# B04 – Assimilating data with different degrees of uncertainty into statistical models for earthquake occurrence

## Objectives

In this project, we will focus on the detection and modelling of gradual and rapid changes in earthquake activity. From the seismological point of view, this topic attracts increasing attention because of induced seismicity related to man-made actions (fracking, geothermal projects and others). So far, changes in seismic activity have been detected using simple methods based on sliding windows, or instantaneous jumps of the intensity in a homogeneous Poisson process are assumed. The self-exciting nature of earthquakes is, however, largely ignored in this context. This means in particular that any kind of spatiotemporal earthquake clustering, e.g. aftershocks is not taken into account. Since large parts of earthquake catalogs are associated with clusters, this can be a serious issue. For this reason, we will consider the modelling framework GP-ETAS (Gauss Process - Epidemic Type Aftershock Sequences model) developed in the first funding period of the CRC in close collaboration with project A06 and implement possible changes in the ETAS parameters. This will include single or multiple change points in time, but also gradual changes. Because man-made activities in particular regions sometimes lead to a seismic activation in adjacent areas, it will also be interesting to study the evolution of spatial seismicity patterns.

## Preprints

Ba, Y., de Wiljes, J., Oliver, D.S., and Reich, S. (2021).

*Randomized maximum likelihood based posterior sampling*. arXiv:2101.03612Holschneider, M., Ferrat, K., Zöller, G., Molkenthin, C., and Hainzl, S. (2020).

*Richter b-value maps from local moments of seismicity*. arXiv:2010.12298Molkenthin, C., Donner, C., Reich, S., Zöller, G., Hainzl, S., Holschneider, M. and Opper, M. (2020).

*GP-ETAS: Semiparametric Bayesian inference for the spatio-temporal Epidemic Type Aftershock Sequence model*. arXiv:2005.12857Nuesken, 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

## Publications

Ba, Y., de Wiljes, J., Oliver, D.S., and Reich, S. (2021).

*Randomized maximum likelihood based posterior sampling*, Computational Geosciences, https://doi.org/10.1007/s10596-021-10100-y arXiv:2101.03612Reich, 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:1911.10832Pathiraja, 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.2019019Shcherbakov, 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/s41467-019-11958-4Somogyvári, M. and Reich, S. (2019).

*Convergence tests for transdimensional Markov chains in geoscience imaging,*Math Geosci, 2019. doi: 10.1007/s11004-019-09811-xLontsi, 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: 1907.04606Salamat, 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/s00024-019-02141-3Fiedler, 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: 10.1785/0120180091Salamat, 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/s10950-018-9780-7Zöller, 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: 10.1029/2017JB015099Fiedler, 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