).

    Google Scholar 

  20. 20.

    Goebel, T. H. W., Schorlemmer, D., Becker, T. W., Dresen, G. & Sammis, C. G. Acoustic emissions document stress changes over many seismic cycles in stick-slip experiments. Geophys. Res. Lett. 40, 2049–2054 (2013).

    ADS  Google Scholar 

  21. 21.

    Amitrano, D. Brittle-ductile transition and associated seismicity: Experimental and numerical studies and relationship with the b value. J. Geophys. Res. 108, 1–15 (2003).

    Google Scholar 

  22. 22.

    Scholz, C. H. The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes. Bull. Seismol. Soc. Am. 58, 399–415 (1968).

    Google Scholar 

  23. 23.

    Schorlemmer, D., Wiemer, S. & Wyss, M. Variations in earthquake-size distribution across different stress regimes. Nature 437, 539–542 (2005).

    ADS  CAS  Google Scholar 

  24. 24.

    Gulia, L. et al. The effect of a mainshock on the size distribution of the aftershocks. Geophys. Res. Lett. 45, 13277–13287 (2005).

    ADS  Google Scholar 

  25. 25.

    Helmstetter, A. Comparison of short-term and time-independent earthquake forecast models for southern California. Bull. Seismol. Soc. Am. 96, 90–106 (2006).

    Google Scholar 

  26. 26.

    Vannucci, G., Gasperini, P., Lolli, B. & Gulia, L. Fast characterization of sources of recent Italian earthquakes from macroseismic intensities. Tectonophysics 750, 70–92 (2019).

    ADS  Google Scholar 

  27. 27.

    Gasperini, P., Lolli, B. & Vannucci, G. Empirical calibration of local magnitude data sets versus moment magnitude in Italy. Bull. Seismol. Soc. Am. 103, 2227–2246 (2013).

    Google Scholar 

  28. 28.

    Wiemer, S. & Wyss, M. Mapping the frequency-magnitude distribution in asperities: an improved technique to calculate recurrence times? J. Geophys. Res. 102, 15115–15128 (1997).

    ADS  Google Scholar 

  29. 29.

    Japan Meteorological Agency. JMA catalogue

  30. 30.

    Earthquake Research Committee. Evaluation of the 2016 Kumamoto Earthquakes (ERC, 2016);

  31. 31.

    Nanjo, K.Z. & Yoshida, A. Anomalous decrease in relatively large shocks and increase in the p and b values preceding the April 16, 2016, M 7.3 earthquake in Kumamoto, Japan. EPS 69, 13 (2017).

    Google Scholar 

  32. 32.

    Omi, T. et al. Implementation of a real-time system for automatic aftershock forecasting in Japan. Seismol. Res. Lett. 90, 242–250 (2019).

    Google Scholar 

  33. 33.

    Tormann, T., Enescu, B., Woessner, J. & Wiemer, S. Randomness of megathrust earthquakes implied by rapid stress recovery after the Japan earthquake. Nat. Geosci. 8, 152–158 (2015).

    ADS  CAS  Google Scholar 

  34. 34.

    Gomber, J. Unsettled earthquake nucleation. Nat. Geosci. 11, 463–464 (2018).

    ADS  Google Scholar 

  35. 35.

    Mignan, A. The debate on the prognostic value of earthquake foreshocks: a meta-analysis. Sci. Rep. 4, 4099 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  36. 36.

    Tape, C. et al. Earthquake nucleation and fault slip complexity in the lower crust of central Alaska. Nat. Geosci. 11, 536–541 (2018); author correction 11, 615 (2018).

    ADS  CAS  Google Scholar 

  37. 37.

    Okada, Y. Internal deformation due to shear and tensile faults in a half-space. Bull. Seismol. Soc. Am. 82, 1018–1040 (1992).

    Google Scholar 

  38. 38.

    European Commission. A Strategy for Europe on Nutrition, Overweight and Obesity Related Health Issues. White Paper COM (2007) 279 (European Commission, 2007);

  39. 39.

    Department of Health. Information for a Healthy New York: Asthma Action Plan (New York State Department of Health, 2002);

  40. 40.

    Bommer, J. J. et al. Control of hazard due to seismicity induced by a hot fractured rock geothermal project. Eng. Geol. 83, 287–306 (2006).

    Google Scholar 

  41. 41.

    Mignan, A., Broccardo, M., Wiemer, S. & Giardini, D. Induced seismicity closed-form traffic light system for actuarial decision-making during deep fluid injections. Sci. Rep. 7, 13607 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  42. 42.

    Li, Z. F., Meier, M. A., Hauksson, E., Zhan, Z. W. & Andrews, J. Machine learning seismic wave discrimination: application to earthquake early warning. Geophys. Res. Lett. 45, 4773–4779 (2018).

    ADS  Google Scholar 

  43. 43.

    Shelly, D. R. A 15 year catalog of more than 1 million low-frequency earthquakes: tracking tremor and slip along the deep San Andreas Fault. J. Geophys. Res. Solid Earth 122, 3739–3753 (2017).

    ADS  Google Scholar 

  44. 44.

    Jordan, T. H. Earthquake predictability, brick by brick. Seismol. Res. Lett. 77, 3–6 (2006).

    Google Scholar 

  45. 45.

    Schorlemmer, D. et al. The collaboratory for the study of earthquake predictability: achievements and priorities. Seismol. Res. Lett. 89, 1305–1313 (2018).

    Google Scholar 

  46. 46.

    Wells, D. L. & Coppersmith, K. J. New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull. Seismol. Soc. Am. 84, 974–1002 (1994).

    Google Scholar 

  47. 47.

    Shi, Y. & Bolt, B. A. The standard error of the magnitude-frequency b value. Bull. Seismol. Soc. Am. 72, 1677–1687 (1982).

    Google Scholar 

  48. 48.

    Dziewonski, A. M., Chou, T. A. & Woodhouse, J. H. Determination of earthquake source parameters from waveform data for studies of global and regional seismicity. J. Geophys. Res. 86, 2825–2852 (1981).

    ADS  Google Scholar 

  49. 49.

    Ekström, G., Nettles, M. & Dziewoński, A. M. The global CMT project 2004–2010: centroid-moment tensors for 13,017 earthquakes. Phys. Earth Planet. Inter. 200–201, 1–9 (2012).

    ADS  Google Scholar 

  50. 50.

    Wiemer, S. & Wyss, M. Minimum magnitude of completeness in earthquake catalogs: examples from Alaska, the Western United States, and Japan. Bull. Seismol. Soc. Am. 90, 859–869 (2000).

    Google Scholar 

  51. 51.

    Woessner, J. & Wiemer, S. Assessing the quality of earthquake catalogues: estimating the magnitude of completeness and its uncertainty. Bull. Seismol. Soc. Am. 95, 684–698 (2005).

    Google Scholar 

  52. 52.

    Tormann, T., Wiemer, S. & Mignan, A. Systematic survey of high-resolution b value imaging along Californian faults: inference on asperities. J. Geophys. Res. 119, 2029–2054 (2014).

    ADS  Google Scholar 

Download references


The figures were produced with the Generic Mapping Tool ( b-value maps were created with ZMAP (

Author information




L.G. and S.W. conceived the analysis method and wrote the paper. L.G. performed the data analysis and created the figures.

Corresponding author

Correspondence to Laura Gulia.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Source data

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gulia, L., Wiemer, S. Real-time discrimination of earthquake foreshocks and aftershocks. Nature 574, 193–199 (2019).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing