Retrospective Forecasting of M ≥ 4.0 Earthquakes in New Zealand

Abstract

We have applied a variation of the Epidemic Type Aftershock Sequence (ETAS) model, which is a stochastic triggering epidemic model incorporating short-term clustering, to data collected by the New Zealand Seismological Observatory-Wellington (Geonet) for forecasting earthquakes of moderate and large magnitude in the New Zealand region. The model uses earthquake data only, with no explicit use of tectonic, geologic, or geodetic information. In this epidemic-type model every earthquake is regarded, at the same time, as being triggered by previous events and triggering following earthquakes. A maximum likelihood estimate of the model parameters has been performed on the learning period from 1960 to 2005 for earthquakes of magnitude 4.0 and larger. Forecast verification procedures have been carried out in a forward-retrospective way on the January 2006 to April 2008 data set, making use of statistical tools as the log-likelihood ratio, the Relative Operating Characteristics (ROC) diagrams, the Molchan error diagrams, the probability gain and the R-score. These procedures show that the clustering epidemic model achieves a log-likelihood ratio per event of the order of some units, and a probability gain up to several hundred times larger than a time-independent spatially uniform random forecasting hypothesis. The results show also that a significant component of the probability gain is linked to the time-independent spatial distribution of the seismicity used in the model.