Adaptive Smoothing of Seismicity in Time, Space, and Magnitude for Time-Dependent Earthquake Forecasts for California

Agnes Helmstetter*, Maximilian J Werner

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

19 Citations (Scopus)
429 Downloads (Pure)


We present new methods for short-term earthquake forecasting that employ space, time, and magnitude kernels to smooth seismicity. These methods are purely statistical and rely on very few assumptions about seismicity. In particular, we do not use Omori-Utsu law, and only one of our two new models assumes a Gutenberg-Richter law to model the magnitude distribution; the second model estimates the magnitude distribution nonparametrically with kernels. We employ adaptive kernels of variable bandwidths to estimate seismicity in space, time, and magnitude bins. To project rates over short time scales into the future, we simply assume persistence, that is, a constant rate over short time windows. The resulting forecasts from the two new kernel models are compared with those of the epidemic-type aftershock sequence (ETAS) model generated by Werner et al. (2011). Although our new methods are simpler and require fewer parameters than ETAS, the obtained probability gains are surprisingly close. Nonetheless, ETAS performs significantly better in most comparisons, and the kernel model with a Gutenberg-Richter law attains larger gains than the kernel model that nonparametrically estimates the magnitude distribution. Finally, we show that combining ETAS and kernel model forecasts, by simply averaging the expected rate in each bin, can provide greater predictive skill than ETAS or the kernel models can achieve individually.

Original languageEnglish
Pages (from-to)809-822
Number of pages14
JournalBulletin of the Seismological Society of America
Issue number2
Early online date18 Feb 2014
Publication statusPublished - Apr 2014


  • Southern California
  • Short-term
  • Likelihood Model
  • Point-processes
  • Long-term
  • Law
  • Occurrences
  • Estimators

Cite this