A random field model is developed to describe the occurrence of earthquakes in the space-time domain. The general theory of stationary random functions is utilized to assess the seismic hazard associated with linearly extending faults. The spatial and temporal correlation characteristics of the strain energy random field are taken into consideration explicitly and particular emphasis is given to the analysis of the correlation structure based on the concepts of scale of fluctuation and variance function. An equation to evaluate the earthquake occurrence probability for spatially varying shock origin is derived under the Gaussian and lognormal random field assumptions and considering rectangular and elliptical rupture shapes. The past earthquake occurrence data associated with the most active portion of the North Anatolian Fault Zone (NAFZ) are compiled and used to show the implementation of the proposed random field models. (C) 2001 Elsevier Science Ltd. All rights reserved.