Retrospective tests of hybrid operational earthquake forecasting models for Canterbury

The Canterbury, NewZealand, earthquake sequence, which began in September 2010, occurred in a region of low crustal deformation and previously low seismicity. Because, the ensuing seismicity in the region is likely to remain above previous levels for many years, a hybrid operational earthquake forecasting model for Canterbury was developed to inform decisions on building standards and urban planning for the rebuilding of Christchurch. The model estimates occurrence probabilities for magnitudes M >= 5.0 in the Canterbury region for each of the next 50 yr. It combines two short-term, two medium-term and four long-term forecasting models. The weight accorded to each individual model in the operational hybrid was determined by an expert elicitation process. A retrospective test of the operational hybrid model and of an earlier informally developed hybrid model in the whole New Zealand region has been carried out. The individual and hybrid models were installed in the New Zealand Earthquake Forecast Testing Centre and used to make retrospective annual forecasts of earthquakes with magnitude M > 4.95 from 1986 on, for time-lags up to 25 yr. All models underpredict the number of earthquakes due to an abnormally large number of earthquakes in the testing period since 2008 compared to those in the learning period. However, the operational hybrid model is more informative than any of the individual time-varying models for nearly all time-lags. Its information gain relative to a reference model of least information decreases as the time-lag increases to become zero at a time-lag of about 20 yr. An optimal hybrid model with the same mathematical form as the operational hybrid model was computed for each time-lag from the 26-yr test period. The time-varying component of the optimal hybrid is dominated by the medium-term models for time-lags up to 12 yr and has hardly any impact on the optimal hybrid model for greater time-lags. The optimal hybrid model is considerably more informative than the operational hybrid model at long time-lags, but less so when the period of the Canterbury earthquakes is excluded from the tests. The results highlight the value of including medium-term models and a range of long-term models in operational forecasting. Based on the tests carried out here, the operational hybrid model is expected to outperform most of the individual models in the next 25 yr.