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 10 15 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.

A space-time envelope of minor seismicity related to major shallow earthquakes is identified from observations of the long-term Precursory Scale Increase (Y) phenomenon, which quantifies the three-stage faulting model of seismogenesis. The envelope, which includes the source area of the major earthquake, is here demarcated for 47 earthquakes from four regions, with tectonic regimes ranging from subduction to continental collision and continental transform. The earthquakes range in magnitude from 5.8 to 8.2, and include the 24 most recent mainshocks of magnitude 6.4 and larger in the San Andreas system of California, the Hellenic Arc region of Greece, and the New Zealand region, together with the six most recent mainshocks of magnitude 7.4 and larger in the Pacific Arc region of Japan. Also included are the destructive earthquakes that occurred at Kobe, Japan (1995, magnitude 7.2), Izmit, Turkey (1999, magnitude 7.4), and W.Tottori, Japan (2000, magnitude 7.3). The space (A P ) in the space-time envelope is optimised with respect to the scale increase, while the time (T P ) is the interval between the onset of the scale increase and the occurrence of the earthquake. A strong correlation is found between the envelope A P T P and the magnitude of the earthquake; hence the conclusion that the set of precursory earthquakes contained in the envelope is intrinsic to the seismogenic process. Yet A P and T P are correlated only weakly with each other, suggesting that A P is affected by differences in statical conditions, such as geological structure and lithology, and T P by differences in dynamical conditions, such as plate velocity. Among other scaling relations, predictive regressions are found between, on the one hand, the magnitude level of the precursory seismicity, and on the other hand, both T P and the major earthquake magnitude. Hence the method, as here applied to retrospective analysis, is potentially adaptable to long-range forecasting of the place, time and magnitude of major earthquakes.

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For a long-term predictor from which a joint distribution of earthquake occurrence time and magnitude has been obtained, and also a record of past successes, false alarms and failures, Bayesian statistical methods yield predictive information of the kind needed as a basis for decision-making on precautionary measures. The information is presented in terms of risk refinement, intensity probability and success probability. After the event the relative likelihood that a prediction was a success or failure can be estimated. Comparisons can also be made of the performance of different forecasting models. The application of these methods is illustrated by an example based on the proposed swarm-magnitude predictor.