Keywords: ground motion models, stochastic processes, spectrum-compatible, spatial variability, seismological parameters.

Seismic analysis of ordinary structures is usually performed via the design response spectrum. For structures that exhibit nonlinear behaviour the direct integration of the equation of motion in conjunction with the simulation of appropriate time-histories is usually preferred. Moreover, the limits of the use of the response spectrum technique for linearly behaving structures such us stiff, slender and non classically damped structures have been highlighted in literature. Therefore, until now, the unique universal method of structural analysis in the case of seismic excitation is the direct integration of the equation of motion in the time-domain. Assuming that a reliable structural model is defined, the crucial point for applying the time domain analysis is the definition of appropriate earthquake ground motion accelerograms. The definition of which methodologies and which hypothesis better represent the reality of ground motion phenomenology is still an open issue in the scientific community and a plethora of methodologies have been proposed in the last four decades to cope with the definition of the design ground motion acceleration. In the framework of seismic engineering it is well known that only a probabilistic approach can afford a rigorous representation of earthquake ground motion.

Moreover, since the resulting ground motion is strongly affected by local geological and seismological conditions and bearing in mind that the basic representation of the seismic action according to international seismic codes is the response spectrum for design applications it is necessary to simulate artificial accelerograms whose mean response spectrum matches, within a certain tolerance and along a defined range of frequencies, a target response spectrum; in a word the accelerograms have to be response-spectrum-compatible. The chapter is devoted to the review of the most common technique to model the ground motion acceleration in a probabilistic sense. Stationary, quasi stationary and fully nonstationary as well as spatially variable stochastic ground motion models will be discussed with particularly emphasis on the response spectrum compatible features. A numerical application to a real structure vibrating under spectrum compatible accelerograms is proposed to highlight the limits of the current code provisions. Recent developments in this field and the future direction of the research are also highlighted.

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