Model-free aftershock forecasts constructed from similar sequences in the past

Nicholas J. van der Elst, & Morgan T. Page

Published August 15, 2017, SCEC Contribution #7836, 2017 SCEC Annual Meeting Poster #007

The basic premise behind aftershock forecasting is that sequences in the future will be similar to those in the past. Forecast models typically use empirically tuned parametric distributions to approximate past sequences, and project those distributions into the future to make a forecast. While parametric models do a good job of describing average outcomes, they are not explicitly designed to capture the full range of variability between sequences, and can suffer from over-tuning of the parameters. In particular, parametric forecasts may produce a high rate of “surprises” – sequences that land outside the forecast range.

Here we present a non-parametric forecast method that cuts out the parametric “middleman“ between training data and forecast. The method is based on finding past sequences that are similar to the target sequence, and evaluating their outcomes. We quantify similarity as the Poisson probability that the observed event count in a past sequence reflects the same underlying intensity as the observed event count in the target sequence. Event counts are defined in terms of differential magnitude relative to the mainshock. The forecast is then constructed from the distribution of past sequences outcomes, weighted by their similarity.

We compare the similarity forecast with the Reasenberg and Jones (RJ89) method, for a set of 2807 global aftershock sequences of M≥6 mainshocks. We implement a sequence-specific RJ89 forecast using a global average prior and Bayesian updating, but do not propagate epistemic uncertainty. The RJ89 forecast is somewhat more precise than the similarity forecast: 90% of observed sequences fall within a factor of two of the median RJ89 forecast value, whereas the fraction is 85% for the similarity forecast. However, the surprise rate is much higher for the RJ89 forecast; 10% of observed sequences fall in the upper 2.5% of the (Poissonian) forecast range. The surprise rate is less than 3% for the similarity forecast.

The similarity forecast may be useful to emergency managers and non-specialists when confidence or expertise in parametric forecasting may be lacking. The method makes over-tuning impossible, and minimizes the rate of surprises. At the least, this forecast constitutes a useful benchmark for more precisely tuned parametric forecasts.

Key Words
Statistical seismology, aftershock forecasting

Citation
van der Elst, N. J., & Page, M. T. (2017, 08). Model-free aftershock forecasts constructed from similar sequences in the past. Poster Presentation at 2017 SCEC Annual Meeting.

Related Projects & Working Groups
Earthquake Forecasting and Predictability (EFP)