Effects on ground motion related to spatial variability

Models of the spectral content and the space-time correlation structure of strong earthquake ground motion are combined with transient random vibration analysis to yield site-specific response spectra that can account for the effect of local spatial averaging of the ground motion across a rigid foundation of prescribed size. The methodology is presented with reference to sites in eastern North America, although the basic approach is applicable to other seismic regions provided the source and attenuation parameters are regionally adjusted. Parameters in the spatial correlation model are based on data from the SMART-I accelerograph array, and the sensitivity of response spectra reduction factors with respect to these parameters is examined. The starting point of the analysis is the Fourier amplitude spectrum of site displacement expresses as a function of earthquake source parameters and source-to-site distance. The bedrock acceleration spectral density function at a point, derived from the displacement spectrum, is modified to account for anelastic attenuation, and where appropriate, for local soil effects and/or local spatial averaging across a foundation. Transient random vibration analysis yields approximate analytical expressions for median ground motion amplitudes and median response spectra of an earthquake defined in terms of its spectral density function and strong motion duration. The methodology is illustrated for three events characterized by their mb magnitude and epicentral distance. The focus in this paper is on the stochastic response prediction methodology enabling explicit accounting for strong motion duration and the effect of local spatial averaging on response spectra. The numerical examples enable a preliminary assessment of the reduction of response spectral amplitudes attributable to local spatial averaging across rigid foundations of different sizes. 36 refs