In this paper, a stochastical approach for the investigation and the comprehension of the spatial variation of the seismic motions is presented. For this purpose, a coherency function analytical model is proposed. The approach regards the seismic motion as the combination of a traveling wave on the site (coherent component) and a zero mean randomizing factor that introduces an incoherence effect. The soil parameters as fundamental frequency and damping coefยฎcient are integrating by modeling the coherent component with the commonly used Kanai-Tajimi power spectral density.
The parametric analysis of the model shows an increase of the coherency with the increase of (i) the apparent propagation velocity of the motions on the ground surface, and (ii) the correlation length. On the other hand, the coherency decrease with the increase of: (i) the frequency content of the motion, (ii) the separation distance between stations and (iii) the scattering parameter which is the randomizing factor standard deviation.
Finally, in order to test the proposed model prediction, its coherency function is compared to empirical results obtained on the EPRI LSST array in Lotung, Taiwan (Abrahamson NA, Shneider JF, Stepp JC. Earthquake Spectra 1991; 7:1ยฑ28). The comparison shows that the proposed model ยฎts the spatial variability of seismic motions on Lotung site.
In the absence of spatially recorded seismic data on a site, the proposed analytical model can be utilised for the description of the spatial variability of the seismic motions for the seismic response analysis of structures with large dimensions as pipes, bridges, tunnelsยผetc.