Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes

Abstract This article discusses several classes of stochastic models for the origin times and magnitudes of earthquakes. The models are compared for a Japanese data set for the years 1885–1980 using likelihood methods. For the best model, a change of time scale is made to investigate the deviation of the data from the model. Conventional graphical methods associated with stationary Poisson processes can be used with the transformed time scale. For point processes, effective use of such residual analysis makes it possible to find features of the data set that are not captured in the model. Based on such analyses, the utility of seismic quiescence for the prediction of a major earthquake is investigated. Key Words: Akaike information criterionEpidemic-type modelsConditional intensityLikelihoodMarked point processSeismic quiescenceTrigger models