Utilising short-term and medium-term forecasting models for earthquake hazard estimation in the wake of the Canterbury earthquakes

Executive summary

Following the damaging Canterbury earthquake sequence, which commenced with the September 2010 M7.1 Darfield earthquake, a hybrid operational earthquake forecasting model is being used for decision-making on building standards and urban planning for the rebuilding of Christchurch city. The model estimates occurrence probabilities of magnitude M ≥ 5.0 for the Canterbury region for each of the next 50 years. It combines short-term, medium-term and long-term forecasting models. Short term models include the STEP (Short-Term Earthquake Probability) and ETAS (Epidemic-Type AfterShock) models, which incorporate the Utsu-Omori inverse power law for decay of aftershock activity. Medium-term models include two versions of the EEPAS (Every Earthquake a Precursor According to Scale) model with different weighting strategies. These are based on the precursory scale increase phenomenon – an increase in the rate of minor earthquake activity which typically precedes major earthquakes – and associated predictive relations for the magnitude, precursor time and precursor area. The long-term models include several different smoothed seismicity models, some designed to forecast main shocks only and others to forecast all earthquakes, including aftershocks. The weight accorded to each individual model in the operational hybrid (the “EE” hybrid model) was determined by an expert elicitation process.

Another hybrid model (the “AVMAX” hybrid model) involving only one model from each class (long-term, medium-term, and short-term) was used prior to the expert elicitation process. For both hybrid models, the annual rate of earthquake occurrence in a particular spatial cell is defined as the maximum of a long-term rate and a time-varying rate. The difference is that in the EE model a weighted average of more individual models is used to compute the longterm and time-varying rates.
In this study we test the individual and hybrid models by comparing their performance over 26 years in the whole New Zealand region (the period during which the earthquake catalogue is adequate for this purpose). We also estimate optimal hybrid model combinations over the same period. Accordingly, the individual models and hybrid models have been 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 ranging from zero up to 25 years. The number of target earthquakes decreases as the time-lag increases, from 303 at a time-lag of zero down to 19 at a time-lag of 25 years.

We report on the performance of the individual and hybrid models for each time-lag, using two standard statistical tests adopted by the Collaboratory for the Study of Earthquake Predictability (CSEP): the N-test, which compares the observed number of earthquakes with the number forecast by the model, and the T-test, which measures the information gain per earthquake (IGPE) of one model over another.

The N-tests show that all models tend to under-predict the number of earthquakes in the test period. This is shown to be mainly due to the unusually large number of earthquakes with M> 4.95 that have occurred in the test region since the M7.8 Dusky Sound earthquake of 15 July 2009, including the Canterbury earthquakes. The T-tests show that both hybrid models are more informative than most of the individual models for all time-lags. Using data from the full 26-year test period, the IGPE relative to a stationary and spatially uniform reference model (a model of “least information”) drops off steadily as the time-lag increases, to become zero at a time-lag of about 20 years. When the unusual period since the Dusky Sound earthquake is removed from the tests, the hybrid models both show a significant positive IGPE over the model of least information at all time-lags, but do not outperform all the individual long-term models at long time-lags. The test results are therefore seen to be sensitive to unusual features of the test catalogue, and a much longer catalogue would be needed to obtain robust results.

An optimal hybrid model with the same general form as the EE and AVMAX hybrid models is computed for each time-lag from the 26-year test period. In the optimal hybrid model, the time-varying component is dominated by the medium-term models, with hardly any contribution from the short-term models for time-lags up to 12 years. The short-term and medium-term model rates diminish with increasing time-lag, with the result that the time-varying component as a whole has hardly any impact on the optimal hybrid model for timelags greater than 12 years.

For short time-lags up to one year, the long-term component of the optimal hybrid model is dominated by a smoothed seismicity model designed to forecast main shocks only – the National Seismic Hazard Model Background model (NSHMBG). For intermediate time-lags it is dominated by a smoothed seismicity model designed to forecast all earthquakes, computed from the locations of earthquakes with magnitude M > 4.95 since 1950 (PPE). For long time-lags greater than 17 years, the long-term rate is dominated by a similar model computed from the locations of earthquakes with M > 5.95 between 1840 and 1950 in the historical and early instrumental catalogue (PPE1950). At long time-lags the optimal hybrid model is considerably more informative than the EE Hybrid model, with an IGPE close to 1.0 for a time-lag of 25 years. This is because the PPE1950 model is the best individual model for forecasting the Canterbury earthquakes at long time-lags. When the years including the Canterbury earthquakes are removed from the test data set, the contribution of the PPE1950 model to the optimal long-term model vanishes and PPE dominates the optimal model for long, as well as intermediate, time-lags. For this reduced data set, the IGPE of the optimal hybrid model over the EE hybrid model is only moderate, in the range 0.2-0.3, for all timelags.

A three-component hybrid model, with cell rates defined as the maximum of long-term, medium-term and short term rates, was also optimised for each time-lag from the 26-year test period. This model was found to be less informative than the two-component model for zero time-lag, but slightly more informative than the two-component at longer time-lags.

The Canterbury earthquakes are an unusual feature in New Zealand seismicity. Never before in the instrumental period has a large earthquake occurred in a region of such low seismicity and low crustal deformation rate as the Darfield earthquake. Although an optimal hybrid model for New Zealand as a whole would have a higher contribution to the time-varying component from medium-term models, the same does not necessarily apply to the Canterbury region. Tests of one-day, three-month and five-year models installed in the New Zealand earthquake forecast testing centre show that, after the Darfield earthquake, the Canterbury earthquakes are well described by short-term one-day models. The 1891 Great Nobi earthquake in Japan, which like the Darfield earthquake was located in a lower seismicity zone slightly away from a plate boundary, had 100 years of aftershocks decaying regularly according to the Omori-Utsu law. This aftershock decay, captured by the short-term models, is the most predictable component of future Canterbury seismicity. The medium term component is less predictable, because the precursor time parameters are not well established for low seismicity regions. There is considerable variation in the estimates from the individual long-term models contributing to the EE Hybrid model. But, based on the tests carried out here, the EE hybrid, which gives appreciable weight to four different long-term models, is likely to outperform most of the individual models in the next 50 years.