Emergent Mind

Modeling the Asymptotic Behavior of Higher-Order Aftershocks with Deep Learning

Published Jan 11, 2024 in physics.geo-ph


Aftershocks of aftershocks - and their aftershock cascades - substantially contribute to the increased seismicity rate and the associated elevated seismic hazard after the occurrence of a large earthquake. Current state-of-the-art earthquake forecasting models therefore describe earthquake occurrence using self-exciting point processes, where events can recursively trigger more events according to empirical laws. To estimate earthquake probabilities within future time horizons of interest, a large number of possible realizations of a process are simulated, which is typically associated with long computation times that increase with the desired resolution of the forecast in space, time, or magnitude range. We here propose a machine learning approach to estimate the temporal evolution of the rate of higher-order aftershocks. For this, we train a deep neural network to predict the output of the simulation-based approach, given a parametric description of the rate of direct aftershocks. A comparison of the two approaches reveals that they perform very similarly in describing synthetic datasets generated with the simulation-based approach. Our method has two major benefits over the traditional approach. It is faster by several orders of magnitude, and it is not susceptible to being influenced by the presence or absence of individual `extreme' realizations of the process, and thus enables accurate earthquake forecasting in near-real-time.

We're not able to analyze this paper right now due to high demand.

Please check back later (sorry!).

Generate a detailed summary of this paper with a premium account.

We ran into a problem analyzing this paper.

Please try again later (sorry!).

Get summaries of trending AI papers delivered straight to your inbox

Unsubscribe anytime.

  1. TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. 2015. Software available from tensorflow.org.
  2. Pseudo-prospective testing of 5-year earthquake forecasts for California using inlabru // Natural Hazards and Earth System Sciences. 2022. 22, 10. 3231–3246.
  3. Chollet François, others . Keras. 2015.
  4. Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)
  5. Using deep learning for flexible and scalable earthquake forecasting // Geophysical Research Letters. 2023. 50, 17. e2023GL103909.
  6. Enabling large-scale viscoelastic calculations via neural network acceleration // Geophysical Research Letters. 2017. 44, 6. 2662–2669.
  7. Prospective and Retrospective Evaluation of the US Geological Survey Public Aftershock Forecast for the 2019–2021 Southwest Puerto Rico Earthquake and Aftershocks // Seismological Society of America. 2022. 93, 2A. 620–640.
  8. Data-driven synthesis of broadband earthquake ground motions using artificial intelligence // Bulletin of the Seismological Society of America. 2022. 112, 4. 1979–1996.
  9. Glorot Xavier, Bengio Yoshua. Understanding the difficulty of training deep feedforward neural networks // Proceedings of the thirteenth international conference on artificial intelligence and statistics. 2010. 249–256.
  10. Gutenberg Beno, Richter Charles F. Frequency of earthquakes in California // Bulletin of the Seismological Society of America. 1944. 34, 4. 185–188.
  11. Harte DS. Log-likelihood of earthquake models: evaluation of models and forecasts // Geophysical Journal International. 2015. 201, 2. 711–723.
  12. Harte DS. Probability distribution of forecasts based on the ETAS model // Geophysical Journal International. 2017. 210, 1. 90–104.
  13. Harte David, Vere-Jones David. The entropy score and its uses in earthquake forecasting // Pure and Applied Geophysics. 2005. 162, 6. 1229–1253.
  14. Helmstetter Agnes, Sornette Didier. Importance of direct and indirect triggered seismicity in the ETAS model of seismicity // Geophysical Research Letters. 2003. 30, 11.
  15. Building high accuracy emulators for scientific simulations with deep neural architecture search // Machine Learning: Science and Technology. 2021. 3, 1. 015013.
  16. Learning skillful medium-range global weather forecasting // Science. 2023. 0, 0. eadi2336.
  17. Llenos Andrea L, Michael Andrew J. Ensembles of ETAS Models Provide Optimal Operational Earthquake Forecasting During Swarms: Insights from the 2015 San Ramon, California SwarmEnsembles of ETAS Models Provide Optimal Operational Earthquake Forecasting During Swarms // Bulletin of the Seismological Society of America. 2019. 109, 6. 2145–2158.
  18. Dying ReLU and Initialization: Theory and Numerical Examples
  19. Lundberg Scott M, Lee Su-In. A unified approach to interpreting model predictions // Advances in neural information processing systems. 2017. 30.
  20. Operational Earthquake Forecasting during the 2019 Ridgecrest, California, Earthquake Sequence with the UCERF3-ETAS Model // Seismological Research Letters. 2020. 91, 3. 1567–1578.
  21. Developing, Testing, and Communicating Earthquake Forecasts: Current Practices and an Elicitation of Expert Recommendations. 2024.
  22. The Effect of Declustering on the Size Distribution of Mainshocks // Seismological Research Letters. 02 2021.
  23. lmizrahi/etas. I 2023.
  24. Deep learning for fast simulation of seismic waves in complex media // Solid Earth. 2020. 11, 4. 1527–1549.
  25. Nair Vinod, Hinton Geoffrey E. Rectified linear units improve restricted boltzmann machines // Proceedings of the 27th international conference on machine learning (ICML-10). 2010. 807–814.
  26. Global models for short-term earthquake forecasting and predictive skill assessment // The European Physical Journal Special Topics. 2021. 230, 1. 425–449.
  27. Forecasting the Full Distribution of Earthquake Numbers Is Fair, Robust, and Better // Seismological Research Letters. 2019a. 90, 4. 1650–1659.
  28. Forecasting the rates of future aftershocks of all generations is essential to develop better earthquake forecast models // Journal of Geophysical Research: Solid Earth. 2019b. 124, 8. 8404–8425.
  29. Ogata Yosihiko. Statistical models for earthquake occurrences and residual analysis for point processes // Journal of the American Statistical association. 1988. 83, 401. 9–27.
  30. Ogata Yosihiko. Space-time point-process models for earthquake occurrences // Annals of the Institute of Statistical Mathematics. 1998. 50, 2. 379–402.
  31. Reasenberg Paul A, Jones Lucile M. Earthquake hazard after a mainshock in California // Science. 1989. 243, 4895. 1173–1176.
  32. Efficient testing of earthquake forecasting models // Acta Geophysica. 2011. 59, 4. 728–747.
  33. ” Why should I trust you?” Explaining the predictions of any classifier // Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. 2016. 1135–1144.
  34. Saichev A, Sornette Didier. Power law distribution of seismic rates: theory and data analysis // The European Physical Journal B-Condensed Matter and Complex Systems. 2006. 49, 3. 377–401.
  35. pyCSEP: A Python Toolkit For Earthquake Forecast Developers // Journal of Open Source Software. 2022. 7, 69.
  36. Dropout: a simple way to prevent neural networks from overfitting // The journal of machine learning research. 2014. 15, 1. 1929–1958.
  37. Forecasting the 2016-2017 Central Apennines Earthquake Sequence with a Neural Point Process // Earth’s Future. 2023.
  38. Prospective and retrospective evaluation of five-year earthquake forecast models for California // Geophysical Journal International. 2017. 211, 1. 239–251.
  39. The Collaboratory for the Study of Earthquake Predictability perspective on computational earthquake science // Concurrency and Computation: Practice and Experience. 2010. 22, 12. 1836–1847.
  40. A neural encoder for earthquake rate forecasting // Scientific Reports. 2023. 13, 1. 12350.

Show All 40

Test Your Knowledge

You answered out of questions correctly.

Well done!