Quantifying the M8 algorithm: model, forecast, and evaluation.

We develop procedures for evaluating the efficacy of the M8 algorithm and producing probability forecasts in both time and space. Our modelling method uses the Critical Series developed by Harte et al. in 2003 as a predictor variable in a logistic regression. The M8 algorithm calculates seven time series, and the Critical Series embodies the nonlinear rules for combining the behaviour of these seven time series. The M8 algorithm is typically evaluated in (spatial) circles of quite large radius. Our implementation of this has many large overlapping circles covering New Zealand. This raises both practical and statistical problems. From a practical perspective, we really want probability forecasts within relatively small non-overlapping synoptic cells. Further, statistical evaluation of the overlapping circles approach is complicated by the lack of independence. In this paper, we develop both the overlapping circle and synoptic forecasting methods and statistical tests for their evaluation. We then compare results of the two approaches. Although the results indicate a significant relationship between the M8 Critical Series and numbers of large earthquake events, the forecasting success may be largely due to their dependence on slow variations in deep activity, which might be better examined directly as a possible source of predictive information. [ABSTRACT FROM AUTHOR]