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

## Objectives

The project deals with the assimilation of data with different degrees of uncertainty into the space-time Epidemic Type Aftershock Sequences Model (ETAS). More specifically, we will use instrumental earthquake catalogs as well as historic and paleoseismic data. Because earthquake data are sparse and inhomogeneous, the frequently used maximum likelihood estimates need to be augmented by a quantification of uncertainties. Here we will follow a Bayesian approach that allows one to quantify the relevant parameters along with their uncertainties in space and time. The project starts with the design of appropriate prior distributions with a spatial correlation structure based on known geological features. In this context, the choice of the spatial discretization in relation to the data availability will be a key issue. The ETAS parameters will then be estimated using instrumental catalogs.

Here Markov chain Monte Carlo (MCMC) and sequential data assimilation techniques will be employed. Finally, pre-instrumental data (historic and paleo earthquakes) will also be considered. This requires an error model and its implementation into the ETAS framework. As a result, we will obtain a flexible tool that allows one to adjust the ETAS model to a wide range of seismic data sets and to continuously update the ETAS model through new incoming data. An important application is the forecast of future earthquake rates based on the earthquake history as performed by the *Collaboratory for the Study of Earthquake Predictability *(CSEP) and used in seismic hazard assessment. In particular, we will be able to add confidence bounds to the forecasted earthquake numbers and to evaluate to what degree existing forecasts and model comparisons are stable.

## Preprints

Reich, S. and Weissmann, S. (2019).

*Fokker-Planck particle systems for Bayesian inference: Computational approaches.*arXiv:1911.10832Nuesken, 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

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.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