Regional Earthquake Likelihood Models II: Information Gains of Multiplicative Hybrids

The Regional Earthquake Likelihood Models experiment in California tested the performance of earthquake likelihood models over a five-year period. First-order analysis showed a smoothed-seismicity model by Helmstetter et al. (2007) to be the best model. We construct optimal multiplicative hybrids involving the best individual model as a baseline and one or more conjugate models. Conjugate models are transformed using an order-preserving function. Two parameters for each conjugate model and an overall normalizing constant are fitted to optimize the hybrid model. Many two-model hybrids have an appreciable information gain (log probability gain) per earthquake relative to the best individual model. For the whole of California, the Bird and Liu (2007) Neokinema and Holliday et al. (2007) pattern informatics (PI) models both give gains close to 0.25. For southern California, the Shen et al. (2007) geodetic model gives a gain of more than 0.5, and several others give gains of about 0.2. The best three-model hybrid for the whole region has the Neokinema and PI models as conjugates. The best three-model hybrid for southern California has the Shen et al. (2007) and PI models as conjugates. The information gains of the best multiplicative hybrids are greater than those of additive hybrids constructed from the same set of models. The gains tend to be larger when the contributing models involve markedly different concepts or data. These results 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 forecasting models at all timescales.