Fig. 11

a Ratio of the torsional component amplitude spectrum density (ASD) (\(Z_{\text{rot}}\)) to the horizontal translational acceleration ASD (\(H_{\text{trans}}\)) for the soft-soil (red) and rock (green) sites. b Ratio of the rocking component ASD (\(H_{\text{rot}}\)) to the vertical translational acceleration component ASD (\(Z_{\text{trans}}\)). In each case, the thick central line is the average ratio from many events with S/N ratio beyond 10, while the thin lines correspond to the average ± one standard deviation