Prediction of large events on a dynamical model of a fault

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Abstract
We present results for long‐term and intermediate‐term prediction algorithms applied to a simple mechanical model of a fault. The long‐term techniques we consider include the slip‐predictable and time‐predictable methods and prediction based upon the distribution of repeat times between large events. Neither the slip‐predictable nor time‐predictable method works well on our model. In comparison, the time interval method is much more effective and is used here to establish a benchmark for predictability. We consider intermediate‐term prediction techniques which employ pattern recognition to identify seismic precursors. These methods are found to be significantly more effective at predicting coming large events than methods based on recurrence intervals. The performances of four specific precursors are compared using a quality function Q, which is similar to functions used in linear cost‐benefit analysis. When the quality function equally weights (1) the benefit of a successful prediction, (2) the cost of maintaining alerts, and (3) the cost of false alarms, we find that Q is optimized in algorithms based on the most conventional precursors when alarms occupy 10–20% of the mean recurrence interval and approximately 90% of the events are successfully predicted. The measure Q is further used to explore optimization questions such as variation in the space, time, and magnitude windows used in the pattern recognition algorithms. Finally, we study the intrinsic uncertainties associated with seismicity catalogs of restricted lengths. In particular, we test the hypothesis that many shorter catalogs are as effective as one long catalog in determining algorithm parameters, and we find that the hypothesis is valid for the model when the catalogs are of the order of the mean recurrence interval.

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