EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

How ETAS Can Leverage Completeness of Modern Seismic Networks Without Renouncing Historical Data

Leila Mizrahi, Shyam Nandan, and Stefan Wiemer
Leila Mizrahi et al.
  • ETH Zurich, Swiss Seismological Service, Depratment of Earth Sciences, Switzerland (

The Epidemic-Type Aftershock Sequence (ETAS) model is often used to describe the spatio-temporal distribution of earthquakes. A fundamental requirement for parameter estimation of the ETAS model is the completeness of the catalog above a magnitude threshold mc. mc is known to vary with time for reasons such as gradual improvement of the seismic network, short term aftershock incompleteness and so on. For simplicity, nearly all applications of the ETAS model assume a global magnitude of completeness for the entirety of the training period. However, in order to be complete for the entire training period, the modeller is often forced to use very conservative estimates of mc, as a result completely ignoring abundant and high-quality data from the recent periods, which falls below the assumed mc. Alternatively, to benefit from the abundance of smaller magnitude earthquakes from the recent period in model training, the duration of the training period is often restricted. However, parameters estimated in this way may be dominated by one or two sequences and may not represent long term behavior.

We developed an alternative formulation of ETAS parameter inversion using expectation maximization, which accounts for a temporally variable magnitude of completeness. To test the adequacy of such a technique, we evaluate its forecasting power on an ETAS-simulated synthetic catalog, compared to the constant completeness magnitude ETAS base model. The synthetic dataset is designed to mimic the conditions in California, where mc since 1970 is estimated to be around 3.5, and where a general decreasing trend in the temporal evolution of mc can be observed. Both models are trained on the primary catalog with identical time horizon. While the reference model is solely based on information about earthquakes of magnitude 3.5 and above, our alternative represents completeness magnitude as a monotonically decreasing step-function, starting at 3.5 and assuming values down to 2.1 in more recent times.

To compare the two models, we issue forecasts by repeated probabilistic simulation of earthquake interaction scenarios, and evaluate those forecasts by assessing the likelihood of the actual occurrences under each of the alternatives. As a measure to quantify the difference in performance between the two models, we calculate the mean information gain due to model extension for different spatial resolutions, different temporal forecasting horizons, and different target magnitude ranges.

Preliminary results suggest that the parameter bias introduced by successive application of simulation and inversion decreases exponentially with an increasing fraction of data used in the inversion. It is therefore expected that also the forecasting power of such a model increases with the amount of data available, indicating substantial importance of the method for the future of probabilistic seismic hazard assessment.

How to cite: Mizrahi, L., Nandan, S., and Wiemer, S.: How ETAS Can Leverage Completeness of Modern Seismic Networks Without Renouncing Historical Data, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5827,, 2020

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Presentation version 1 – uploaded on 30 Apr 2020
  • CC1: Comment on EGU2020-5827, Angela Stallone, 04 May 2020

    In your application to Southern California catalog, you account for time-varying magnitude of completeness due to the improvement of the seismic network. How do you account for short-term aftershock incompleteness?

    • AC1: Reply to CC1, Leila Mizrahi, 04 May 2020

      We estimate time-varying completeness with a temporal resolution of one year, so we do not explicitly account for short-term aftershock incompleteness. However, in years with large events we do see an increase in mc.
      It is possible to apply the same method with a higher time-resolution for mc(t), accounting more specifically for short-term aftershock incompleteness. I think it would be interesting to see how the time-resolution of mc(t) influences the forecasting accuracy of the model!

      • CC2: Reply to AC1, Angela Stallone, 04 May 2020

        Thank you Leila! Indeed, it would be very interesting to see at which extent short-term incompleteness affects parameter estimation.