1. Data assimilation - the collaborative research centre SFB1294
  2. Research
  3. Research Area B
  4. B04

B04 – Point process modelling of seismicity: deaggregation and model reduction

The state-of-the-art statistical tool for simulating earthquakes is the Epidemic Type Aftershock Sequences (ETAS) model, which is a point process of Hawkes type and has been extended in this project by the use of flexible Gaussian process (GP) modelling to the new GP-ETAS model. In the present form, GP-ETAS allows handling the complex likelihood function without any significant approximation at the cost that the sampling of the posterior function is numerically extremely expensive. Since we plan to implement GP-ETAS on a platform for daily operational forecasts, we aim to implement sparse sampling techniques for Bayesian inference without losing too much accuracy. In data-rich situations, we will test the replacement of the process prior with an appropriate proxy that does not depend on the number of observations and can be precomputed and the use of adaptive methods for the spatial resolution, e.g. in the context of triangulation. Furthermore, the covariance structure of the GP can be represented by a stochastic differential equation, which is then solved on the mesh. To this end more flexibility is gained and computational resources are optimized.
An important next step towards operational earthquake forecasting will be identifying the most important model aspects. It is shown that the forecasting power of GP-ETAS is superior to the frequently used benchmark model, e.g. a standard ETAS model with spatially smoothed background activity instead of a Gaussian process, and maximum likelihood estimated model parameters. However, it remains an open question why this is the case. Possible options include the good performance of the Gaussian process model for the background activity, the exact treatment of the likelihood function in GP-ETAS, the choice of the Bayesian priors, or the different ways of uncertainty assessment. To address this issue, it is fortunate that several models similar to GP-ETAS have been developed recently, e.g. using deep learning techniques for the Gaussian process , or “inlabru” where a decomposition of the likelihood function and a linearisation of the individual parts leads to an extremely efficient algorithm. Other studies use bootstrapping methods for uncertainty assessment. Deaggregation of model components, especially in the context of forecasts on different time scales, will ideally allow the identification of unnecessary elements and, finally, the design of a reduced model with optimal forecast performance. It will also enable us to test whether additional aspects such as considering data incompleteness or knowledge on physics [18, 19] and the assimilation of more available data can further improve the forecast power. In detail, we will consider temporal and spatial forecasts with appropriate metrics to evaluate the forecast power.
The final goal of the project will be the implementation of an optimized GP-ETAS version on the established platform CSEP (Collaboratory for the Study of Earthquake Predictability) running prospective tests of earthquake forecasts, and eventually its use for operational earthquake forecasting.

  • Holschneider, M., Ferrat, K., Zöller, G., Molkenthin, C., and Hainzl, S. (2020). Richter b-value maps from local moments of seismicity.  arXiv:2010.12298

  • Nuesken, N. and Reich, S. (2019). Note on Interacting Langevin diffusions: Gradient structure and ensemble Kalman sampler by Garbuno-Inigo, Hoffmann, Li and Stuart. arXiv:1908.10890

  • Hainzl, S., Dahm, T., and Tramelli, A. (2026): A deformation-driven earthquake interaction model for seismicity at Campi Flegrei, Communications Earth and Environment, Vol. 7, 244. doi:110.1038/s43247-026-03296-3

  • Maleki Asayesh, B., Hainzl, S., Tatar, M., Zöller, and M., Soltani Moghadam, S. (2026): Reservoir related seismicity changes around the Gotvand Dam (south west of Iran), Geophysical Journal International, Vol. 245 (1), ggag043. doi:10.1093/gji/ggag043

  • Hainzl, S., Dahm, T., and Zöller, G. (2025): Modeling induced seismicity in Groningen based on subcritical stressed faults, Geophysical Journal International, Vol. 241 (2), 840-851. doi:10.1093/gji/ggaf064

  • Maleki Asayesh, B., Hainzl, S., and Zöller, G. (2025): Improved aftershock forecasts using mainshock information in the framework of the ETAS model, Journal of Geophysical Research: Solid Earth, Vol. 130(2), e2024JB030287. doi:10.1029/2024jb030287

  • Grimm, C., Hainzl, S., Käser, M., and Küchenhoff, H. (2024): A New Statistical Perspective on Båth’s Law, Seismological Research Letters, Vol. 95(1), 488-498. doi:10.1785/0220230147

  • Molkenthin, C., Zöller, G., Hainzl, S., and Holschneider, M. (2024): Bayesian Earthquake Forecasting Using Gaussian Process Modeling: GP-ETAS Applications, Seismolgical Research Letters doi:10.1785/0220240170

  • Zöller, G. (2024): Recurrence times of large earthquakes: assimilating the effect of seismic coupling into a renewal model. Bulletin of the Seismological Society of America, Vol. 114(3),1754-1761. doi:10.1785/0120230257

  • Zöller, G. and Hainzl, S. (2023). Seismicity scenarios for the remaining operating period of the gas field in Groningen, Netherlands. Seismological Research Letters, Vol. 94(2A), 805-812. doi:10.1785/0220220308

  • Sharma, S., Hainzl, S., and Zöller, G. (2023): Seismicity parameter dependence on mainshock induced co-seismic stress. Geophysical Journal International, Vol. 135(1), 509-517. doi:10.1093/gji/ggad201

  • Maleki Asayesh,B., Hainzl, S., Zöller, G. (2023): Depth‐Dependent Aftershock Trigger Potential Revealed by 3D‐ETAS Modeling. Journal of Geophysical Research, Vol. 128(6), e2023JB026377. doi:10.1029/2023JB026377

  • Zöller, G. (2022): A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen gas field. Bulletin of the Seismological Society of America, Vol. 112(4), 1825-1831. doi:10.1785/0120210307

  • Molkenthin, C., Donner, C., Reich, S., Zöller, G., Hainzl, S., Holschneider, M. and Opper, M. (2022): GP-ETAS: Semiparametric Bayesian inference for the spatio-temporal Epidemic Type Aftershock Sequence model. Statistics and Computation, Vol. 32, 29. doi:10.1007/s11222-022-10085-3.

  • Ba, Y., de Wiljes, J., Oliver, D.S., and Reich, S. (2021). Randomized maximum likelihood based posterior sampling, Computational Geosciences. doi: 10.1007/s10596-021-10100-y, arXiv:2101.03612

  • Reich, S. and Weissmann, S. (2021). Fokker-Planck particle systems for Bayesian inference: Computational approaches, SIAM/ASA J. Uncertainty Quantification, 9(2), 446–482. doi: 10.1137/19M1303162;  arXiv:1911.10832

  • Pathiraja, S. and Reich, S. (2019). Discrete gradients for computational Bayesian inference. Journal of Computational Dynamics, 6, 385-400. arXiv:1901.06300; doi: 10.3934/jcd.2019019

  • Shcherbakov, R., Zhuang, J., Zöller, G. and Ogata, Y. (2019). Forecasting the magnitude of the largest expected earthquake, Nature Communications, 10, nr. 4051. doi: 10.1038/s41467-019-11958-4

  • Somogyvári, M. and Reich, S. (2019). Convergence tests for transdimensional Markov chains in geoscience imaging, Math Geosci, 2019. doi: 10.1007/s11004-019-09811-x

  • Lontsi, A. M., García-Jerez, A., Molina-Villegas, J. C., Sánchez-Sesma, F. J., Molkenthin, C., Ohrnberger, M., Krüger, F., Wang, R. and Fäh, D. (2019). A generalized theory for full microtremor horizontal-to-vertical [H/V(z, f)] spectral ratio interpretation in offshore and onshore environments, Geophysical Journal International, 218(2), 1276–1297. doi: 10.1093/gji/ggz223 arXiv: 1907.04606 

  • Salamat, M., Zöller, G. and Amini, M. (2019). Prediction of the Maximum Expected Earthquake Magnitude in Iran: From a Catalog with Varying Magnitude of Completeness and Uncertain Magnitudes, Pure and Applied Geophysics, 176 (8): 3425–3438. doi: 10.1007/s00024-019-02141-3

  • Fiedler, B., Hainzl, S., Zöller, G. and Holschneider, M. (2018). Detection of Gutenberg–Richter b-value changes in earthquake time series, Bulletin of the Seismological Society of America, 108(5A), 2778–2787. doi: 10.1785/0120180091

  • Salamat, M., Zöller, G. Zare, M. and Amini, M. (2018). The maximum expected earthquake magnitudes in different future time intervals of six seismotectonic zones of Iran and its surroundings, Journal of Seismology, 22, 1485–1498. doi: 10.1007/s10950-018-9780-7

  • Zöller, G. (2018): A Statistical Model for Earthquake Recurrence Based on the Assimilation of Paleoseismicity, Historic Seismicity, and Instrumental Seismicity. Journal of Geophysical Research: Solid Earth, 123, 4906-4921. doi: 10.1029/2017JB015099

  • Fiedler, B., Zöller, G., Holschneider, M. and Hainzl, S. (2018). Multiple Change‐Point Detection in Spatiotemporal Seismicity Data, Bulletin of the Seismological Society of America. 108 (3A): 1147-1159. doi: 10.1785/0120170236