Numerical evaluation of the effect of cross-coupling of different components of ground motion in site response analyses

Abstract The effect of cross-coupling between the three components of ground motion in the evaluation of site-response functions, such as standard spectral ratios (SSRs) and horizontal-to-vertical spectral ratios (HVSRs), is analyzed in this article. Numerical analyses of the seismic response of fully 3D geological structures, namely, a real topographic irregularity and an ideal stratigraphic inclusion, have been carried out to obtain a 3D transfer function in the form of a 3 × 3 matrix. Each element of this matrix contains the frequency response in the i th direction due to an input motion in the j th direction. A synthetic set of acceleration time histories at the surface of the geological irregularity has been created by convolution with the 3D transfer function, using as input motion different real multicomponent strong-motion accelerograms recorded at stiff-soil or rock sites. The SSRs and HVSRs are calculated and compared with the theoretical 3D transfer function in order to highlight the effect of cross-coupling terms. These are found to generate a rather large dispersion in the site-response functions, as well as response peaks that could be misleading in the interpretation of both numerical and observed spectral ratios.

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