Space–Time Earthquake Prediction: The Error Diagrams

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.