Long-range Earthquake Forecasting with Every Earthquake a Precursor According to Scale

Scaling relations previously derived from examples of the precursory scale increase before major earthquakes show that the precursor is a long-term predictor of the time, magnitude, and location of the major earthquake. These relations are here taken as the basis of a stochastic forecasting model in which every earthquake is regarded as a precursor. The problem of identifying those earthquakes that are actually precursory is thus set aside, at the cost of limiting the strength of the resulting forecast. The contribution of an individual earthquake to the future distribution of hazard in time, magnitude and location is on a scale determined, through the scaling relations, by its magnitude. Provision is made for a contribution to be affected by other earthquakes close in time and location, e.g., an aftershock may be given low weight. Using the New Zealand catalogue, the model has been fitted to the forecasting of shallow earthquakes exceeding magnitude 5.75 over the period 1965–2000. It fits the data much better than a baseline Poisson model with a location distribution based on proximity to the epicenters of past earthquakes. Further, the model has been applied, with unchanged parameters, to the California region over the period 1975–2001. There also, it performs much better than the baseline model fitted to the same region over the period 1951–1974; the likelihood ratio is 1015 in favor of the present model. These results lend credence to the precursory scale increase phenomenon, and show that the scaling relations are pervasive in earthquake catalogues. The forecasting model provides a new baseline model against which future refinements, and other proposed models, can be tested. It may also prove to be useful in practice. Its applicability to other regions has still to be established.