Regional earthquake likelihood models II: Information gains of multiplicative hybrids

David A. Rhoades, Matthew C. Gerstenberger, Annemarie Christophersen, Jeremy D. Zechar, Danijel Schorlemmer, Maximilian J. Werner, & Thomas H. Jordan

Published September 1, 2014, SCEC Contribution #1837

The Regional Earthquake Likelihood Models experiment in California tested the performance of a variety of earthquake likelihood models over a five-year period. First-order analysis by the Collaboratory for the Study of Earthquake Predictability showed a smoothed-seismicity model by Helmstetter et al. to be the best model, and a Bayesian analysis of additive hybrids showed that a probability-weighted linear combination of the models does not appreciably outperform the best individual model. A different picture emerges when multiplicative hybrids are considered. We construct optimal multiplicative hybrids involving the best individual model as a baseline and one or more conjugate models. The baseline model is not transformed in any way. Conjugate models are transformed using an order-preserving function applied to their total rate in each spatial cell. Two parameters for each conjugate model and an overall normalising constant are fitted to optimise the hybrid model. Many two-model hybrids have an appreciable information gain per earthquake, corrected for parameter-fitting and the number of target earthquakes, relative to the best individual model. For the whole of California, the Bird and Liu NeoKinema model and the Holliday et al. Pattern Informatics (PI) model both give gains close to 0.25. For southern California, the Shen et al. geodetic model gives a gain of more than 0.5, and the Ward geodetic, Ward combo, and Kagan et al. models give gains of about 0.2. The best three-model hybrid for the whole region has the Neokinema and PI models as conjugates and a gain of 0.35. The best three-model hybrid for southern California has the Shen et al. and PI models as conjugates and a gain of 0.79. It is observed that larger information gains are obtained when the contributing models involve markedly different concepts or data. The results from retrospective fitting need to be confirmed by further prospective tests. Multiplicative hybrids will be useful for assimilating other earthquake-related observations into forecasting models and for combining models from CSEP forecasting experiments at all time-scales.

Citation
Rhoades, D. A., Gerstenberger, M. C., Christophersen, A., Zechar, J. D., Schorlemmer, D., Werner, M. J., & Jordan, T. H. (2014). Regional earthquake likelihood models II: Information gains of multiplicative hybrids. Bulletin of the Seismological Society of America, 104(6), 2203-2215. doi: 10.1785/0120140035.

Related Projects & Working Groups
Collaboratory for the Study of Earthquake Predictability