# Space–Time Earthquake Prediction: The Error Diagrams

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## Abstract

The quality of earthquake prediction is usually characterized by a two-dimensional diagram *n* versus *τ*, where *n* is the rate of failures-to-predict and *τ* is a characteristic of space–time alarm. Unlike the time prediction case, the quantity *τ* is not defined uniquely. We start from the case in which *τ* is a vector with components related to the local alarm times and find a simple structure of the space–time diagram in terms of local time diagrams. This key result is used to analyze the usual 2-d error sets {*n*, *τ* _{ w }} in which *τ* _{ w } is a weighted mean of the *τ* components and *w* is the weight vector. We suggest a simple algorithm to find the (*n*, *τ* _{ w }) representation of all random guess strategies, the set *D*, and prove that there exists the unique case of *w* when *D* degenerates to the diagonal *n* + *τ* _{ w } = 1. We find also a confidence zone of *D* on the (*n*, *τ* _{ w }) plane when the local target rates are known roughly. These facts are important for correct interpretation of (*n*, *τ* _{ w }) diagrams when we discuss the prediction capability of the data or prediction methods.

## Keywords

Prediction earthquake dynamics statistical seismology## Notes

### Acknowledgements

This work was supported by the Russian Foundation for Basic Research through grant 08-05-00215. I thank D.L. Turcotte for useful discussions, which have stimulated the writing of the present paper.

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