A random field model for the estimation of seismic hazard

Abstract A stochastic framework is developed, in terms of the theory of homogeneous random functions, to estimate the seismic hazard associated with linearly extending seismic sources. The formulation is carried out in the space-time domain. An earthquake having at least a magnitude of m is assumed to occur whenever the total strain energy accumulated over the potential rupture plane exceeds the energy level corresponding to this magnitude, m. An alternative formulation, in which an earthquake is generated when the total shear force exceeds the total static friction force developed over the ruptured portion of the fault plane, is also described. Equations to compute the earthquake occurrence probability for a fixed and spatially varying shock origin are derived. A method to compute the most likely rupture length is developed. Significant analytical simplicity is achieved in the computation of the asymptotic results for the mean “upcrossing” rates by using a separable correlation model for the underlying space-time random process and by introducing spatial and temporal scales of fluctuation to describe the correlation structure. The past earthquake occurrence data recorded over the most active portion of the North Anatolian fault are utilized to demonstrate the implementation of the proposed model.