In seismic soil-structure interaction analysis, the common practice in Civil Engineering is to consider a uniform movement of free field at any point on the ground surface. However, that assumption is not realistic since the seismic ground motions can vary spatially due to wave passage effects, dispersions and reflections of wave propagating in the random heterogeneous media and site effects. To be more realistical in soil-structure interaction analysis, the spatial incoherence of seismic ground motions due to dispersions and reflections of seismic wave can be modelled by a "coherency function". In this manuscript, a sophisticated theoretical analysis of spatial variability of seismic motions is presented and compared to the statistical analyses of real earthauqke data in order to construct and validate a parametrical coherency function which can be used in the soil-structure interaction analysis.

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